Glider circuits: components and contraptions

PM 2Ring · Post by **PM 2Ring** » April 3rd, 2010, 2:48 am

calcyman wrote:
Collatz sequence generator
I am absolutely stunned! You've probably found more uses for that adder circuit than anyone else.

Thanks, calcyman! It's fun building these things, and actually I'm a little surprised that there aren't more patterns floating around that use that adder circuit.

From what I can see, it appears to operate in binary, with a LWSS read-out device at the top of the pattern. I guess that tripling a number is accomplished by shift addition, whereas halving a number is a simple binary shift.

Yes. Binary shifting is easy, and can generally be performed by a simple delay (although some of my circuits have used the inline advancer). The adder circuit is used to add n & 2n+1, the 2n+1 is formed by inserting a copy of the parity bit (which is the LSB of n) in front of n. That was rather tricky to synchronize in space and time.

What are you using the bistable switch for?

It's part of the switchable glider reflector subsystem. If n is odd, the reflector gets turned on before the data arrives, and it needs to be turned off before the next cycle. The reflector gets turned on by one copy of the parity bit, and it's essentially turned off with another copy. A delay circuit of period around 7000 would be too large (although I did build a pretty Herschel based one), so instead I use the bistable switch as a simple 1 bit memory.

A copy of the parity bit sets the switch (from block to boat), so when the reflector reset bit arrives from the p7680 gun in the southeast corner it get's reflected by the switch into the p60 stream that controls the switchable p60 LWSS gun that is the heart of the switchable glider reflector. If the bistable switch is off, the reset bit travels through the switch & hits an eater.

The switchable glider reflector is a toggle switch, so attempting to turn it on when it's already on will turn it off, and vice versa. The former would never happen in this application, since an odd number in the Collatz sequence must always be followed by an even one. But it's nice to make these things work properly.

I'm sure there are other applications for a mechanism that converts a toggle switch into one with separate on & off inputs.

That's very compact as well; if I attempted to make such a device, it would have been larger than 20000 * 20000.

Your computation-oriented structures do tend to be very large!

I think I need to upgrade Golly (& my OS) before I can play with your recent constructions. I'd love to see how your efforts at display circuitry are going.

I suppose I could've made my Collatz generator a little bit smaller, but once I realized the period was going to be around 7000, I decided to make it p7680 so I could use that very compact p7680 glider gun. And so I didn't bother optimizing the space that much, and besides, I needed some space for all those Buckaroos that were required to get the glider spacing & timing correct.

It's a shame that your device only has finite memory. Since you like p30-oriented technology so much, I recommend that you have a look at Paul Callahan's extensible delay-line memory:
[...]
The data is contained in a loop of MWSSes, which circulate between two eaters. LWSSes can be launched to extend the delay-line memory, in order to accommodate more bits. I'd like to see a pattern exploting this beautiful mechanism; you might be the first to use it in an arithmetic/logic circuit.

Alternatively, you might want to use sliding-block memory, but I think that delay-line memory is more suited to your style of computation.

Thanks for that! I'll certainly play around with it, and see what I can do with it. I've looked at the sliding-block memory, but you're right, it's not my style. It's too bulky, and I prefer to work with bitstrings. OTOH, I do have a soft spot for any reactions that push, pull, or otherwise transform still-lifes, as you may have noticed from my avatar.

TLUL · Post by **TLUL** » May 24th, 2010, 2:49 am

calcyman wrote: It's a shame that your device only has finite memory. Since you like p30-oriented technology so much, I recommend that you have a look at Paul Callahan's extensible delay-line memory:

Code: Select all

x = 400, y = 131, rule = S23/B3
129bo$127boo$128boo14$379b4o$378bo3bo12bobbo$382bo16bo$378bobbo13bo3bo
$396b4o$373bo$374bo$372b3o$389bo4boo$386b4o3booboo$368bo16b5o4bobbo$
369bo14bo9bobbo$367b3o15boo8boo$386bo$354b5o$353bo4bo4bo24boo5bobbo$
358bo5bo22b4o8bo$44boo307bo3bo4b3o22booboo3bo3bo$43bo3bo307bo26boo5boo
5b4o$27boo13bo5bo318bo12booboo$20b3o4boo13bo3boboobboo257b4o43bo8bo8bo
3b4o$19b5o6boo10bo5bo3boo256bo3bo12bobbo28bo11boobbobo3boo$18bobo3bo5b
3o10bo3bo266bo16bo25b3obboo6bobboo3bo$18boo3bo6boo12boo264bobbo13bo3bo
39boobbobo3boo$27boo9bobo287b4o35bo8bo3b4o$27boo10boo13boo311bo12boob
oo$39b3o12boo326boo$41boo260bo13boo$42boo260bo7bo4boo$41bo13boo245b3o
6b3o13b3o45boo$53boboo253bo18bo44b4o$15boo29bo6bo256b5o7boo3bobo44boob
oo$16bo30boo4bo244bo20bo7boo47boo15boo$16bobo4bo9boo11boo5bobbo242bo
91booboo$17boo3bobo7b4o18boo230b5o6b3o91b4o$21boboo5b3obbobbobo244bo4b
o29boo5bobbo12bo17boo29boo$20booboo9boobbobbo248bo28b4o8bo12bo12b4oboo
$21boboo6bo9boo242bo3bo3bo25booboo3bo3bo10b3o12b6o3bobo13bo3bo$22bobo
5bo8bo3boo242bo6bo19boo5boo5b4o26b4o5boo13boo5b3o$23bo6bo10boo108bobo
138b3o8bo8booboo50bo9boo9bob3o$38bobbo5boo97bo4bobbo146bobo4bo3b4o60bo
6bo8boo$38bobo6bobo61boo34boo5boo8bo135bobbo5bo3boo60bo3bo3b8obo$49bo
60bo3bo27boo8bo3boo5bobo134bo6bobbo50bobo12bo3bo7b4o$49boo43boo13bo5bo
26boo10boo6boboo134bobbo5bo3boo47boo16bo8bo$87b3o4boo13bo3boboobboo30b
obbo6booboo10boo123bobo4bo3b4o46bo$86b5o6boo10bo5bo3boo30bobo8boboo10b
oo125bo8booboo65bobbo$61bo23bobo3bo5b3o10bo3bo48bobo148boo59boo9bo6boo
$62boo21boo3bo6boo12boo27boo22bo118bo72bo17b4o4bo3bo4booboo$61boo31boo
9bobo32boo142bo69b3obobo13booboo4b4o4b4o$94boo10boo13boo29boo128b3o22b
oo45boo9b3oboo5boo14boo$106b3o12boo29boo152b4o18bo25boboo6boo5bo$108b
oo29boobo163booboo18bo25boo6bo7boo$109boo29bobo165boo17b3o34boo5bo$
108bo13boo17bo37boo184b3oboo5boo$120boboo16boo37bo194booboo$82boo29bo
6bo19boo4bo11b3o9boo5bobo194b4o$83bo30boo4bo19boo4bobo9bo9bobbo5boo
196boo$83bobo4bo9boo11boo5bobbo22boo5bo5bo7bo$84boo3bobo7b4o18boo28b4o
12bo$88boboo5b3obbobbobo42boboboo11bo20bo$87booboo9boobbobbo40bobbob3o
11bobbo16b3o$88boboo6bo9boo39booboboo14boo19bo$89bobo5bo8bo3boo35b3ob
4o35boo76bo$90bo6bo10boo36bobo4bo95b3o17bo39b3o$105bobbo5boo30bo101b5o
14b3o38b5o$36bo68bobo6bobo28boo100boob3o54boob3o$34bobo79bo131boo58boo
$24boo6boo25bobo54boo$23bo3bo4boo12boo10bo$22bo5bo3boo12boo5boobbo4bo
297boo$12boo8bo3boboo4bobo16boobobboboo66boboo58boo145b3o18b4o$12boo8b
o5bo7bo20boo69boboboo54b3oboo143boboo18booboo$23bo3bo101b4o55b5o91b4o
45bo5boo9b3oboo5boo$24boo104boo57b3o91bo3bo44bo16boo5bo$35bo213boo36bo
44bo6bo8bo7boo$31boo3boo10boo199bo33bobbo50boo10boo5bo$30bobooboo9boob
oo199b3o77boobo4bo11b3oboo5boo14boo$32bo13b4o202bo76boboobobo22booboo
4b4o4b4o$31b3o13boo241b4o35bobbo5bo20b4o4bo3bo4booboo$32boo255bo3bo36b
3o6bo20boo9bo6boo$31bobbo16bo233bo7bo37boboo4boo26bobbo$32bo13boobo3bo
boo223b7obbobbo45b3o$46bo9bo222bobb3oboo53bo6bo16boo$23b3o21boo5boo
224b7obbobbo48boo5boo15boo8boo$25bo18b3obb5obb3o211bo14bo7bo47boo4bobo
14bo3bo5bobbo$24bo19bobbo7bobbo203boo6boo17bo3bo12boo57bo3bo4bobboo$
12bo32boo9boo211bobo18b4o3b4o4b4o56bo4bobbobboo$11boo26b3o254bo3bo4boo
boo33b4o6bo13bobo3b4o$oo8boo4boo5bo15bo61boo163boo32bo6boo33b6o5boo$oo
7b3o4boo3bobo16bo9bo50bo161b3oboo6bo20bobbo42b4oboo3bobo$10boo4boobbob
o26bobo39bo7bobo161b5o7boo69boo29boo$11boo6bobbo14bobo8boboo10boo25bob
o7boo163b3o7bobo99b4o$12bo7bobo14bobbo6booboo10boo15boo6boo199b3o13boo
70booboo$21bobo16boo6boboo26bo3bo4boo198b4o13bobo54boo15boo$23bo14bo3b
oo5bobo25bo5bo3boo191bo6bo3bo12boboo51booboo$40boo8bo26bo3boboo4bobo
188boo6b3o14boo52b4o$37bobbo36bo5bo7bo187bobo6b3o3boo9bo54boo$37bobo
29boo7bo3bo23boo186boo$68bobo8boo24bobbo$68bo21bo14bo200boo$67boo22boo
12bo199b4o$90boo3boo8boboo196booboo$96boo9boo181boo15boo$95bo192booboo
$288b4o$106boo181boo$81bo24boo$78b4o3boboo$70boo5b4o4boboboobboo$70boo
5bobbo3booboboobbobo$77b4o3boo8b3o7boo$78b4o3boo8b3o6boo$81bo12b3o$93b
obo$93boo!

The data is contained in a loop of MWSSes, which circulate between two eaters. LWSSes can be launched to extend the delay-line memory, in order to accommodate more bits. I'd like to see a pattern exploting this beautiful mechanism; you might be the first to use it in an arithmetic/logic circuit.

Ooh, that's a pretty mechanism.

I also tend to prefer p30 technology (my last experiment with herschels ended up with three conduits in the hospital), but my best attempt at a memory circuit was far more inefficient than this, was fixed to p30 (whereas this can be adapted to any common period), and had no extensibility. I think I'll use this in a few of my patterns, it's the best I've seen yet.

If anyone's interested in my not-so-great memory loop, here it is, complete with set and unset streams:

Code: Select all

x = 124, y = 92, rule = B3/S23
42b2o$43bo$43bobo8b2o$29b2o13b2o6bo2bo7bo$29b2o20bo7b2o3bo$51bo6bo5bo$
51bo7b5o$52bo2bo$30bo23b2o$29b3o$28bo3bo$27bob3obo$28b5o5$43bo$41b3o$
40bo$40b2o2$27b2o$28bo$25b3o$25bo2$38b2o$31b2o5bobo$30bobo5bo$32bo3$
46b2o8bo$46bo2bo6bobo$41b2o2bo3bo7bobo4b2o38b2o$23b3o14b3o2b2o2bo7bo2b
o3b2o38b2o$25bo4b2o5bob2o16bobo$24bo5b2o5bo2bo8b3o4bobo$37bob2o15bo$
40b3o$41b2o2$16b2o$15bobo86bo$17bo48b2o35b3o$66bo35b5o$64bobo3b2o29b2o
3b2o$64b2o4b2o3$8b3o92b3o$10bo92b3o$9bo$70b3o33bo$60b3o42bobo$54b3o3bo
9bobo31bo3bo$56bo4bo7b5o31b3o$b2o52bo12b2o3b2o23bo4b2o3b2o$obo65b2o3b
2o16b2o5bobo$2bo88b2o5b2o2$68b2o$47b2o17b2obo$46bobo17bo$48bo42bo$67b
3obo18bo$71bo18b3o15b2o$71bo36bo$109b3o$111bo$39b3o$41bo$40bo25b2o3b2o
$68b3o$67bo3bo$68bobo9b2o$69bo9b4o5b2o$32b2o44bo2bobo4bobo$31bobo43bob
o2b2o4bo$33bo42bobo$68b2o5b2o24b2o$68b2o5b3o23bobo$76bobo12bo4b2o4b3o$
77b2o11bobob2o2bo4b3o6b2o$89bo3bob3o4b3o7b2o6b2o$24b3o62bo3bob2o4bobo
16bobo$26bo62bo3b2o6b2o19bo$25bo54b2o8bobo29b2o$79bobo9bo$79bo$78b2o!

Phantom Hoover · Post by **Phantom Hoover** » May 24th, 2010, 11:42 am

Apropos of nothing, there is a binary adder in WireWorld that can handle arbitrarily large integers at http://www.quinapalus.com/wires8.html. This should be translatable into Life, though stabilising it might be tricky.

Extrementhusiast · Post by **Extrementhusiast** » May 25th, 2010, 11:07 am

My triple-vanish reaction (kudos to PM 2Ring? need to confirm):

Code: Select all

x = 13, y = 11, rule = B3/S23
bo$2bo$3o3$8b4o$8bo3bo$8bo$b3o5bo2bo$3bo$2bo!

Naszvadi · Post by **Naszvadi** » December 17th, 2016, 1:25 pm

So many cool patterns... I wonder if other glider-compatible included nontotalistic rules are supported by any of them. I am working on collecting common circuit components in rules B3[678]/S23[678] in order to prove universality. included my partial results in one of my topics. (And subscribed here)

gameoflifemaniac · Post by **gameoflifemaniac** » March 17th, 2017, 11:02 am

PM 2Ring wrote:Binary arithmetic with gliders

This circuit calculates the Fibonacci sequence in binary using p60 and p30 glider
streams. Output is displayed using LWSS bits. A new Fibonacci number is
generated every 2100 generations.

The arithmetic unit at the heart of this construction is the amazing
Binary Adder circuit created by David Buckingham in 1975, with size
optimization by Mark Niemec. This circuit adds two binary numbers
represented by p60 glider streams, with the least significant bits
leading. This allows numbers of any length to be added. Input data
enters the adder circuit at its upper left and the sum begins to emerge
from the circuit at its lower right after 600 steps.

How it works
The Fibonacci numbers are defined as follows:
F(0) = 0, F(1) = 1, and for n>1, F(n+1) = F(n) + F(n-1).

This circuit loops two copies of the output stream back into the adder
input, with one copy delayed so that the last two results get added
together.

The cycle starts with p60 glider streams representing the previous two
Fibonacci numbers entering the left side of the adder.

Step 600: The sum starts to emerge from the right of the adder.

Step 1200: The p60 data hits a p30 stream, which causes each p60 data
bit to create a pair of inverted p30 data bits.

Step 1500: The inverted p30 stream meets a p60 stream, which splits the
data into two streams. One copy of the data collides with the p60
stream, uninverting the data & sending it back up towards the adder
input. The other copy of the data passes through the p60 stream & heads
towards a p30 inverting reflector, which sends it up to a p30 inverting
reflector/duplicator.

Step 2960: Data hits the inverting reflector/duplicator. One copy of the
data (still inverted) continues around the loop, back towards the adder.
The other copy (now uninverted) heads towards the output section. This
data stream allows the output of a p60 gun to reach a glider to LWSS
converter, which creates the output display. The output region at the top
of the pattern show the last two Fibonacci numbers calculated. So this pattern can also be conidered as a calculator for phi, the golden ratio, in binary fraction form.

Meanwhile, at step 1860, data from the previous cycle in the big loop
reaches a p60 gun near the adder, which inverts it, sending it back up
into the adder.

Code: Select all

#C AdderLoopFib by PM 2Ring, April 2009.
#C
#C Calculates the Fibonacci sequence in binary using p60 and p30 glider
#C streams. Output is displayed using LWSS bits. A new Fibonacci number is
#C generated every 2100 generations.
#C
#C The arithmetic unit at the heart of this construction is the amazing
#C Binary Adder circuit created by David Buckingham in 1975, with size
#C optimization by Mark Niemec. This circuit adds two binary numbers
#C represented by p60 glider streams, with the least significant bits
#C leading. This allows numbers of any length to be added. Input data
#C enters the adder circuit at its upper left and the sum begins to emerge
#C from the circuit at its lower right after 600 steps.
#C
#C How it works
#C ------------
#C The Fibonacci numbers are F(0) = 0, F(1) = 1, F(n+1) = F(n) + F(n-1).
#C This circuit loops two copies of the output stream back into the adder
#C input, with one copy delayed so that the last two results get added
#C together.
#C
#C The cycle starts with p60 glider streams representing the previous two
#C Fibonacci numbers entering the left side of the adder.
#C Step 600: The sum starts to emerge from the right of the adder.
#C Step 1200: The p60 data hits a p30 stream, which causes each p60 data
#C bit to create a pair of inverted p30 data bits.
#C Step 1500: The inverted p30 stream meets a p60 stream, which splits the
#C data into two streams. One copy of the data collides with the p60
#C stream, uninverting the data & sending it back up towards the adder
#C input. The other copy of the data passes through the p60 stream & heads
#C towards a p30 inverting reflector, which sends it up to a p30 inverting
#C reflector/duplicator.
#C Step 2960: Data hits the inverting reflector/duplicator. One copy of the
#C data (still inverted) continues around the loop, back towards the adder.
#C The other copy (now uninverted) heads towards the output section. This
#C data stream allows the output of a p60 gun to reach a glider to LWSS
#C converter, which creates the output display.
#C Meanwhile, at step 1860, data from the previous cycle in the big loop
#C reaches a p60 gun near the adder, which inverts it, sending it back up
#C into the adder.

x = 1687, y = 554, rule = B3/S23
141b2o$141b2o3$141bo$140b3o$139bo3bo$141bo$138bo5bo$138bo5bo$139bo3bo$
140b3o7$134b2o$126bo7bo2bo$125bo3b2o7bo$125bo5bo6bo$126b5o7bo$134bo2bo
$134b2o$1683b2o$1683bobo$1685bo$167b2o9b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o5b2o$167b2o9b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o2$
628b2o1048b2o$166b3o459b2o1048b2o$166b3o$628b2o1048b2o$628b2o1048b2o2$
164b2o3b2o$165b5o$166b3o$167bo7$169b2o$169bo$170b3o$172bo8$157b3o$151b
3o3bo$153bo4bo$152bo12$172b3o$136b3o33bo$138bo34bo$137bo2$126b2o$126bo
$117b2o5bobo53b2o9b2o$116b3o5b2o34b2o18bobo7bobo$104bo8bob2o44b2o11bo
5bo8bo6b2o2b2o$104bobo6bo2bo33bo9bo12bobo13bo2bo2bo2bob2o$92b2o11bobo
5bob2o33bobo19bob2o13bo6b2o$92b2o11bo2bo7b3o19b2o11bobo9b2o6b2ob2o14bo
bo$105bobo9b2o19b2o11bo2bo7b3o7bob2o15b2o$104bobo44bobo5bob2o5b2o3bobo
$104bo9bo35bobo6bo2bo4bo2bo3bo$115b2o4b3o26bo8bob2o5b2o$114b2o7bo38b3o
$122bo40b2o6$116b2o$116b2o4$103bo$103b2o24bo$102bobo25b2o$129b2o12$88b
o$88b2o54bo$87bobo55b2o$144b2o12$73bo$73b2o84bo$72bobo85b2o$159b2o12$
58bo$58b2o114bo$57bobo115b2o$174b2o12$43bo$43b2o144bo$42bobo145b2o$
189b2o8$2o$bo$bobo$2b2o$28bo$28b2o174bo$27bobo175b2o$204b2o$2bo$2b3o$
5bo$4b2o$13b2o$13bobo$13bo3$4b2o3b2o$4b2o3b2o10b2o$5b5o3bo7b2o$6bobo4b
2o204bo$12bobo205b2o$6b3o210b2o5$9bo$8bobo$7bo3bo$8b3o$6b2o3b2o14b2o$
26b2o$28bo2$234bo$235b2o$234b2o5$8b2o$8b2o3$42b2o$41b2o$43bo2$249bo$
250b2o$249b2o3$580bo$578b3o$577bo$577b2o2$586bo$57b2o527b3o$56b2o517bo
13bo$58bo515b3o11b2o$574b3o$264bo$265b2o305b2o3b2o$264b2o306b2o3b2o12b
o$590b3o$590b3o$555b2o17b2o$555b3o16bobo11b2o3b2o$541bo15b2obo12bo2b2o
10b2o3b2o$539bobo4b3o8bo2bo14b2o$538bobo16b2obo14b2o$537bo2bo7bo2b2o2b
3o6b2o10bo14b2o$72b2o345b2o117bobo7bo3bo2b2o7bobo23bobo$71b2o348bo112b
2o3bobo6bo2bo14bo3bo5bo12b2o2bo$73bo334b2o12bo110bobo5bo8b2o14b2o2bo5b
o13b2o$408b2o4bo7bo110bo37bo3bo6bo7b2o$279bo125b2o5b2o8bo109b2o38b3o5b
obo7bo$280b2o122b3o5bo2b2o4bo7b2o150b2o$279b2o124b2o6b5ob2o8bobo121b2o
4bo30bo5bo$399b2o7b2o4bo16bo120bobo2bobo30bo5bo$398bobo7b2o21b2o121bo
3b2o25b2o4bo3bo$398bo186b2o5b3o$397b2o23bo104b2o$423bo104bo$421b3o104b
obo5bo8b2o$529b2o3bobo6bo2bo25b2o$416b3o114bobo7bo3bo2b2o20b2o$87b2o
329bo14b2o19b2o76bo2bo7bo2b2o2b3o24bo$86b2o304b2o23bo16bo19bo78bobo16b
2obo20bo13b2o$88bo304bo40bob2o5b2o7bobo79bobo4b3o8bo2bo20b3o12bo$393bo
bo7b2o30bo7bobo6b2o82bo15b2obo32b3o$294bo99b2o7b2o4bo29bo4b3o103b3o7b
2o2b2o22bo$295b2o103b2o6b5ob2o21bo2bo4b3o102b2o8bobo2bo$294b2o103b3o5b
o2b2o4bo21b2o4b3o28bo65b2o19b2o10bo8bo$400b2o5b2o8bo25bobo28bobo19b2o
44bo19bo9bobo6b3o$403b2o4bo7bo8b2o15b2o29bobo19bo45bobo9bo5bobo10b2o5b
o$403b2o12bo8b2o24b2o19b2obobo5bo9bobo46b2o8bobo4b2o18b2o$416bo20bo15b
o19bo3b2o4bobo8b2o56bo3b2o$414b2o22bo14bobo6bo8bobo7b2o3bo65bo3b2o$
436b3o15b2o6b2o7b2o8b2o3bo65bo3b2o19b3o$457b2o4b2o16b2o3bo66bobo21b3o$
457b2o4b3o17bobo68bo21bo3bo$102b2o353b2o4b2o19bo77bo12bo5bo$101b2o359b
2o11b3o83bo14bo3bo$103bo358bo14bo76bo6b3o13b3o$476bo75b2o$309bo243b2o$
310b2o$309b2o$564bo4b2o$562b2o5bobo$563b2o4bo$452bo127b2o$453bo37bobo
86bo$451b3o38b2o87b3o$492bo90bo2$117b2o428bo$116b2o342b3o83bo$118bo
343bo76bo6b3o$461bo75b2o$324bo213b2o$325b2o$324b2o$549bo10bo23b2o$547b
2o11bobo21bobo$431bo116b2o13b2o6b2o11bo21b2o$431b2o34bo95b2o4bo3bo31bo
bo$430bobo35bo37bobo54b2o3bo5bo20b2o7bo13bobo$466b3o38b2o42b2o7bobo4b
2obo3bo20b2o7bo2bo6b2o2bo2bo$507bo42bobo7bo7bo5bo29bo8bobo5b2o$550bo
18bo3bo7b2o22bobo3bo3bo3bo3b2o$532bo16b2o20b2o8bobo22b2o2b2ob3o5b2o$
445b3o83bo29bo21bo29b2o3bo2bo5b2o$447bo76bo6b3o25b2o22b2o33bobo6bobo$
446bo75b2o36b2o67bo$339bo145bo37b2o104b2o$340b2o141b3o118bo$339b2o141b
o54b3o64bobo$482b2o50bo2bo27b2o32b2o3b2o$426bo105b2o4bo25b2o22b2o9bobo
$424b3o101b3o2b2o31bo21bo10bo$423bo63b2o19b2o18bo47b2o8bobo35b2o$423b
2o55bo7bo19bo12bobo5bo44bo3bo7b2o36bo$473bobo2b2ob2o5bobo10bo4bobo13b
2o41bo7bo5bo10b2o21bobo6bobo$441b2o30b2o14b2o9bobo3b2o14b2o41bobo4b2ob
o3bo11bo16b2o3bo2bo5b2o$441b2o31bo2bo5bo15bo3b2o20bo42b2o3bo5bo11bobo
7b2o2b2ob3o5b2o$147b2o271b3o76bo3b2o12bo5b2o29b2o12b2o4bo3bo13b2o6bobo
3bo3bo3bo3b2o$146b2o282b3o44b2obob2o15bo3b2o11bo7b2o20bo7b2o12b2o6b2o
21bo8bobo5b2o$148bo271bobo9bo67bobo6bo6b3o25b2o19bobo31bo2bo6b2o2bo2bo
$419b5o7bo69bo5b2o36b2o18bo33bo13bobo$354bo63b2o3b2o83b2o90bobo$355b2o
61b2o3b2o15b3o90bo36bobo28b2o$354b2o74b3o100b4o15b3o15bo2bo$430bo9bobo
91b4o14bo8b2o10b2o8bo$423b2o6bo7b5o33b2o55bo2bo15bo7b2o8bo3b2o5bobo$
423bob2o11b2o3b2o33bo55b4o28b2o5b2o6bob2o$426bo11b2o3b2o30b3o47b2o6b4o
5b2o21bo4bo2bo6b2ob2o$325b2o148bo48bobo6bo8bobo25bobo8bob2o$325b2o94bo
b3o32bobo63bo19bo37bobo8b2o$421bo16b2o8bo9b2o63b2o19b2o27bo9bo9bobo$
421bo14b2obo8b3o8bo112bo22bo$162b2o272bo14bo50bo69b3o20b2o$161b2o287b
2o49bo14bo$163bo273b3obo59b3o10b3o$441bo52bo18bo$420b2o3b2o14bo71b2o3b
o$422b3o57bo8b2o25b3o$421bo3bo26b3o25b3o9bo17bo10bo45b3o20b2o$422bobo
26b2ob2o23bo9b3o18bo9b2o45bo22bo$323b5o95bo27b2ob2o23b2o8bo4b2o15bo44b
2o10bo9bo9bobo$322bob3obo107b2o3b2o8b5o37bobo61bo19bobo8b2o$323bo3bo
97b2o11b3o9b2o3b2o36bo63bobo5bobo8bob2o$324b3o98bo11bo3bo50b2o14b2o3b
2o43b2o5bo2bo6b2ob2o$325bo100b3o9bobo67bo5bo53b2o6bob2o$428bo10bo82b3o
41bo3b2o5bobo$476b3o30bo3bo7bo3bo42b2o8bo$177b2o173b2o87b2o32bo3bo30b
3o7bo5bo38bo2bo$176b2o145bo29b2o86bo32bo5bo39b2obob2o38bobo$178bo144bo
28bo89b3o5b2o22b2obob2o$322bobo5bo113bo6bo$321b2ob2o2bobo117b3o72bo$
320bo5bo2b2o117bo28bo35b2o7bobo$323bo113b2o37bobo34bo8bobo$320b2o3b2o
108bo2bo7bo7bo21bobo35b3o6b2o$422bobo9bo7b2o3bo6b2o20b2o38bo8bo$422bo
3bo7bo6bo5bo5bobo19bo48b3o$323bo102bo7bo7b5o27b3o46bo3bo$322bobo97bo4b
o7bo2bo34bo3bo44bob3obo$322bobo101bo10b2o33bob3obo39bo4b5o$323bo90b2o
6bo3bo46b5o4bo33b2o$325b3o85bobo6bobo8bobo47b2o32b2o$192b2o131b3o9b2o
74bo20b2o46b2o$191b2o131bo3bo9b2o72b2o20bo$193bo129bo5bo7bo$324bo3bo$
325b3o$509bobo$489bobo17b2o11b2o$330bo86b2o20bo37b2o11b2o18bo12bo$330b
2o86bo20b2o36bo12bo29b3o$329bobo86bobo6bobo8bobo10b2o25b3o39bo$419b2o
6bo3bo19bo28bo$431bo10b2o5bobo$427bo4bo7bo2bo5b2o52bo$431bo7bo57bo3b2o
$427bo3bo7bo58b2o2b2o$207b2o218bobo9bo57b2o$206b2o120bo111bo2bo$208bo
118b3o112b2o$326b5o$325bobobobo$325b2o3b2o3$328bo$327bobo$327bobo$328b
o$328b2o$328b2o$328b2o$222b2o$221b2o$223bo13$237b2o$236b2o$238bo13$
252b2o$251b2o$253bo13$267b2o$266b2o$268bo13$282b2o$281b2o$283bo5$290bo
$289b2o$266bo22bobo$266b2o$265bobo4$297b2o$296b2o$298bo$257b3o$257b3o$
255bob2o$253b2o$256bobo46bo$257b3o44b2o$251bo6bo45bobo$251b2o10b2o$
250bobo10bobo$263bo$238b2o$237bobo$227b2o7bo6b2o4bo62b2o$227b2o7bo2bo
2bo2bo2bobo20b2o8bo29b2o$236bo6b3obob2o20bo2bo6bobo29bo$237bobo6b2ob2o
15b2o2bo3bo7bobo4b2o$238b2o7bob2o14b3o2b2o2bo7bo2bo3b2o$248bobo11bob2o
16bobo$249bo12bo2bo8b3o4bobo$262bob2o15bo38bo$265b3o51b2o$266b2o51bobo
6$327b2o$326b2o$328bo5$335bo$334b2o$334bobo6$342b2o$341b2o$343bo5$350b
o$349b2o$349bobo6$357b2o$356b2o$358bo5$365bo$364b2o$364bobo2$377b2o$
377bobo$367bo4b2o6bo$366bobo2bo2bo2bo2bo7b2o$366b2obob3o6bo7b2o$354b2o
10b2ob2o6bobo$354b2o10b2obo7b2o$366bobo$367bo!

I also have a larger version of this pattern, which I'll upload if anyone's interested. It's only advantage is that it can calculate much larger Fibonacci numbers before the delay loops "overflow". It's quite easy to convert this pattern to calculate Lucas numbers. Just change the initial data from 0 & 1 to 2 & 1.

I usually run this pattern with a step size of 2100^1, and hit TAB to get it to show the next number. But sometimes I'll run it continuously a slower speed, like 30^1 or even 2^2.

Upload it please.

pcallahan · Post by **pcallahan** » April 10th, 2019, 9:22 pm

calcyman wrote:I'd like to see a pattern exploting [the extensible delay line]; you might be the first to use it in an arithmetic/logic circuit.

I realize this reply is a long time in coming (from 2010!) but I at least wrote a binary counter based on some version of the extensible delay line. It used ripple increment and it would extend the line every time the carry overflowed. I think it missed some values around the overflows. I do not know what I did with that. It is possible I posted it to comp.theory.cell-automata in the 90s.

ADDED: Hmm... after some digging, I see that I made the first version of the delay line in early 1991 (?!) and that wound up in the XLife 3.0 distribution. Unfortunately, it's in #I format, so I can't import it into anything else. But I don't think that did anything with the delay line.

So I am left with a fairly vivid memory of watching some version of it implement a simple binary ripple counter. I.e.: invert 1s to 0s until you reach the first 0 and set that to 1. It would somehow determine overflow, maybe with another loop recirculating a marker, and in that case, it would extend the loop length.

I also remember it was rather buggy. E.g., instead of going from 11111 to 100000, it would somehow skip to something like 100101 (maybe it repeated some values without the leading 1). But all I have is the memory. I do not know if I published that pattern anywhere. It was pretty slow in Xlife on an old Sun workstation, but I'd like to see it run in Golly today.

Post by **dvgrn** » April 11th, 2019, 1:42 pm

pcallahan wrote:... I am left with a fairly vivid memory of watching some version of it implement a simple binary ripple counter. I.e.: invert 1s to 0s until you reach the first 0 and set that to 1. It would somehow determine overflow, maybe with another loop recirculating a marker, and in that case, it would extend the loop length.

I also remember it was rather buggy. E.g., instead of going from 11111 to 100000, it would somehow skip to something like 100101 (maybe it repeated some values without the leading 1). But all I have is the memory. I do not know if I published that pattern anywhere. It was pretty slow in Xlife on an old Sun workstation, but I'd like to see it run in Golly today.

This message from 1994 looks like a good match for your description:

pcallahan wrote:From: Paul Callahan
Date: Sat, 18 Jun 94 01:24:38 EDT
Subject: Self-extending binary integer counter (almost)

Having built a smaller extensible delay line (my last mailing), I decided to construct something that actually does some computation with it. A natural choice was a an integer counter, because you can increment an integer in a delay line in one pass: You just maintain a carry bit. While the carry is 1, you replace every 1 that passes with a 0 until a 0 comes by. In this case you replace it with a 1 and reset the carry to 0. While the carry is 0, you recirculate the data unchanged. If an external clock pulse supplies "restore carry" signals at the appropriate times (just before the least significant bit comes along), you have a k-bit counter, where k is the length of the delay line.

Now the question is how to store the carry bit. I found a way that seemed parsimonious. The only component aside from the p120 delay line of MWSSs is a pair of p60 glider guns that interact with a block-producing collision. This is a standard way of doubling gun period (in a lot of Dean's patterns, anyway). Additionally, if you delete the block at any point, you phase-shift the gun by 60 steps, and this block can thus be used to store a bit. In the first state of the gun (representing a carry of 0), the spaceships narrowly avoid both the glider and the block produced once every 120 steps. In the second state (representing a carry of 1), the negative-logic left-going spaceships will destroy the block (resetting the carry) while the gliders from the gun will destroy the corresponding right-going positive logic spaceships, replacing 1 (negative logic, no spaceship) with 0 (positive logic, no spaceship).

Now, to make the counter self-extending, one must detect overflow. This can be done rather simply as well. The signal to restore the carry consists of a spaceship aimed to destroy a block. But if there is no block to destroy, the spaceship continues through. This can only happen if the entire length of the delay line consists of 1s (or else the carry would have been reset, resulting in a block). Fortunately, this happens to be the overflow condition.

I used a downward MWSS to restore the carry. This has the advantage that if it continues through, it can be converted into a right-going LWSS that deletes an eater, extending the delay line by 1 bit. I used the following reaction (I found it by search, but it's probably old):
Code: Select all
     .**
     .***
     .***
     *.**
     ***
     .*
     .
     .
     ..**
     ...**
     ..*
     ........***
     ........*
     .........*
The two gliders normally annihilate each other, but the collision of all three components produces an LWSS traveling to the right.

So far, so good, except for the clock pulse. This must grow in period as the number of bits grows, and this poses a problem I have yet to solve satisfactorily. I use a second delay line to store the clock pulse, and this is tied to the first in a way that forces it to (eventually) attain the same length. However, the transition between the k-bit and (k+1)-bit counters is rather problematic, and I have yet to characterize the sequence produced (I'll supply the whole construction below; it is big, but not at all bad with Xlife or Alan Hensel's program).

I also want to draw attention to a nice non-destructive reader for the delay line that can reside entirely to one side of the stream (clearly, there are several of these involving gliders that cross the stream). I found this useful for producing the output stream of the constuction. This too was produced by a search, and again may very well be old news.
Code: Select all
     ...*****
     ..*....*
     .......*
     ..*...*
     ....*
     .
     .
     .
     ***...***
     ..*...*..*
     .*....*
     ......*
     .......*.*
The upward spaceship and the glider will normally annihilate. However, this annihilation is converted by the MWSS spark into a glider traveling down and to the right. I found this useful for tapping the value of a p120 MWSS stream, though I haven't checked to see how small the period can be made (it's fairly fast).

Finally, the construction follows. For efficiency in observing, I have not used puffers for the extensible section. Hence, the period is large but finite. There should be no problem making the extensible section (eaters and left-going MWSSs) with p60 gliders, though I haven't worked out the close spacing of the two delay lines.
Code: Select all
x = 616, y = 283, rule = B3/S23
137bo$137b3o$140bo$128b2o9b2o$128b2o3$128bo12b3o$127bobo$126bo3bo10bob
o$126b5o9b5o$125b2o3b2o7b2o3b2o$126b5o8b2o3b2o$127b3o$128bo$142b2o$
140b2ob2o$140bo2bo$127bo15bo$129b2o9bo$128b3o10b2o$128b2o$129bo$128bob
o10b2o3b2o$129b2o11b5o$136bo6b3o$144bo$123b2obob2o3b2o2$123bo5bo2$124b
2ob2o$126bo19b2o$146bo$147b3o$149bo2$126b2o15bobo$126b2o4bo2b2o7b2o$
131bo3b2o2b2o3bo14b4o$131bo7b2o17b6o$132b4o21b8o$156b2o6b2o$157b8o$
158b6o$159b4o6$115bo$115b3o$118bo44b2o$106b2o9b2o45bo$106b2o56bobo7b2o
$159b2o4b2o7b2o$158b2o11b2o10bo4bo$160bo9b3o10bo4bobo$171b2o10bo7b2o$
117b2o3b2o50b2o2b2o11b2o$117b2o3b2o50b2o2bo2b2o8b2o355bo$118b5o35b2o
19b4o5bobo4b2o350bobo$119bobo35bo2bo19bo7bo6bobo332b2o14bo3b2o$106bo
53bo36bo332bobo13bo3b2o3b2o$105b3o11b3o38bo36b2o326b2o4b3o12bo3b2o3b2o
$104b5o48b2obo360b4o2bo4b3o12bobo$69bobo31b2o3b2o47b2o362b3ob2o4b3o7bo
6bo$68bo2bo32b5o421bobo9b2o$67b2o10bo6bo17bo3bo421b2o9b2o14b2o$59b2o4b
2o3bo8bo5bobo17bobo50b2o104b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o
51bo2bo$59b2o6b2o9bo6b2obo17bo10bo40b2o14b2o9b2o77bo29bo29bo29bo29bo
29bo29bo29bo29bo39bo$68bo2bo2b2o9b2ob2o3b2o21bo56b2o9bobo75bobo27bobo
27bobo27bobo27bobo27bobo27bobo27bobo27bobo39b2o11bo2bo$69bobo2bo2b3o5b
2obo4b2o21b3o49bo6bo7b3o4b2ob3o66b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o39bobo10bo2bo$74b4o7bobo16bo17bo44bobo12b3o4bo2b4o360bobo$57b2o
16b2o9bo15b2ob2o14b3o36b2o3b2o3bo12b3o4b2o326b2o28bobo6bo$56bo2bo51bo
8b5o35b2o3b2o3bo13bobo332bo29b2o$56bo44bo5bo4bo6b2o3b2o39b2o3bo14b2o
332bobo6bo7bo12bo7b2o13b3o$56bo53b3o54bobo350b2o4bobo5b4o19b2o13b3o$
56bob2o8bo3b2o27b2obob2o60bo355b2o8b2o2bo2b2o30bo$58b2o6b2o3b2o48bo
402b2o11b2o2b2o30bo$67b2o4bo22b2o23bo402b2o7bo10b2o27bo$96bo85b2o86b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o14bobo4bo10b3o25bobo$57b2o26b
2o7bobo27b2o56bo87bo29bo29bo29bo29bo29bo29bo29bo29bo17bo4bo10b2o$41b3o
13b2o26bo2bo5b2o28bo45bo9bobo85bobo27bobo27bobo27bobo27bobo27bobo27bob
o27bobo27bobo30b2o7b2o$40bo3bo30bo3b3o7bo35b3o40bobo9b2o86b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o31b2o7bobo19bobo$40bo3bo29b5o3bo6bo37b
o33b2o4bobo382bo20bo$41b3o29b2ob2o3bo7bo71b2o3bo2bo29bo352b2o19bo$72b
3ob2o3bo3bo2bo15b2o45bobo13bobo29b3o371bo$73b2ob4o5b2o17b2o8bo35bo17bo
bo6bo24bo369b3o$64b2o8b4o31b3ob2o2b2o31bo3bo15bo6bobo21b2o10bo119bo59b
o59bo59bo49bobo6b3o$63bobo9bo33b4o4b2o7bo23bo26b2o32bo3bo115bo3bo55bo
3bo55bo3bo55bo3bo48b2o$41b3o19bo49b2o12bo22bo2bo56bo119bo59bo59bo59bo
53bo$40bo3bo17b2o61b3o22b3o57bo4bo114bo4bo54bo4bo54bo4bo54bo4bo55b2o$
40bo3bo165b5o115b5o55b5o55b5o55b5o55b2o$41b3o528bo7b2o$581bo$581bobo7b
o$68b5o55b5o55b5o389b2o7bobo$67bo4bo54bo4bo54bo4bo401b2o6b2o$72bo59bo
59bo401b2o4bo3bo$34b2o31bo3bo55bo3bo55bo3bo402b2o3bo5bo$34bo34bo59bo
59bo70b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o89bobo4b2obo3bo$25b2o
5bobo225bo29bo29bo29bo29bo29bo29bo29bo29bo90bo7bo5bo$23bo2bo5b2o152bo
74b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o27b3o71b2o23bo3bo7b2o$10bobo9b
o161b4o75bo29bo29bo29bo29bo29bo29bo29bo29bo71b2o25b2o8bobo$10bo3bo7bo
160bobob2o403bo21bo$14bo7bo155b2o2bo2bob3o400b2o22b2o$10bo4bo7bo2bo
151b2o3bobob2o387b2o8b2o3b2o$14bo10b2o157b4o9b2o375bob2o7b2o$2b2o6bo3b
o24b2o145bo10bobo374bo12bo$bobo6bobo8bobo13bo2bo158bo374bo$bo20b2o175b
2o373bo2bo$2o20bo14bo2bo534b2o24bo$38bo2bo552b2obo3b4o$27bo11bobo92bo
33bo351b2o66b2o2b2obobo4b4o5b2o$27b2o11bo91bobo33b2o350bobo64bobo2b2ob
ob2o3bo2bo5b2o$26bobo94bo7bobo16b2o11b2o4b2o13b2o5bo315bobo13bo53b2o7b
3o8b2o3b4o$39b2o81b2o6bo2bo16b2o7b2o2b2o4b3o11b3o3bo3bo312bo2bo2b2o6bo
2bo7b2o44b2o6b3o8b2o3b4o$14b2o23b2o80b2o4b2o2bobo25b2o2b2o4b2o9bob2o5b
o315b2o5bobo8bo7b2o53b3o12bo$13bobo95b2o7b3o4b2o3bobo8b2o23b2o10bo2bo
4bo5bo302b2o4b2o3bo3bo3bo3bobo64bobo$3b2o7bo6b2o4bo54b2o29b2o8b2o4b2o
5bo8bobo22bo11bob2o9b2o302b2o6b2o5b3ob2o2b2o66b2o$3b2o7bo2bo2bo2bo2bob
o52b3o40b2o21bo26bo10b3o320bo2bo3b2o$12bo6b3obob2o10b2o37bob2o15bo27bo
21b2o25bobo9b2o321bobo23b2o$13bobo6b2ob2o10b2o30b2o5bo2bo8b3o4bobo37bo
36b2o359b2o$14b2o7bob2o42b2o5bob2o16bobo37bo22b2o360b2o$24bobo52b3o2b
2o2bo7bo2bo3b2o29b3o22bobo359b2o$25bo54b2o2bo3bo7bobo4b2o56bo371b3o$
85bo2bo6bobo63b2o354b2o15b2o$67b2o16b2o8bo12b2o86b2o296b2o20bobo12b2o$
67b2o40bo19b3o64bo298bo22bo12b3o$67b2o40bobo6bo12bo45bo2bo8bo4bobo298b
obo9bo24bobo$67bo42b2o6b4o8bo46bo10bobo3b2o300b2o8b4o23b2o$66bobo8bo4b
2o35b4o10b2o38bo2bo3b2o5bo3b2o312b2obobo6bobo$66bob2o7bobo2bobo34bo2bo
9bobo35b4o3b2obobo4bo3b2o311b3obo2bo3bo3bo28b3o$77b2o3bo23b2o11b4o8b3o
35b4o14bo3b2o312b2obobo4bo32bobo$106bo11b4o8b3o36bo2bo8b2o5bobo315b4o
4bo4bo28b3o$67b2o26b2o7bobo11bo12b3o23bo11b4o16bo317bo7bo32b3o$52bo14b
2o26bobo6b2o26bobo5b2o15bobo4b2o4b4o341bo3bo6b2o20b3o$51b3o31bo4b2o4b
3o34b2o5bobo7bo6b2o4bobo7bo343bobo6bobo19b3o$50b5o29bobob2o2bo4b3o42bo
8bo11bo364bo19bobo$83bo3bob3o4b3o28bo14b2o5b3o10b2o364b2o18b3o$83bo3bo
b2o4bobo29b3o$83bo3b2o6b2o33bo21b2o$74b2o8bobo42b2o21b2o$73bobo9bo92b
3o57b3o57b3o57b3o57b3o57b3o57b3o$73bo103b5o55b5o55b5o55b5o55b5o55b5o
55b5o$50b5o17b2o102b2ob3o54b2ob3o54b2ob3o54b2ob3o54b2ob3o54b2ob3o54b2o
b3o$51b3o123b2o58b2o58b2o58b2o58b2o58b2o58b2o$52bo503b2o$557bo$557bobo
4bo$80b2o476b3ob4o$77b3ob2o477b2obob2o14b2o$77b5o478bo2bob3o11bo2bo$
44b2o32b3o47bo432bobob2o11bo$44bo81b2o24b3o33b2o28b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o132b4o12bo$35b2o5bobo82b2o25bo33bo29bo29bo29bo29bo
29bo29bo29bo29bo128b2o5bo5bo7bo$34bobo5b2o109bo5bo29b3o27b3o27b3o27b3o
27b3o27b3o27b3o27b3o27b3o119b2o4bobo9bo9bo2bo5b2o$20bo12b3o87b2o11b2o
20b2o31bo29bo29bo29bo29bo29bo29bo29bo29bo119b2o4bo11b3o9b2o5bobo$20b4o
8b3o87bobo12bo20bobo250b2o138b2o37bo$21b4o8b3o86bo11b3o274bobo138bo37b
2o$21bo2bo9bobo84b2o11bo278bo137bobo$21b4o10b2o376b2o135b2obo$12b2o6b
4o8bo16b2o512b2o$11bobo6bo12bo14bobo512b2o$11bo19b3o13b3o501b2o$10b2o
35b2o69bo432b2o22bo$50b2o66b3o453bobo$49b3o69bo440bobo8bob2o10b2o$36b
3o81b2o440bo2bo6b2ob2o10b2o$38bo184bo329b2o10b2o6bob2o$37bo11b2o96b2o
71b4o329b2o8bo3b2o5bobo$25bo23b2o97b2o69b4o16bo318b2o5b2o8bo$24b2o121b
o64b2o5bo2bo8b2o5bobo316bo4bo2bo$13b2o8b2o4b2o5bo175b2o5b4o14bo3b2o
319bobo$13b2o7b3o4b2o3bobo183b4o3b2obobo4bo3b2o3b2o$23b2o4b2o2bobo11b
2o74bo99bo2bo3b2o5bo3b2o3b2o$24b2o6bo2bo11b2o73b3o34b2o66bo10bobo$25bo
7bobo85b5o33b2o49b2o15bo2bo8bo$34bobo83b2o3b2o82bobo$36bo84b5o82b3o$
121bo3bo32b2o14b2o32b2o$122bobo33b2obo12bobo34b2o7bo3b3o$123bo37bo4bo
4b2obobo33b3o6bo4bo$161bo3b3o3bobobo43b3o3bo23b2o$120b2o36bo2bo3bob2o
4bo75bo$121bo5b2o30b2o5b3o3bo2bo34b2o26b2o7bobo$118b3o5b2o38b2o4bo16bo
20b2o21bo4b2o7b2o$118bo9bo43bo3bo11b2o37b2ob5o6b2o$172bo15bobo35bo4b2o
2bo5b3o$172bo2bo49bo8b2o5b2o$173bo51bo7bo4b2o$119b2o50bobobo49bo12b2o$
119bo51b2obobo40b2o7bo$111bo5bobo54bobo39bobo8b2o$111bobo3b2o28b2o25b
2o40bo$94bo17bobo28b2obo2bob2o62b2o$94b2o16bo2bo27bo4bo2b2o$90b2o3b2o
15bobo32bo8b2o8bo$95b3o13bobo30bobo9b2o7b3o$95b2o7bobo4bo52b2obo29bo$
87b2o5b2o9b2o10b2o5b2o8bo7b2o20b3o29bobo$86bobo5bo10bo12b2o3bo2bo7b3o
4b2o22b2o28bo3b2o$86bo30bo5bo13bo5bo40b2o9bo3b2o$85b2o36bo12b2o46b2o9b
o3b2o$123bob2o69bobo4b2o$125b2o70bo5bobo$112b2o91bo$112b2o35b2o54b2o$
124b2o23b2o3b2o3b2o$98bobo23b2o10b2obob2o$98bo3bo33bo5bo12bo3bo$88b2o
12bo10b2o22bo3bo14b3o$88b2o8bo4bo7bo2bo7bo15b3o3bo11b3o7bo$102bo7bo7b
2o3bo20b2o19b3o$98bo3bo7bo6bo5bo19bobo19bob2o$98bobo9bo7b5o32bo10b3o$
111bo2bo39b3o9b2o$113b2o38bo3bo23b2o$155bo25b2o$152bo5bo$141bo10bo5bo$
141bo11bo3bo$140bobo11b3o$139b2ob2o$138bo5bo$141bo40bo$138b2o3b2o36b3o
$166bo13b5o$165b3o11bobobobo$157b2o5b2obo11b2o3b2o$157bo6b3o$158b3o4b
2o$143b2o15bo21bo$143bo9bo27bobo$144b3o6b3o25bob2o$146bo9bo25b3o$155b
2o25bo2bo$183b3o$182bo3bo$181bo5bo$176bo5bo3bo$175bo7b3o$158bo7bo8b3o$
157b3o5b3o$156b5o4bob2o$155b2o3b2o4b3o$166b2o2$160b2o$162bo$159bo$159b
o2bo$158b2ob2o$159b2o$171b3o6b3o$171bo7bo3bo$157b2o3b2o8bo5bo5bo$157b
2o3b2o14b2obob2o$158b5o$159bobo$178bo$159b3o16b2o2$177b2obo$177b2o2bo$
178b4o2$160b2o$160b2o14b2o3b2o$179bo$176bo5bo$177b2ob2o$178bobo$179bo$
179bo5$178b2o$178b2o!
--Paul

pcallahan · Post by **pcallahan** » April 11th, 2019, 1:52 pm

dvrgn wrote:This message from 1994 looks like a good match for your description:

OMG, thank you! It lives! I must have the original email on an archive of an archive somewhere but I haven't looked at any of that in a long time. I am also surprised that I was working on a delay line as early as Jan. 1991. I was still very naive about CGOL at the time, but I must have been plugging away. By 1994, I had done a lot more, and I guess I had already been invited to the email list.

Post by **dvgrn** » April 11th, 2019, 5:17 pm

pcallahan wrote:
dvrgn wrote:This message from 1994 looks like a good match for your description:
OMG, thank you! It lives!

It's looking pretty good for quarter-century-old technology!

With today's mechanisms we could theoretically build a delay-line memory that extended itself on every overflow, and allowed storage of an unlimited number of bits without needing a linear-growth puffer to build Way Too Many Extension Units.

Anything like that would still be a painfully big and ugly pattern, though -- a universal regulator attached to huge memory loop containing single-channel recipe for a boojum reflector, or two p8 bouncers or two Snarks or whatever.

Maybe a more interesting memory-management project would be a modern rebuild of calcyman's O(sqrt(log(t))) pattern, which does its binary counting by storing bits as stable objects a growing triangle out in plain old empty space, no superstructure needed. Retrieving those bits and working with them isn't particularly easy, of course. But I wonder what a simplest-possible O(log(t)) binary counter would look like these days.

pcallahan · Post by **pcallahan** » April 11th, 2019, 7:29 pm

I'm in the process of revisiting the delay line approach. Below is a modernized version of the delay line I posted on my web page a long time ago. A smaller, more direct design using two queenbee shuttles is used to make the LWSS to extend the line, and the MWSS source is simplified. I haven't taken't a look at the puffers.

One thing about this design is that it automatically recirculates the contents of memory. In practice, that will probably not allow for easy stream-based computation. You can set or reset a bit by deleting an MWSS on either the forward or backward stream, but by the time you have processed the bits, it is too late to do much with the backward stream, so it is probably better to convert the MWSSs into a glider stream for processing and forgo the elegance of automatic recirculation.

Note: when lengthening the line, it is important to know where the insertion occurs. In this case it should occur just before the MWSS (or empty space) that follows the LWSS. (Update: I slimmed this down further using a dvgrn's p120 MWSS based on Michael Simkin's small p120 in "unsure discoveries" thread)

Code: Select all

x = 255, y = 122, rule = B3/S23
163bobo$163b2o$164bo15$235b2o$233b2ob2o13b2o$233b4o13b4o$234b2o14b2ob
2o$252b2o3$233bo4b2o$224bo7b3o3b2o9b2o$225b2o4b2ob2o12bo2bo$224b2o4b3o
b3o11bo2b2o$230b3ob2o11bo2b2o$232bobo12b4o$133bobo83bo$133b2o76b2o7b2o
$134bo73b3ob2o5b2o30b2o$208b5o29b4o4b4o$209b3o22bo2bo3bo3bo4b2ob2o$
214bo23bo6bo6b2o$215b2o9bo7bo3bo2bo2bo$167b2o45b2o8b3o3bo4b4o$165b2ob
2o13b2o39b2o5b2o$165b4o13b4o37bo6b3o$166b2o14b2ob2o37b2o5b2o$161bo22b
2o38b3o3bo4b4o$160bo65bo7bo3bo$160b2o76bo$159b2o73bo2bo$181b2o$175b3o
3bobo$154bo17b3o6bob2o44b4o$155b2o15bo9b2o44bo3bo12bo2bo$154b2o16b3o7b
o49bo16bo$199bo13b2o13bo2bo13bo3bo$143b2o55b2o9bo4bo29b4o$140b3ob2o3bo
33b2o14b2o16bo7b3o$140b5o5b2o22b4o4b4o25bo5bo$141b3o5b2o15bo2bo3bo3bo
4b2ob2o25b6o6bo2bo14b2o$5b2o163bo6bo6b2o38bobo18bo$5b2o159bo3bo2bo2bo
42bo20b2o4b2o$156b2o9b4o49bo18b2o6bo$41bo113b2o5b3o53b3o17b2o7bo$39b3o
109b3o6b2ob2o74bo3bo2bo$38bo64bobo49b2o5b3o79bo$38b2o63b2o51b2o9b4o43b
o$104bo34bo26bo3bo44bo22b2o5bo2bo$140b2o28bo30bo11b3o21b4o8bo$5b3o131b
2o25bo2bo30bo28b4o4b2ob2o3bo3bo$4bo3bo175bo15bo17bo9bo3bo6b2o5b4o$3bo
5bo32b2o5b2o134b2o32b2o11bo$3b2obob2o32b2o5b2o110b4o19b2o30b3o5b2o2bo
2bo$160bo3bo50b3o6b3o$45b2o117bo51b3o5b2o2bo2bo$6bo38b2o113bo2bo34bobo
18b2o11bo$5bobo189b2ob3o15bo9bo3bo$5bobo188b3ob2o27b4o$5b2o190b5o$4bo
17b2o174bobo$3b3o16b2o11b2o2bo159bo$2bo3bo27b3o2b2o6bo$bob3obo10b2o5b
2o8b2o2b3o5b3o74bo$2b5o4bo6b2o5b2o8b2o2b2o9bo74b2o$12b2o35b2o73b2o$11b
2o156bo4bo$51b5o55b5o54b2obo$51bo4bo54bo4bo52b2o2b2o3bo$51bo59bo66bo$
52bo3bo55bo3bo59bo$44bo9bo49bo9bo62bo$18bobo21bo3bo55bo3bo89b2o$19b2o
26bo59bo88b3o15b4o$19bo22bo4bo54bo4bo84b2o5bo3bo9bo3bo$3b2o38b5o55b5o
32b2o49b8o5b2o11bo$3b2o133b2ob2o48bo2bob2o3b3o5b2o2bo2bo$10bobo95b2o
28b4o53b2o3b3o6b3o$10bo3bo93bo30b2o54b2o4b3o5b2o2bo2bo$2o12bo94b3o83b
2obo5b2o11bo$2o8bo4bo4b3o88bo77bo4bo4bo3bo9bo3bo6b2o5b4o$14bo5b3o123b
2o42b10o14b4o4b2ob2o3bo3bo$10bo3bo4bo3bo111bo8b2ob2o42b5o3bo22b4o8bo$
10bobo5bo5bo32bo75bobo4bo3b4o51b3o21b2o5bo2bo$19bo3bo32bobo73bo2bo5bo
3b2o53b2o$20b3o32bob2o73bo6bo2bo56b2o27b2o$49b2o3b2ob2o6b2o56bo8bo2bo
5bo3b2o65bob2o11b5o$49b2o4bob2o63b2o9bobo4bo3b4o62bo5bo10bo4bo$56bobo
76bo8b2ob2o55b3o9bo10b3o2bo$57bo61bo26b2o5b2o5b4o42bo3bo5bo11bo2b2o$
63bo53bo3bo4b3o22b2ob2o3bo3bo41bo5bo3bo2b2o9b2o$64bo57bo5bo22b4o8bo33b
6o9b3o3b2o$64bo52bo4bo4bo24b2o5bo2bo33bo5bo$118b5o79bo$150bo45bo4bo29b
4o$21b2o39b2o3b2o62b3o15b2o8b2o37b2o13bo2bo13bo3bo$21b2o42bo67bo14bo9b
o2bo55bo16bo$62bo5bo63bo16b5o4bo2bo51bo3bo12bo2bo$63b2ob2o82b4o3b2ob2o
52b4o$64bobo86bo4b2o$65bo70b3o$65bo72bo$137bo$160b4o$142bo2bo13bo3bo$
146bo16bo$65b2o75bo3bo12bo2bo$65b2o76b4o!

This shows three gliders entering to trigger three lenghtening LWSSs. The second illustrates the fact that they do not collide with either forward or backward MWSSs.

dvgrn wrote:storage of an unlimited number of bits without needing a linear-growth puffer to build Way Too Many Extension Units.

I'd like to think we're getting these for free, since it is a periodic structure and we have a nice way to make it. But I could be persuaded of a different esthetic depending on my mood.

There is also the "pollution" issue of gliders emitted at different points as the loop extends. I am not sure what to think about that. Of course we could add another puffer to build eaters for them, but I'm not sure what we're trying to optimize in that case. They can also be thought of as a computation trail or log. I guess it depends on the design.

ADDED: Is there any reason this could not be made to work at p60? I would need different puffers of course to produce the backward MWSS stream. Eater spacing could be the same as long as you don't mind inserting two spaces each time.

pcallahan · Post by **pcallahan** » April 19th, 2019, 9:45 pm

I used this implementing rule110 on a p120 MWSS stream (other thread) but I think this is a pretty nice stream gadget. Maybe it's been used before and I just didn't notice. It is based on the fact that an MWSS can delete an LWSS passing in the the opposite direction without itself being deleted.

So this means that if your bitstream contains consecutive bits represented as MWSSs, you can easily check if there is a gap of k consecutive MWSSs in the stream. If a missing MWSS represents 1 (inverted logic) this is the AND of k consecutive bits. If it represents 0 (positive logic) you can think of it as NOR.

This illustrates a device for detecting gaps of 3 missing MWSSs in a p120 MWSS stream (including overlapping gaps; e.g. a gap of 4 is two overlapping gaps of 3) without affecting the MWSS stream. The output is a glider steam, also negative logic. I guess in positive logic, you could say the output stream consists of the OR of three consecutive bits.

Code: Select all

x = 643, y = 80, rule = B3/S23
514bo$514b3o$517bo$516b2o2$625b2o$625b2o2$505b2o5b2o$505b2o5b2o112bo$
625bobo$509b2o113bo3bo$509b2o113b5o$623b2o3b2o$624b5o$625b3o$532b2o92b
o$517b4o11b2o$516bo$515bo4bo8b2o5b2o$516bob2o9b2o5b2o$517bo2$632b2o$
631bobo$630b3o4b2ob3o$629b3o4bo2b4o$630b3o4b2o$631bobo$632b2o4$618b3o$
3b2o238b2o178b2o118b2o58b2o15bo$3ob2o234b3ob2o174b3ob2o114b3ob2o54b3ob
2o13bo$5o235b5o175b5o115b5o55b5o$b3o237b3o177b3o117b3o57b3o21$591bobo$
587bo3bobo8b2o5b2o$593b2o7b2o5b2o$593bo$587bobobo13b2o$587b3obo2bo10b
2o$588bo3bo3$582b2o$582b2o2$578b2o5b2o$578b2o5b2o5$589b2o$590bo$587b3o
$587bo!

Note that this is useful in rule110 because the one non-monotonic case is when all three bits in the 3-cell neighborhood are 1. Then the result is 0. I had avoided implementing it this way until realizing how easy it is to implement on the inverted logic stream.

Maybe this would be useful in implementing some other 1D CA of interest. The nice part is that you can accumulate the results of k bits without increasing the cell count of the device.

pzq_alex · Post by **pzq_alex** » June 8th, 2021, 9:35 am

calcyman wrote: June 10th, 2009, 11:49 am
Such circuits are a bit more advanced than glider circuits, and tend to frighten the newbies.
Stable circuits (e.g. Herschel tracks) don't need phase synchronisation, so they're easier to build (you only have to contend with space, and not time). For example, I've made a universal computer-constructor with stable reflectors, but I wouldn't even attempt to mirror that feat using periodic circuitry.

I totally agree. Period duplicators that doesn't rely on Herschel technology is pretty clunky, especially when you need the gliders' color/parity to sync up.
Here's a ticker I built purely using stable duplicators:

Code: Select all

x = 1675, y = 356, rule = B3/S23
bo26bo11b2o$b3o23bobo10b2o$4bo10bo3bo3b2o2bobo$3b2o8b3o2bobo2bo2b2ob2o
$12bo5bobo3bobo$12b2o5bob4o2bob2o$21bo3bobob2o$20bo3bobo$19bo3bobo$19b
2o3bo4$32b2o$32b2o$47b2o$46bo2bo$47b2obo$2o48bo$2o48b2o$35b2o$36bo$33b
3o$21b2o10bo11b3o$21bobo21bo$23bo22bo$23b2o15$17bo$18b2o$17b2o2$461bo
26bo11b2o$68b3o390b3o23bobo10b2o$68bo395bo10bo3bo3b2o2bobo$69bo393b2o
8b3o2bobo2bo2b2ob2o$472bo5bobo3bobo$472b2o5bob4o2bob2o$468b2o11bo3bobo
b2o$468bobo9bo3bobo$470b2o7bo3bobo$470b2o7b2o3bo$467bo2b3o3$492b2o$
470b2o20b2o$470b2o35b2o$506bo2bo$507b2obo$460b2o9b2o37bo$40bo419b2o5b
2o2b2o37b2o$41b2o423b3o2b2o22b2o$40b2o423bo30bo$464bo6b3o19b3o$465bo
15b2o10bo$91b3o211bobobo3bobobo3bobobo4bobobo3bobobo3bobobo130bobo$91b
o379b3o9bo$92bo212bo3bo7bo3bo8bo3bo7bo3bo122b2ob2o9b2o$468bo3b2o$305bo
bobo3bobobo3bobobo4bobobo3bobobo3bobobo117bo2bo$468bobo$309bo3bo7bo3bo
8bo3bo7bo3bo117b3o2$305bobobo3bobobo3bobobo4bobobo3bobobo3bobobo10$63b
o$64b2o$63b2o$577bo26bo11b2o$577b3o23bobo10b2o$580bo10bo3bo3b2o2bobo$
579b2o8b3o2bobo2bo2b2ob2o$588bo5bobo3bobo$588b2o5bob4o2bob2o$597bo3bob
ob2o$596bo3bobo$595bo3bobo$595b2o3bo4$608b2o$608b2o$623b2o$622bo2bo$
623b2obo$576b2o48bo$576b2o48b2o$611b2o$612bo$609b3o9b2o$597b2o10bo11bo
bo$597bobo21bo$137b3o459bo$137bo461b2o$138bo4$141b3o367bobo$140bobob2o
366b2o$139bo2bo3bo365bo$139b2obo$141b2o420b2o$126b2o15b2o418bobo$127bo
16bo418bo$127bobo15bo$117bo10b2o13b2obo$115b3o25bobo$114bo$114b2o477bo
bo$99b2o8bo32b3o4b2o443b2o$100bo9b2o29bob2o4b2o443bo190bo26bo11b2o$
100bob2o5b2o29b3o501b2o139b3o23bobo10b2o$101bo2bo16bo3b2o517bobo141bo
10bo3bo3b2o2bobo$102b2o14bo3bob2obo516bo142b2o8b3o2bobo2bo2b2ob2o$117b
o2bobo4b2o667bo5bobo3bobo$117b2o2b3o2b2o668b2o5bob4o2bob2o$122b2o681bo
3bobob2o$172b2o630bo3bobo$172b2o629bo3bobo$126bo3b2o671b2o3bo$125bobo
3bo$124bobo3bo690b2o$120b2obobo3bo691bob2o$120b2obo2b4obo5b2o684b2o$
124bobo3bobo5bo8bo673bob2o$120b2ob2o2bo2bobo2b3o7bobo673b2o8b2o$121bob
o2b2o3bo3bo10b2o682bo2bo$109b2o10bobo41b3o3b3o657b2obo$109b2o11bo42bo
2bobo2bo610b2o48bo$165bo7bo610b2o48b2o$819b2o$166bo5bo443bobo201bo$
167b2ob2o445b2o198b3o$617bo187b2o10bo$667b2o136bobo$667bobo137bo$667bo
139b2o$166bo$4b2o44b2o44b2o67bobo$3b2ob2o41b2ob2o41b2ob2o65bobo$4b4o
42b4o42b4o64bo3bo$5b2o44b2o44b2o65b2ob2o$164bo3bo$165b3o$165b3o4b2o$
172b2o2$586b2o$587bo$587bobo$577bo10b2o$575b3o$574bo227bo$574b2o19b2o
3b2o201b2o$559b2o34bobo2bobo6b2o28bobo160b2o$560bo36b2o3b2o5b2o29b2o$
560bob2o34b2o2bo37bo$561bo2bo34b3o$562b2o36bo$577b2o922bo26bo11b2o$
577b2o922b3o23bobo10b2o$1504bo10bo3bo3b2o2bobo$632b2o869b2o8b3o2bobo2b
o2b2ob2o$632b2o878bo5bobo3bobo$587b2ob2o920b2o5bob4o2bob2o$585bobo3bo
929bo3bobob2o$584bobo3bo929bo3bobo$580b2obobo3bo929bo3bobo$580b2obo2b
4obo5b2o920b2o3bo$584bobo3bobo5bo$580b2ob2o2bo2bobo2b3o$581bobo2b2o3bo
3bo$569b2o10bobo41b3o3b3o898b2o$569b2o11bo42bo2bobo2bo887b3o8b2o$625bo
7bo889bo23b2o$1515b4o3bo23bo2bo$626bo5bo881b2o31b2obo$627b2ob2o868b2o
11b2obo2bo30bo$1500b2o12bobob2o30b2o$1515b2obo16b2o$713b2o801b2o18bo$
713bobo817b3o$580b2o44bo86bo807b2o10bo$4b2o90b2o182b2o90b2o205b4o42bob
o893bobo$3b2ob2o87b2ob2o179b2ob2o87b2ob2o202b2ob2o42bobo895bo$4b4o88b
4o180b4o88b4o203b2o43bo3bo894b2o$5b2o90b2o182b2o90b2o249b2ob2o88b2o$
624bo3bo88b2ob2o$625b3o88bo4bo$625b3o4b2o81bo2bo2bo$632b2o81bo3bo$715b
2o3bo833b3o$702b2o17bo832bo$703bo17bo833bo$703bobo12b2ob2o$693bo10b2o
12b2ob2o$691b3o26bo$690bo29bo$690b2o27bo$675b2o43bo4b2o$676bo8bobo28bo
3bo4b2o$676bob2o6b2o13bo14bob2o$677bo2bo5bo15b2o12b2o$678b2o23b2o814bo
bo$693bo11bo814b2o$693b2o5b5o815bo$703bo$748b2o$748b2o$702bo3b2o$701bo
bo3bo$700bobo3bo$696b2obobo3bo203b2o$696b2obo2b4obo5b2o194bobo$700bobo
3bobo5bo8bo185bo667b3o$696b2ob2o2bo2bobo2b3o10bo852bo$697bobo2b2o3bo3b
o10b3o16b3o3b3o828bo$685b2o10bobo40bo2bo3bo2bo$685b2o11bo41b2obo3bob2o
8$1542bobo$580b2o44b2o44b2o68bo800b2o$4b2o44b2o44b2o90b2o44b2o44b2o90b
2o44b2o44b2o113b4o42b4o42b4o65b2ob2o798bo$3b2ob2o41b2ob2o41b2ob2o87b2o
b2o41b2ob2o41b2ob2o87b2ob2o41b2ob2o41b2ob2o110b2ob2o41b2ob2o41b2ob2o
65b2ob2o$4b4o42b4o42b4o88b4o42b4o42b4o88b4o42b4o42b4o111b2o44b2o44b2o$
5b2o44b2o44b2o90b2o44b2o44b2o90b2o44b2o44b2o272bobobobo2$740b2ob2o$
741b3o4b2o$742bo5b2o$910b2o$911bo688b3o$911bobo686bo$901bo10b2o687bo$
899b3o$898bo$898b2o$883b2o48b2o$884bo48b2o$884bob2o$885bo2bo$886b2o$
892b2o$894bo2b2o$890bo5bo$889bo2bo2b2o3bo55b2o$895bo5bo54b2o$890bo10bo
8bo3b2o$891bo7b2o8bobo3bo$898b2o8bobo3bo$893bo10b2obobo3bo$892b2ob2o7b
2obo2b4obo5b2o$892b2ob2o11bobo3bobo5bo$894bo9b2ob2o2bo2bobo2b3o27b3o3b
3o$893b2o10bobo2b2o3bo3bo29bo2bobo2bo$893b2o10bobo40bo3bobo3bo$893b2o
11bo41b4o3b4o$949bo7bo7$943bo6bo$672b2o90b2o178bo4b3o$96b2o90b2o182b2o
90b2o205b4o88b4o175b3o3bo3bo635bobo$95b2ob2o87b2ob2o179b2ob2o87b2ob2o
202b2ob2o87b2ob2o181b2ob2o636b2o$96b4o88b4o180b4o88b4o203b2o90b2o183b
2ob2o636bo$97b2o90b2o182b2o90b2o$948b2ob2o$948b2ob2o$948bo3bo3b2o$949b
3o4b2o$950bo5$1626b2o$1627bo$1627bobo$1617bo10b2o$1615b3o$1614bo$1614b
2o$1599b2o48b2o$1600bo48b2o$1600bob2o$1601bo2bo6bobo14b2o$1602b2o8b2o
13b2ob2o$1612bo4b2o8b2ob2o$1617b2o10b3o2$1672b2o$1672b2o$1626bo3b2o$
1625bobo3bo$1624bobo3bo$1620b2obobo3bo35b3o3b3o$1620b2obo2b4obo5b2o25b
o2bo3bo2bo$1624bobo3bobo5bo29bobo$1620b2ob2o2bo2bobo2b3o26b2o7b2o$
1621bobo2b2o3bo3bo28b2o7b2o$1609b2o10bobo43bo3bo$1609b2o11bo44b2ob2o$
1665b3o3b3o$1665b2o5b2o$1665bo7bo3$1666bo$1666bo2$580b2o44b2o44b2o90b
2o44b2o44b2o90b2o44b2o44b2o$4b2o44b2o44b2o90b2o44b2o44b2o90b2o44b2o44b
2o113b4o42b4o42b4o88b4o42b4o42b4o88b4o42b4o42b4o111b2o44b2o44b2o90b2o
44b2o44b2o90b2o44b2o44b2o47b2o3b2o$3b2ob2o41b2ob2o41b2ob2o87b2ob2o41b
2ob2o41b2ob2o87b2ob2o41b2ob2o41b2ob2o110b2ob2o41b2ob2o41b2ob2o87b2ob2o
41b2ob2o41b2ob2o87b2ob2o41b2ob2o41b2ob2o110b2ob2o41b2ob2o41b2ob2o87b2o
b2o41b2ob2o41b2ob2o87b2ob2o41b2ob2o41b2ob2o$4b4o42b4o42b4o88b4o42b4o
42b4o88b4o42b4o42b4o111b2o44b2o44b2o90b2o44b2o44b2o90b2o44b2o44b2o113b
4o42b4o42b4o88b4o42b4o42b4o88b4o42b4o42b4o$5b2o44b2o44b2o90b2o44b2o44b
2o90b2o44b2o44b2o688b2o44b2o44b2o90b2o44b2o44b2o90b2o44b2o44b2o3$1663b
2o3b2o2b2o$1672b2o2$1666bo$1666bo!

Entity Valkyrie 2 · Post by **Entity Valkyrie 2** » June 8th, 2021, 9:00 pm

pzq_alex wrote: June 8th, 2021, 9:35 am Here's a ticker I built purely using stable duplicators:
Code: Select all
RLE

Why not use a stable G-to-LWSS too? As long as the gap between the gliders is 78 or over, this can be used on any period. I chose a G-to-LWSS that has fairly high clearance.

Code: Select all

x = 201, y = 326, rule = B3/S23
18b2o$2o16b2o$bo$bobo$2b2o8$4b2o$3bobo$3bo$2b2o3$3b2o$2bo2bo2b2o$3b2o
2bobo3b3o$5b2o7bo8b2o$5bo8b3o6bo$2b2obo2bo15b3o$2bob2obobo16bo$6bobo$
3b2o2bo$b3ob2o45bo$o52b2o$b3ob2o45b2o$3bob2o2$13b2o$13b2o7b2o$22bo$20b
obo$20b2o4$2o$2o5$16bo$15bobo$15bobo$16bo$17b3o$19bo7$36b2o$36bobo$36b
o18$55b3o$55bo$56bo8$114bo$112bobo$113b2o27$141bobo$142b2o$142bo8$105b
2o$104b2o$106bo6$169bo$169b3o$172bo$171bobo$171bobo$172bo5$187b2o$187b
2o4$167b2o$166bobo$166bo$165b2o7b2o$174b2o2$182b2obo$182b2ob3o$188bo$
182b2ob3o$181bo2b2o$180bobo$179bobob2obo$162b2o16bo2bob2o$163bo19bo$
163bobo16b2o$164b2o13bobo2b2o$179b2o2bo2bo$184b2o4$151bo$150b2o$150bob
o4$165b2o15b2o$165b2o15bobo$184bo$184b2o6$166b3o$166b3o8b2o$164b2o11bo
$164bo2b3o5bobo$175b2o$164bo$164bo3b2o$165bo2bo10bo$165bobo10bobo$178b
obo$177b2ob3o$183bo$177b2ob3o$177b2obo2$184b2o$164b2o18bo$163bobo16bob
o$163bo12b4ob3o$162b2o12b2ob3o$174bo2bo2b2o$174b3o3bo$173bo2bo2bo$173b
obo$174b2o$165bo$163b2o$164b2o7bo$172bobo$172bobo$173bo$177b2o$177bobo
$148bo30bo$146b3o30b2o$145bo$144bobo$144bobo$145bo4$191bo$129b2o58b3o$
129b2o57bo$188b2o3$149b2o45b2o$149bobo45bo$151bo45bob2o$142b2o7b2o36b
2o4b3o2bo$142b2o45b2o3bo3b2o$194b4o$132bob2o39b2o3b2o15bo$130b3ob2o39b
obobobo12b3o$129bo47bobo13bo$130b3ob2o40bo2bo14b5o$132b2o2bo39bobo19bo
$135bobo39bo18bo$131bob2obobo3bobo10bo40b2o$131b2obo2bo4bo10b3o$134bo
9bobo5bo$134b2o10bo5b2o$132b2o2bobo6bobo13b2o$131bo2bo2b2o7b2o13b2o$
132b2o14bo$146b2o$146bo27bobo$174b2o5b2o$157b2o16bo5bobo$157bo25bo$
155bobo16b2o7b2o$155b2o17b2o2$164bob2o$141b2o19b3ob2o$140bobo18bo$140b
o21b3ob2o$139b2o23b2o2bo$159b2o6bobo$160bo2bob2obobo16bo$157b3o3b2obo
2bo15b3o$157bo8bo17bo$166b2o16b2o$150b2o12b2o2bobo$150b2o11bo2bo2b2o$
164b2o4$189b2o$189bo$140b2o45bobo$141bo45b2o$141bobo$142b2o$173b2o$
172bobo$172bo$161bo9b2o$159b3o29b2o$158bo33bo$158b2o19b2o8b3o$178bo2bo
7bo$178bo2bo$178bo$178b2o3bo$166b2o11bo2b2obo$137b2o28bo12b3o2bo$138bo
28bob2obo$138bobo25b2obob2o$139b2o$166b3o$166bo2bo2b2o$168b2o3bo5b3o$
173bobo3bo2b2o$162bobo9b2o4b3o$163b2o16bo$163bo$157b2o$157bo35bo$158b
3o30b3o$160bo29bo$190b2o13$185b2o$185b2o!

Jormungant · Post by **Jormungant** » July 13th, 2021, 8:03 pm

Well well, feels like it has been a while since I posted some contraption, here is one I had in mind: a 2D array of flip flops.

Code: Select all

x = 767, y = 775, rule = LifeHistory
52$431.D$432.D$348.6D2.2D6.6D4.2D4.6D44.3D$348.6D2.2D6.6D4.2D4.6D$
348.2D6.2D6.2D7.4D3.2D2.2D$348.2D6.2D6.2D7.D2.D3.2D2.2D47.D2.D$348.2D
6.2D6.4D5.D2.D3.2D2.2D48.D2.D$348.2D6.2D6.4D4.6D2.4D51.D2.D$348.2D6.
2D6.2D6.6D2.4D52.D2.D54.C$348.2D6.2D6.2D6.2D2.2D2.2D2.2D51.D2.D54.C$
348.6D2.6D2.6D2.2D2.2D2.2D2.2D52.D2.D51.3C$348.6D2.6D2.6D2.2D2.2D2.2D
2.2D53.D2.D$440.D2.D35.D$441.D2.D35.2D$442.D2.D33.2D$443.D2.D$444.D2.
D60.2A$445.D2.D59.2A$446.D2.D$447.D2.D$448.D2.D$449.D2.D$450.D2.D$
451.D2.D$452.D2.D$453.D2.D42.2A$454.D2.D36.D4.2A$455.D2.D36.D$456.D2.
D33.3D$457.D2.D$458.D2.D$459.D2.D$460.D2.D54.D.D2.D31.2A$461.D2.D32.
3D19.D.D2.D31.A$462.D2.D33.D20.D.D2.D27.3A$463.D2.D31.D4.D.D2.D9.D2.D
.D2.D26.A56.2A$464.D2.D36.D.D2.D9.D2.D.D2.D21.2A59.A$465.D2.D36.D.D2.
D9.D2.D.D2.D21.A57.A.A$466.D2.D33.D2.D.D2.D9.D2.D.D2.D20.A.A2.A52.2A$
467.D2.D33.D2.D.D2.D9.D2.D.D2.D18.2A.4A$468.D2.D33.D2.D.D2.D9.D2.D.D
2.D$469.D2.D33.D2.D.D2.D9.D2.D.D2.D16.2A.2A$470.D2.D33.D2.D.D2.D9.D2.
D.D2.D15.2A.A.A$471.D2.D33.D2.D.D2.D9.D2.D.D2.D19.A$472.D2.D33.D2.D.D
2.D9.D2.D.D2.D17.2A.2A.A$473.D2.D33.D2.D.D2.D9.D2.D.D2.D19.A.2A$474.D
2.D33.D2.D.D2.D9.D2.D.D2.D18.A$475.D2.D28.A4.D2.D.D2.D9.D2.D.D2.D16.
2A$476.D2.D25.3A5.D2.D.D2.D9.D2.D.D2.D$477.D2.D8.A14.A9.D2.D.D2.D9.D
2.D.D2.D$478.D2.D7.3A12.2A9.D2.D.D2.D9.D2.D.D2.D$479.D2.D9.A23.D2.D.D
2.D9.D2.D.D2.D$480.D2.D7.2A24.D2.D.D2.D9.D2.D.D2.D$481.D2.D33.D2.D.D
2.D9.D2.D.D2.D10.2A$482.D2.D33.D2.D.D2.D4.2A3.D2.D.D2.D9.2A$483.D2.D
5.2A26.D2.D.D2.D3.2A4.D2.D.D2.D$484.D2.D4.2A17.2A8.D2.D.D2.D9.D2.D.D
2.D$485.D2.D22.2A9.D2.D.D2.D9.D2.D.D2.D$486.D2.D33.D2.D.D2.D9.D2.D.D
2.D11.A$487.D2.D33.D2.D.D2.D9.D2.D.D2.D8.3A$488.D2.D33.D2.D.D2.D9.D2.
D.D2.D6.A$489.D2.D33.D2.D.D2.D9.D2.D.D2.D5.2A$490.D2.D33.D2.D.D2.D9.D
2.D.D2.D$491.D2.D13.2A18.D2.D.D2.D9.D2.D.D2.D$367.D124.D2.D12.A20.D2.
D.D2.D9.D2.D.D2.D$368.D124.D2.D13.A13.2A4.D2.D.D2.D9.D2.D.D2.D$366.3D
125.D2.D11.2A12.A.A5.D2.D.D2.D9.D2.D.D2.D2.4D$495.D2.D6.2A16.A8.D2.D.
D2.D9.D2.D.D2.2D4.D$496.D2.D5.A14.2A.2A8.D2.D.D2.D9.D2.D.D4.2C.D$372.
D124.D2.D5.3A12.A.A10.D2.D.D2.D4.3D2.D2.D.D3.2C.D$370.D2.D124.D2.D6.A
11.A2.A.A9.D2.D.D2.4D3.D2.D2.D.2D4.D$371.D2.D124.D2.D17.2A2.A.A9.D2.D
.D6.D2.D2.D2.D2.4D$372.D2.D54.C69.D2.D21.2A10.D2.D.D4.D.D.D3.D2.D$
373.D2.D54.C45.2A5.2A15.D2.D33.D2.D.D4.2D.D4.D2.D$374.D2.D51.3C46.A5.
2A16.D2.D33.D2.D.3D4.D5.D2.D$375.D2.D99.A.A22.D2.D33.D2.D3.4D7.D2.D$
376.D2.D35.D63.2A23.D2.D33.D2.D14.D2.D$377.D2.D35.2D65.2A20.D2.D33.D
2.D14.D2.D10.2A$378.D2.D33.2D65.A.A10.2A9.D2.D33.D2.D14.D2.D9.2A$379.
D2.D100.A11.2A10.D2.D33.D2.D14.D2.D$380.D2.D60.2A33.A28.D2.D33.D2.D
14.D2.D$381.D2.D59.2A32.3A28.D2.D33.D2.D14.D2.D8.A$382.D2.D91.A.3A28.
D2.D33.D2.D14.D2.D6.A.A$383.D2.D89.A3.A30.D2.D33.D2.D14.D2.D6.A$384.D
2.D87.A3.A32.D2.D26.2A5.D2.D14.D2.D6.3A$385.D2.D85.3A.A27.2A5.D2.D25.
2A6.D2.D14.D2.D7.A$386.D2.D85.3A7.2A19.A7.D2.D33.D2.D3.2D9.D2.D$387.D
2.D85.A9.A17.A.A8.D2.D33.D2.D2.D.D9.D2.D$388.D2.D94.A.A15.2A10.D2.D
33.D2.D3.D10.D2.D5.2A$389.D2.D42.2A50.2A4.A23.D2.D33.D2.D2.2D10.D2.D
4.2A$390.D2.D36.D4.2A55.A.A23.D2.D33.D2.D5.2A7.D2.D$391.D2.D36.D60.A.
A24.D2.D33.D2.D4.2A3.A4.D2.6D$392.D2.D33.3D61.A10.2A14.D2.D33.D2.D7.A
.A4.D7.D$393.D2.D107.A.A14.D2.D33.D2.D7.A.A4.D7.D$394.D2.D108.A15.D2.
D4.2A27.D2.D8.A5.D3.2D2.D$395.D2.D107.2A15.D2.D3.2A28.D2.D7.2A5.D2.D.
D2.D$396.D2.D54.D.D2.D31.2A31.D2.D33.D2.D14.D2.D.D2.D$397.D2.D32.3D
19.D.D2.D31.A32.D2.D33.D2.D5.2A7.D2.D.D2.D$398.D2.D33.D20.D.D2.D27.3A
20.A13.D2.D33.D2.D4.2A8.D2.D.D2.D$399.D2.D31.D4.D.D2.D9.D2.D.D2.D26.A
22.3A12.D2.D33.D2.D14.D2.D.D2.D$400.D2.D36.D.D2.D9.D2.D.D2.D21.2A28.A
12.D2.D33.D2.6D9.D2.D.D2.D$401.D2.D36.D.D2.D9.D2.D.D2.D21.A27.2A13.D
2.D33.D7.D9.D2.D.D2.D$402.D2.D33.D2.D.D2.D9.D2.D.D2.D20.A.A2.A38.D2.D
33.D7.D9.D2.D.D2.D$403.D2.D33.D2.D.D2.D9.D2.D.D2.D18.2A.4A39.D2.D33.D
3.2D2.D9.D2.D.D2.D$404.D2.D33.D2.D.D2.D9.D2.D.D2.D64.D2.D33.D2.D.D2.D
9.D2.D.D2.D31.2A$405.D2.D33.D2.D.D2.D9.D2.D.D2.D16.2A.2A43.D2.D33.D2.
D.D2.D9.D2.D.D2.D31.A$406.D2.D33.D2.D.D2.D9.D2.D.D2.D15.2A.A.A43.D2.D
33.D2.D.D2.D9.D2.D.D2.D27.3A$407.D2.D33.D2.D.D2.D9.D2.D.D2.D19.A44.D
2.D33.D2.D.D2.D9.D2.D.D2.D26.A56.2A$408.D2.D33.D2.D.D2.D9.D2.D.D2.D
17.2A.2A.A28.2A10.D2.D33.D2.D.D2.D9.D2.D.D2.D21.2A59.A$409.D2.D33.D2.
D.D2.D9.D2.D.D2.D19.A.2A21.2A5.A.A10.D2.D33.D2.D.D2.D9.D2.D.D2.D21.A
57.A.A$410.D2.D33.D2.D.D2.D9.D2.D.D2.D18.A24.2A7.A11.D2.D33.D2.D.D2.D
9.D2.D.D2.D20.A.A2.A52.2A$411.D2.D28.A4.D2.D.D2.D9.D2.D.D2.D16.2A33.
2A11.D2.D33.D2.D.D2.D9.D2.D.D2.D18.2A.4A$412.D2.D25.3A5.D2.D.D2.D9.D
2.D.D2.D64.D2.D33.D2.D.D2.D9.D2.D.D2.D$413.D2.D8.A14.A9.D2.D.D2.D9.D
2.D.D2.D36.A27.D2.D33.D2.D.D2.D9.D2.D.D2.D16.2A.2A$414.D2.D7.3A12.2A
9.D2.D.D2.D9.D2.D.D2.D34.A.A.2A24.D2.D33.D2.D.D2.D9.D2.D.D2.D15.2A.A.
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2.D.D4.C.C.D3.D2.D69.D2.D34.2A$167.2A4.A23.D2.D33.D2.D2.2D10.D2.D4.2A
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D2.D33.A$172.A.A23.D2.D33.D2.D5.2A7.D2.D36.A.3A28.D2.D33.D2.D14.D2.D
6.A.A36.A5.2A16.D2.D33.D2.D.3D4.D5.D2.D69.D2.D33.3A$172.A.A24.D2.D33.
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2.D26.2A5.D2.D14.D2.D6.3A35.2A23.D2.D33.D2.D14.D2.D69.D2.D$184.A.A14.
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33.D2.DC13.D2.D4.2A32.3A28.D2.D33.D2.D14.D2.D8.A60.D2.D$169.3A20.A13.
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195.A12.D2.D33.D2.6D9.D2.D.D2.D37.A10.2A14.D2.D33.D2.D7.A.A4.D7.D27.A
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2D2.D25.3A7.2A19.A7.D2.D33.D2.D14.D2.D69.D2.D$211.D2.D33.D3.2D2.D9.D
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14.D2.D.D2.D34.A.A15.2A10.D2.D33.D2.D14.D2.D69.D2.D$105.3D105.D2.D33.
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106.D108.D2.D33.D2.D.D2.D9.D2.D.D2.D26.A22.3A12.D2.D33.D2.D14.D2.D.D
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3A20.A13.D2.D33.D2.D87.D2.D$192.A.A.A.A24.D2.D15.C17.D2.D.D2.D9.D2.D.
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2A13.D2.D33.D$191.2A4.A28.D2.D33.D2.D.D2.D9.D2.D.D2.D18.A24.2A7.A11.D
2.D33.D2.D.D2.D9.D2.D.D2.D20.A.A2.A38.D2.D33.D$197.A.A27.D2.D28.A4.D
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2.D.D2.D9.D2.D.D2.D16.2A.2A43.D2.D$230.D2.D7.3A12.2A9.D2.D.D2.D9.D2.D
.D2.D34.A.A.2A24.D2.D33.D2.D.D2.D9.D2.D.D2.D15.2A.A.A43.D2.D$231.D2.D
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33.D2.D.D2.D9.D2.D.D2.D17.2A.2A.A28.2A10.D2.D$233.D2.D33.D2.D.D2.D9.D
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5.A.A10.D2.D$234.D2.D33.D2.D.D2.D4.2A3.D2.D.D2.D9.2A18.2A4.A28.D2.D
33.D2.D.D2.D9.D2.D.D2.D18.A24.2A7.A11.D2.D$235.D2.D5.2A26.D2.D.D2.D3.
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9.D2.D.D2.D9.D2.D.D2.D36.A27.D2.D$238.D2.D33.D2.D.D2.D9.D2.D.D2.D11.A
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2.D29.2A.A.A.A.A2.A22.D2.D$241.D2.D33.D2.D.D2.D9.D2.D.D2.D5.2A57.D2.D
33.D2.D.D2.D9.D2.D.D2.D10.2A16.A2.A2.2A.4A23.D2.D$242.D2.D33.D2.D.D2.
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243.D2.D13.2A18.D2.D.D2.D9.D2.D.D2.D64.D2.D5.2A26.D2.D.D2.D3.2A4.D2.D
.D2.D34.A.A27.D2.D$244.D2.D12.A20.D2.D.D2.D9.D2.D.D2.D64.D2.D4.2A17.
2A8.D2.D.D2.D9.D2.D.D2.D34.2A28.D2.D$245.D2.D13.A13.2A4.D2.D.D2.D9.D
2.D.D2.D64.D2.D22.2A9.D2.D.D2.D9.D2.D.D2.D64.D2.D$246.D2.D11.2A12.A.A
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247.D2.D6.2A16.A8.D2.D.D2.D9.D2.D.D2.2D4.D58.D2.D33.D2.D.D2.D9.D2.D.D
2.D8.3A53.D2.D$248.D2.D5.A14.2A.2A8.D2.D.D2.D9.D2.D.D4.2D.D59.D2.D33.
D2.D.D2.D9.D2.D.D2.D6.A57.D2.D$249.D2.D5.3A12.A.A10.D2.D.D2.D4.3D2.D
2.D.D3.2D.D60.D2.D33.D2.D.D2.D9.D2.D.D2.D5.2A57.D2.D$250.D2.D6.A11.A
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D2.D.D2.D64.D2.D$252.D2.D21.2A10.D2.D.D4.C.C.D3.D2.D69.D2.D12.A20.D2.
D.D2.D9.D2.D.D2.D64.D2.D$229.2A5.2A15.D2.D33.D2.D.D4.2C.D4.D2.D69.D2.
D13.A13.2A4.D2.D.D2.D9.D2.D.D2.D64.D2.D$230.A5.2A16.D2.D33.D2.D.3D4.D
5.D2.D69.D2.D11.2A12.A.A5.D2.D.D2.D9.D2.D.D2.D2.4D58.D2.D$230.A.A22.D
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231.2A23.D2.D33.D2.D14.D2.D69.D2.D5.A14.2A.2A8.D2.D.D2.D9.D2.D.D4.2D.
D59.D2.D$235.2A20.D2.D33.D2.D14.D2.D10.2A57.D2.D5.3A12.A.A10.D2.D.D2.
D4.3D2.D2.D.D3.2D.D60.D2.D$234.A.A10.2A9.D2.D33.D2.D14.D2.D9.2A58.D2.
D6.A11.A2.A.A9.D2.D.D2.4D3.D2.D2.D.2D4.D61.D2.D$235.A11.2A10.D2.D33.D
2.D14.D2.D69.D2.D17.2A2.A.A9.D2.D.D6.C2.D2.D2.D2.4D63.D2.D$231.A28.D
2.D33.D2.D14.D2.D69.D2.D21.2A10.D2.D.D4.C.C.D3.D2.D69.D2.D34.2A$230.
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5.D2.D69.D2.D33.3A$228.A3.A30.D2.D33.D2.D14.D2.D6.A37.A.A22.D2.D33.D
2.D3.4D7.D2.D69.D2.D34.A$227.A3.A32.D2.D26.2A5.D2.D14.D2.D6.3A35.2A
23.D2.D33.D2.D14.D2.D69.D2.D$226.3A.A27.2A5.D2.D25.2A6.D2.D14.D2.D7.A
39.2A20.D2.D33.D2.D14.D2.D10.2A57.D2.D$227.3A7.2A19.A7.D2.D33.D2.D14.
D2.D45.A.A10.2A9.D2.D33.D2.D14.D2.D9.2A58.D2.D$228.A9.A17.A.A8.D2.D
33.D2.D.2C11.D2.D45.A11.2A10.D2.D33.D2.D14.D2.D69.D2.D$238.A.A15.2A
10.D2.D33.D2.C.C12.D2.D5.2A33.A28.D2.D33.D2.D14.D2.D69.D2.D$239.2A4.A
23.D2.D33.D2.DC13.D2.D4.2A32.3A28.D2.D33.D2.D14.D2.D8.A60.D2.D$244.A.
A23.D2.D33.D2.D5.2A7.D2.D36.A.3A28.D2.D33.D2.D14.D2.D6.A.A60.D2.D$
244.A.A24.D2.D33.D2.D4.2A3.A4.D2.6D29.A3.A30.D2.D33.D2.D14.D2.D6.A62.
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2.D6.3A60.D2.D$256.A.A14.D2.D33.D2.D7.A.A4.D7.D25.3A.A27.2A5.D2.D25.
2A6.D2.D14.D2.D7.A61.D2.D$258.A15.D2.D4.2A27.D2.D8.A5.D3.2D2.D25.3A7.
2A19.A7.D2.D33.D2.D14.D2.D69.D2.D$258.2A15.D2.D3.2A28.D2.D7.2A5.D2.D.
D2.D25.A9.A17.A.A8.D2.D33.D2.D14.D2.D69.D2.D$243.2A31.D2.D33.D2.D14.D
2.D.D2.D34.A.A15.2A10.D2.D33.D2.D14.D2.D69.D2.D$244.A32.D2.D33.D2.D5.
2A7.D2.D.D2.D34.2A4.A23.D2.D33.D2.D14.D2.D69.D2.D$241.3A20.A13.D2.D
33.D2.D4.2A8.D2.D.D2.D38.A.A23.D2.D33.D2.D5.2A7.D2.D69.D2.D$241.A22.
3A12.D2.D33.D2.D14.D2.D.D2.D37.A.A24.D2.D33.D2.D4.2A3.A4.D72.D2.D$
267.A12.D2.D33.D2.6D9.D2.D.D2.D37.A10.2A14.D2.D33.D2.D7.A.A4.D72.D2.D
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2A12.A.A5.D2.D.D2.D9.D2.D.D2.D2.4D58.D2.D$319.D2.D6.2A16.A8.D2.D.D2.D
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2.D6.A11.A2.A.A9.D2.D.D2.4D3.D2.D2.D.2D4.D61.D2.D$109.2D212.D2.D17.2A
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2.D9.2A58.D2.D$245.2C60.A11.2A10.D2.D33.D2.D14.D2.D69.D2.D$244.C.C56.
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316.A.A23.D2.D33.D2.D5.2A7.D2.D69.D2.D$316.A.A24.D2.D33.D2.D4.2A3.A4.
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D7.A.A4.D72.D2.D$330.A15.D2.D4.2A27.D2.D8.A78.D2.D$330.2A15.D2.D3.2A
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313.3A20.A13.D2.D33.D2.D$313.A22.3A12.D2.D33.D2.D$339.A12.D2.D33.D$
338.2A13.D2.D33.D$354.D2.D33.D$355.D2.D$356.D2.D$249.3D105.D2.D$251.D
106.D2.D$250.D108.D2.D$348.2A10.D2.D$341.2A5.A.A10.D2.D$341.2A7.A11.D
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2.D$341.A.A27.D2.D$342.2A28.D2.D$373.D2.D$374.D2.D$375.D2.D$41.6D3.6D
2.2D4.2D10.6D3.6D3.2D6.6D2.6D2.6D252.D2.D$41.6D3.6D2.2D4.2D10.6D3.6D
3.2D6.6D2.6D2.6D253.D2.D$41.2D2.2D3.2D2.2D2.2D4.2D10.2D7.2D7.2D6.2D6.
2D8.2D256.D2.D$41.2D2.2D3.2D2.2D2.2D4.2D10.2D7.2D7.2D6.2D6.2D8.2D257.
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14.2D3.2D7.2D6.2D6.2D8.2D261.D2.D$41.2D2.2D3.6D3.7D10.6D3.6D3.6D2.6D
2.6D4.2D262.D2.D$41.2D2.2D3.6D4.4D12.6D3.6D3.6D2.6D2.6D4.2D263.D2.D$
386.D2.D$387.D2.D$388.D2.D34.2A$389.D2.D33.A$390.D2.D33.3A$391.D2.D
34.A$392.D2.D$393.D2.D$394.D2.D$181.2C212.D2.D$180.C.C213.D2.D$182.C
214.D2.D$398.D2.D$399.D2.D$400.D2.D$401.D2.D$402.D2.D$403.D2.D$404.D
2.D$405.D2.D$406.D2.D$407.D2.D$408.D2.D$409.D2.D$410.D2.D$411.D2.D56$
253.2D$252.D.D$254.D!

I am sure this was done before, but no clue if this design is more compact or not. Also... I am sure I should claim bonus points for that glider lane hershell track unlikely-to-work overlap.

I nearly made it a stable circuit, but some snark would not fit easily. But I am sure that could be changed as this section could use more space, but I liked that a p256 gun picked the row, which probably will not be possible anymore.

GilGil · Post by **GilGil** » December 23rd, 2021, 9:59 pm

Here some P60 devices :

32-line P60 ticker with extansible memory block (Merry Christmas).mc: (92.01 KiB) Downloaded 110 times

32-line P60 ticker with extansible memory block (encrypt).mc: (integrated XOR logic function); (70.19 KiB) Downloaded 108 times

32-line P60 ticker with extansible memory block (decrypt).mc: (integrated XOR logic function); (109.32 KiB) Downloaded 1199 times

GilGil · Post by **GilGil** » December 23rd, 2021, 10:24 pm

32-line P60 ticker loop (extansible) without memory block.mc: (148.26 KiB) Downloaded 97 times

64-line P60 pictures projector with extansible memory block (all pictures).mc: (92.89 KiB) Downloaded 120 times

64-line P60 pictures projector with extansible memory block (fly).mc: (88.97 KiB) Downloaded 101 times

GilGil · Post by **GilGil** » December 23rd, 2021, 10:53 pm

64-line P60 pictures projector loop (extansible) without memory block (all pictures) A.mc: (299.49 KiB) Downloaded 103 times

64-line P60 pictures projector loop (extansible) without memory block (all pictures) B.mc: (318.59 KiB) Downloaded 100 times

These ones run faster than the model with the incorporated memory block

otismo · Post by **otismo** » February 24th, 2022, 4:44 pm

@ GilGil

I finally discovered your goodies - Thank You for Sharing !

I made a practice pattern :

64-line P60 pictures projector ALL Home Improvement Guys.mc: next I will figure out how to display them inline...; (378.72 KiB) Downloaded 71 times

Please do not forget about c/10 !

Cheers !

Hippo.69 · Post by **Hippo.69** » December 26th, 2022, 2:45 pm

PM 2Ring wrote: April 2nd, 2010, 2:33 am Collatz sequence generator

Here's my most ambitious arithmetic-oriented pattern to date.

This pattern calculates the Collatz sequence in binary, using p60 / p30
technology. Input and output is done using LWSS bits. The next number in
the Collatz sequence is generated after 7680 (= 128 * 60) steps.

The arithmetic unit at the heart of this construction is the amazing
Binary Adder circuit created by David Buckingham in 1975, with size
optimization by Mark Niemec. This circuit adds two binary numbers
represented by p60 glider streams, with the least significant bits
leading. This allows numbers of any length to be added. Input data
enters the adder circuit at its upper left and the sum begins to emerge
from the circuit at its lower right after 600 steps.

This pattern uses a couple of p7680 guns, which utilize a period
multiplier based on a sequence of glider reactions that create a base 4
counter using (nothing) - boat - blinker - block as the base 4 digits.
This pattern also uses the bistable switch found by Paul Callahan.

The Collatz Sequence
--------------------

The Collatz sequence for a positive integer n is defined as follows:

Let C(0) = n
If C(i) is even, C(i+1) = C(i) / 2
Else C(i) is odd, C(i+1) = 3*C(i) + 1

The Collatz Conjecture is that all sequences eventually reach the cycle
1, 4, 2, 1, ...

For example, the Collatz sequence for 7 is:
7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.

The pattern is currently set to calculate the Collatz sequence of 27.
For more details on the Collatz Conjecture, see Wikipedia.

How it works
------------

The data starts out at the top of the pattern, in the Input / Output
Display section, as a sequence of LWSSs. It is converted into p60
glider data by a pair of p60 guns, using the "zap" reaction to
delete gliders without harming the LWSSs. This enables the output
section to be expanded to display more bits, if desired.

The data then passes through a duplicator. One copy of the data enters
a small delay loop, the other (inverted) copy passes through the Parity
Detector, which determines if the number is odd. A p7680 gun generates a
parity detection bit which will only pass through the Parity Detector if
the LSB of the current number is 1.

The parity bit is duplicated several times. Two copies of the parity bit
go to the Switchable p60 Glider Reflector: one copy turns it on, the
second copy sets a bistable switch to enable the gate to be turned off
by the parity reset bit, which is generated by the p7680 gun in the
lower right of the pattern.

The Switchable p60 Glider Reflector consists of a switchable p60 glider
gun which feeds a glider to LWSS converter. When the data stream emerges
from the delay loop, if it's an odd number the Switchable Glider
Reflector will be on and the LWSSs reflect the data stream upwards,
otherwise, it's an even number and the data passes straight through.

Even number data continues downwards, passing through a few Buckaroos
to delay it, until it hits the p60 Output Collector stream.

Odd number data follows an upwards path into the Data Duplicator, where
it meets the third copy of the parity bit. Two copies of the number are
created, and the parity bit is prepended to one of these copies. If the
original number is n, then the Data Duplicator outputs n & 2n+1. These
outputs travel through a few Buckaroos, etc, to synchronize them, and
then they enter the Binary Adder, which outputs 3n+1, sending the data
to the p60 Output Collector stream.

The data from the Output Collector travels up through a few more
Buckaroos to delay it. It then passes through a glider to LWSS converter
into the Input / Output Display section, and the cycle is complete.

Collatz2cA.rle

Code: Select all

#C Collatz by PM 2Ring, March 2010.
#C 
#C This pattern calculates the Collatz sequence in binary, using p60 / p30
#C technology. Input and output is done using LWSS bits. The next number in
#C the Collatz sequence is generated after 7680 (= 128 * 60) steps.
#C  
#C The arithmetic unit at the heart of this construction is the amazing
#C Binary Adder circuit created by David Buckingham in 1975, with size
#C optimization by Mark Niemec. This circuit adds two binary numbers
#C represented by p60 glider streams, with the least significant bits
#C leading. This allows numbers of any length to be added. Input data
#C enters the adder circuit at its upper left and the sum begins to emerge
#C from the circuit at its lower right after 600 steps. 
#C 
#C This pattern uses a couple of p7680 guns, which utilize a period
#C multiplier based on a sequence of glider reactions that create a base 4
#C counter using (nothing) - boat - blinker - block as the base 4 digits.
#C This pattern also uses the bistable switch found by Paul Callahan.
#C 
#C The Collatz Sequence
#C --------------------
#C 
#C The Collatz sequence for a positive integer n is defined as follows:
#C     
#C Let C(0) = n
#C If C(i) is even,  C(i+1) = C(i) / 2      
#C Else C(i) is odd, C(i+1) = 3*C(i) + 1
#C 
#C The Collatz Conjecture is that all sequences eventually reach the cycle
#C 1, 4, 2, 1, ...
#C 
#C For example, the Collatz sequence for 7 is:    
#C 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1.
#C 
#C The pattern is currently set to calculate the Collatz sequence of 27.
#C For more details on the Collatz Conjecture, see Wikipedia.
#C 
#C How it works
#C ------------
#C 
#C The data starts out at the top of the pattern, in the Input / Output
#C Display section, as a sequence of LWSSs. It is converted into p60 
#C glider data by a pair of p60 guns, using the "zap" reaction to
#C delete gliders without harming the LWSSs. This enables the output
#C section to be expanded to display more bits, if desired.
#C 
#C The data then passes through a duplicator. One copy of the data enters
#C a small delay loop, the other (inverted) copy passes through the Parity
#C Detector, which determines if the number is odd. A p7680 gun generates a
#C parity detection bit which will only pass through the Parity Detector if
#C the LSB of the current number is 1. 
#C 
#C The parity bit is duplicated several times. Two copies of the parity bit
#C go to the Switchable p60 Glider Reflector: one copy turns it on, the
#C second copy sets a bistable switch to enable the gate to be turned off
#C by the parity reset bit, which is generated by the p7680 gun in the
#C lower right of the pattern.
#C 
#C The Switchable p60 Glider Reflector consists of a switchable p60 glider
#C gun which feeds a glider to LWSS converter. When the data stream emerges
#C from the delay loop, if it's an odd number the Switchable Glider
#C Reflector will be on and the LWSSs reflect the data stream upwards,
#C otherwise, it's an even number and the data passes straight through.
#C 
#C Even number data continues downwards, passing through a few Buckaroos
#C to delay it, until it hits the p60 Output Collector stream.
#C 
#C Odd number data follows an upwards path into the Data Duplicator, where
#C it meets the third copy of the parity bit. Two copies of the number are
#C created, and the parity bit is prepended to one of these copies. If the
#C original number is n, then the Data Duplicator outputs n & 2n+1. These
#C outputs travel through a few Buckaroos, etc, to synchronize them, and
#C then they enter the Binary Adder, which outputs 3n+1, sending the data
#C to the p60 Output Collector stream.
#C 
#C The data from the Output Collector travels up through a few more
#C Buckaroos to delay it. It then passes through a glider to LWSS converter
#C into the Input / Output Display section, and the cycle is complete.
#C 
x = 929, y = 524, rule = B3/S23
794bo$793bobo$776b2o14bo3b2o$776bobo13bo3b2o3b2o$771b2o4b3o12bo3b2o3b
2o$767b4o2bo4b3o12bobo$767b3ob2o4b3o7bo6bo$776bobo9b2o$776b2o9b2o2$
790bo$790b2o$789bobo2$794bobo$795b2o$16b2o756bo7bo12bo$16b2o754bobo5b
4o$764b2o4b2o8b2o2bo2b2o$764b2o4b2o11b2o2b2o$770b2o7bo10b2o$772bobo4bo
10b3o$774bo4bo10b2o$787b2o7b2o$787b2o7bobo$798bo$798b2o2$14b5o$13bob3o
bo789bobo$14bo3bo791b2o$15b3o792bo$16bo2$12bo$11b2o$2o8b2o4b2o$2o7b3o
4b2o$10b2o4b2o672b2o28b2o58b2o28b2o$11b2o675b2ob2o25b2ob2o55b2ob2o25b
2ob2o$12bo675b4o26b4o56b4o26b4o$689b2o28b2o58b2o28b2o93b2o$904bobo$
906bo$29b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b
2o13bobo12b2o28b2o28b2o5b2o$29b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o28b2o
28b2o28b2o28b2o28b2o28b2o14b2o12b2o28b2o28b2o$825bo$127bo681b2o$127b3o
679b2o$130bo$129b2o678b2o$809b2o$121bo$119b3o$118bo13bo$118b2o11b3o$
131b3o2$129b2o3b2o$116bo12b2o3b2o703bobo$115b3o722b2o$115b3o722bo$132b
2o17b2o$113b2o3b2o11bobo16b3o$113b2o3b2o10b2o2bo12bob2o15bo$131b2o14bo
2bo8b3o4bobo$131b2o14bob2o16bobo$115b2o14bo10b2o6b3o2b2o2bo7bo2bo$115b
obo23bobo7b2o2bo3bo7bobo117b2o$114bo2b2o12bo5bo3bo14bo2bo6bobo3b2o112b
o$116b2o13bo5bo2b2o14b2o8bo5bobo110bo12b2o$116b2o7bo6bo3bo37bo110bo7bo
4b2o$117bo7bobo5b3o38b2o109bo8b2o5b2o$125b2o150b2o7bo4b2o2bo5b3o$111bo
5bo30bo4b2o121bobo8b2ob5o6b2o551bobo$111bo5bo30bobo2bobo120bo16bo4b2o
7b2o546b2o$112bo3bo4b2o25b2o3bo121b2o21b2o7bobo545bo$113b3o5b2o186bo$
179b2o104bo23b2o$179bo104bo$161b2o8bo5bobo104b3o$134b2o25bo2bo6bobo3b
2o$134b2o20b2o2bo3bo7bobo114b3o$81b2o47bo24b3o2b2o2bo7bo2bo76b2o19b2o
14bo$81b2o33b2o13bo20bob2o16bobo78bo19bo16bo23b2o$116bo12b3o20bo2bo8b
3o4bobo79bobo7b2o5b2obo40bo$117b3o32bob2o15bo82b2o6bobo7bo30b2o7bobo$
119bo22b2o2b2o7b3o103b3o4bo29bo4b2o7b2o$142bo2bobo8b2o102b3o4bo2bo21b
2ob5o6b2o591bo$124bo8bo10b2o19b2o65bo28b3o4b2o21bo4b2o2bo5b3o560bobo
27b2o$124b3o6bobo9bo19bo44b2o19bobo28bobo25bo8b2o5b2o562b2o22b2o4b2o
13b2o5bo$80b3o44bo5b2o10bobo5bo9bobo45bo19bobo29b2o15b2o8bo7bo4b2o565b
o19b2o2b2o4b3o11b3o3bo3bo$79bo3bo42b2o18b2o4bobo8b2o46bobo9bo5bobob2o
19b2o24b2o8bo12b2o585b2o2b2o4b2o9bob2o5bo$150b2o3bo56b2o8bobo4b2o3bo
19bo15bo20bo607b2o10bo2bo4bo5bo$78bo5bo65b2o3bo65bo3b2o7bobo8bo6bobo
14bo22b2o605bo11bob2o9b2o$78b2o3b2o43b3o19b2o3bo65bo3b2o8b2o7b2o6b2o
15b3o631bo10b3o$24b2o102b3o21bobo66bo3b2o16b2o4b2o654bo9b2o$25bo101bo
3bo21bo68bobo17b3o4b2o650bo2bo$25bobo8b2o43bo44bo5bo12bo77bo19b2o4b2o
649bo$26b2o8b2o42bo46bo3bo14bo83b3o11b2o654bo$33b2o6bo3b2o33bo47b3o13b
3o6bo76bo14bo395b2o258bo$32b3o5bo3bobo107b2o75bo410bo$33b2o6b5o37b2o
68b2o487bobo6bobo242bo$7b2o27b2o4b3o38bo559b2o5bo2bo241bo$7b2o27b2o46b
3o562b2o10bo6bo215bobo8b3o10bo2bo8bo$86bo50b2o4bo503b2o3bo8bo5bobo215b
2o21bo10bobo$136bobo5b2o503b2o9bo6b2obo4b2o208bo18bo2bo3b2o5bo3b2o3b2o
$138bo4b2o482b2o12b2o7bo2bo2b2o9b2ob2o3b2o224b4o3b2obobo4bo3b2o3b2o$
126b2o127bo371b2o13bo8bobo2bo2b3o5b2obo229b4o14bo3b2o$127bo86bobo37bo
61b2o324bobo11b4o7bobo230bo2bo8b2o5bobo$124b3o87b2o38b3o59bo326b2o12b
2o9bo231b4o16bo$124bo90bo98bobo311bo266b2o4b4o$314b2o311bobo264bobo7bo
$8bo151bo465bo3bo263bo$7b3o151bo83b3o378b5o18b2o2b2o238b2o$6b5o148b3o
6bo76bo379b2o3b2o17bobo3bo$5b2o3b2o157b2o75bo70bo308b5o18bo4bo$6b5o
157b2o146b3o308b3o$6bo3bo304b5o308bo24bo$7bobo640bo2bo$8bo113b2o23bo
10bo492b2o8bo$121bobo21bobo11b2o499b2o$5b2o93b2o21bo11b2o6b2o13b2o248b
2o217bo32bobo$6bo93bobo31bo3bo4b2o95bo167bo220b2o$3b3o81bobo13bo7b2o
20bo5bo3b2o54bobo37bo158bo7bobo219b3o$3bo82bo2bo2b2o6bo2bo7b2o20bo3bob
2o4bobo7b2o42b2o38b3o73b5o78bobo5b2o220b2o$62b2o21b2o5bobo8bo29bo5bo7b
o7bobo42bo115b3o15b2o51b2o12b2o226bo$61bo3bo17b2o3bo3bo3bo3bobo22b2o7b
o3bo18bo159bo16bo52b2o12b2o46b2o177bobo$36b2o22bo5bo18b2o5b3ob2o2b2o
22bobo8b2o20b2o16bo147bobo6bobo66b2o46bo179b2o37b2o$36b2o22bo3bob2o2b
2o7b2o5bo2bo3b2o29bo21bo29bo83b3o60bo2bo5b2o64bobo39bo6bobo217b2o$60bo
5bo3b2o6bobo6bobo33b2o22b2o25b3o6bo76bo65b2o70bo40b2o6b2o220bo$51b2o8b
o3bo12bo67b2o36b2o75bo62bo3b2o98b2o8b2o4b2o177b2obob2o10b2o$50bobo9b2o
13b2o104b2o37bo96bo6b2o100b2o7b3o4b2o194b2o$50bo52bo118b3o94bo3bo2bo
111b2o4b2o177bo5bo6bo$49b2o50bobo64b3o54bo97bobo9bo103b2o196b2o$102b2o
3b2o32b2o27bo2bo50b2o108b3o103bo183b2ob2o7b2o38bo$106bobo9b2o22b2o25bo
4b2o105bo51b2ob2o84b2o202bo48b2o$108bo10bo21bo31b2o2b3o101b3o48b3ob3o
76bob2o3b3o250bobo$82b2o35bobo8b2o47bo18b2o19b2o63bo47b3ob3o72bo2bo3bo
5b2obo5b2o$83bo36b2o7bo3bo44bo5bobo12bo19bo7bo55b2o47b3ob3o71b2o2bo4bo
4bo2bo5b2o188b2o5b2o$83bobo6bobo21b2o10bo5bo7bo41b2o13bobo4bo10bobo5b
2ob2o2bobo97b3ob3o70b2o5b4o4b2obo196bo6bo$84b2o5bo2bo3b2o16bo11bo3bob
2o4bobo41b2o14b2o3bobo9b2o14b2o30b2o66b2ob2o61b2o7b3o7bo3b3o196b3o4b3o
12bobo$90b2o5b3ob2o2b2o7bobo11bo5bo3b2o42bo20b2o3bo15bo5bo2bo31b2o67b
3o62b2o8b2o11b2o197bo6bo15b2o$88b2o3bo3bo3bo3bobo6b2o13bo3bo4b2o12b2o
29b2o5bo12b2o3bo76b3o47bo16b2o56b2o4b2o226bo38b2o$90b2o5bobo8bo21b2o6b
2o12b2o7bo20b2o7bo11b2o3bo15b2obob2o44b3o74bo58bo3b2o265b2o$91bo2bo2b
2o6bo2bo31bobo19b2o25b3o6bo6bobo67bo9bobo55b2o5bobo62b2o267bo$92bobo
13bo33bo18b2o36b2o5bo69bo7b5o54b2o5b2o65bo471b2o$105bobo90b2o83b2o3b2o
50b2o547b2o$105b2o28bobo36bo90b3o15b2o3b2o49b3o309bo$134bo2bo15b3o15b
4o100b3o62b2o310b2o248b2o$124bo8b2o10b2o8bo14b4o91bobo9bo65b2o306b2o
38bo210b2o$123bobo5b2o3bo8b2o7bo15bo2bo55b2o33b5o7bo6b2o58b2o79bo265b
2o$123b2obo6b2o5b2o28b4o55bo33b2o3b2o11b2obo138b2o46b2o217bobo$123b2ob
2o6bo2bo4bo21b2o5b4o6b2o47b3o30b2o3b2o11bo141bobo46bo$62b2o59b2obo8bob
o25bobo8bo6bobo48bo239bobo4bo408b3o12bo$62b2o49b2o8bobo37bo19bo63bobo
32b3obo186b2o3bobo406bo3bo10b3o$62b2o48bobo9bo9bo27b2o19b2o63b2o9bo8b
2o16bo190bob2o15b2o160bobo240bo3bo$62bo49bo22bo112bo8b3o8bob2o14bo189b
2ob2o14bobo161b2o225bo5bo7bob3obo$61bobo47b2o20b3o69bo50bo14bo205bob2o
13bo6b2o2b2o152bo38b2o186b2o3b2o8b5o$61bobo127bo14bo49b2o173b2o45bobo
13bo2bo2bo2bob2o190b2o$62bo128b3o10b3o59bob3o159b2o47bo5bo8bo6b2o196bo
$194bo18bo52bo165bo52bobo7bobo391bo$189bo3b2o71bo14b2o3b2o14bo139b2o
41b2o9b2o389b2obo$59b2o3b2o121b3o25b2o8bo57b3o14bobo137bo3bo221bo223bo
$59bobobobo50b2o20b3o45bo10bo17bo9b3o25b3o26bo3bo5b2o4b2o131bo7bo5bo
221b2o217bo3bo11bo2b2o$60b5o52bo22bo45b2o9bo18b3o9bo23b2ob2o26bobo6b2o
4b2o131bobo4b2obo3bo8b2o210b2o38bo179bo2bo12bobo$61b3o53bobo9bo9bo10b
2o44bo15b2o4bo8b2o23b2ob2o27bo13b2o134b2o3bo5bo8b2o249b2o178b5o11b2o$
62bo55b2o8bobo19bo61bobo37b5o8b2o3b2o28bobo131b2o4bo3bo33bo226bobo177b
5o10b2o$128b2obo8bobo5bobo63bo36b2o3b2o9b3o11b2o19bo131b2o6b2o33bo406b
2o3b2o9b2obo$128b2ob2o6bo2bo5b2o43b2o3b2o14b2o50bo3bo11bo139b2o7bobo
43b3o395b2o8b5o11b3o$128b2obo6b2o53bo5bo67bobo9b3o139bobo7bo443b2o9b3o
5bobo$128bobo5b2o3bo41b3o82bo10bo141bo59b2o190bobo211bo7b2o$129bo8b2o
42bo3bo7bo3bo30b3o78b2o3b2o103b2o59b2o191b2o219b3o4b2o3b2o$64b2o73bo2b
o38bo5bo7b3o30bo3bo32b2o407bo38b2o182b2o6bo$64bo75bobo38b2obob2o39bo5b
o32bo44bo3bo33bobo360b2o183b2o3bo5bo$65b3o159b2obob2o22b2o5b3o46b3o29b
o4bo2bo117bo243bo161bo26b2ob2o$67bo188bo6bo48b3o30b2o5b2o116bobo403bo
27bobo$184bo72b3o80b2o8bo3b2o114b2o403bobo27bo$183bobo7b2o35bo28bo80b
2o10b2o327bo192b2ob2o5b2o19bo$33b2o148bobo8bo34bobo37b2o78bo2bo6b2o
321b2o189bo5bo5bo$33b2o148b2o6b3o35bobo21bo7bo7bo2bo76bobo7bobo319b2o
38bo154bo5b3o10bobo$182bo8bo38b2o20b2o6bo3b2o7bo9bobo26b2o47bo358b2o
66b2o83b2o3b2o2bo15bo8b2o$181b3o48bo19bobo5bo5bo6bo7bo3bo26b2o47b2o
100bo256bobo65b2o104bo4bo2b2o3bo$180bo3bo46b3o27b5o7bo7bo44b2o134bo
431b2obo2bob2o4b3o$35b2o45b2o95bob3obo44bo3bo34bo2bo7bo4bo40b2o4b4o
126b3o411bo21b2o10bo$82bo97b5o4bo39bob3obo33b2o10bo33b2o6b2o6b6o540b2o
$71bobo6bobo107b2o33bo4b5o46bo3bo6b2o21b2o5b3o5bo3b2obo281b2o67bobo$
70bo2bo6b2o107b2o32b2o47bobo8bobo6bobo28b2o6bo5bo281bo69b2o179b2o7bo$
61b2o6b2o153b2o46b2o20bo31b2o8bo273bo6bobo69bo38b2o139bobo4bobo12b2o$
31b2o3b2o23b2o4b2o3bo200bo20b2o30b2o85b2o195bobo4b2o108b2o139b3o5bo14b
2o$32b5o32b2o342bo41bo142b2o11bobo115bo59bo69b2o6b3o$32b2ob2o33bo2bo
259b2o3b2o60bo10bobo41bobo140b2o11bo2bo173b3o68b2o7b3o10b2o$32b2ob2o
34bobo259b2o3b2o59bobo9b2o42b2o154bobo173b5o59b2o16bobo9b2o7b3o$33b3o
160bobo193b2o3b2o3bo207bobo83bo89b2o3b2o59bo17b2o18b3o$184b2o11b2o17bo
bo116b3o54b2o3b2o3bo207bo86b2o153bobo7bo$184bo12bo18b2o11b2o37bo20b2o
44b3o59b2o3bo293b2o38bo116b2o4b4o$185b3o29bo12bo36b2o20bo46bo62bobo
333b2o121b4o9b2o$187bo39b3o25b2o10bobo8bobo6bobo110bo42bo291bobo50b3o
56b2o9bo2bo9b2o15b2o3b2o$31b2o194bo28bo19bo3bo6b2o152bobo6b2o336b3o56b
o2bo7b4o5bo21b5o$32bo74b2o147bobo5b2o10bo156b2o4b2o18b2o398b4o4bo22b3o
$29b3o75b2o95bo52b2o5bo2bo7bo4bo152b2o4b2o17bo3bo324bo63bo10bo28bo$29b
o77b2o96b2o3bo57bo7bo162b2o16bo5bo239bobo27b2o51bobo$107bo96b2o2b2o58b
o7bo3bo54b2o104bobo2bob2o7bo3bob2o2b2o235b2o27b2o50bo3bo59b2o$106bobo
100b2o57bo9bobo54b2o90bobo13bo2bobo8bo5bo3b2o235bo38b2o41b3o59bo$106bo
bo155bo2bo157bo3bo17bo10bo3bo279b2o40b2o3b2o4bo$107bo156b2o147b2o10bo
12b2o19b2o272bo10bo48bobo5b2o$413bo2bo7bo4bo8b2o292bobo59b2o5b2o42b2o
3b2o17bo23b2o$405b5o7bo7bo305bo3bo109b2o3b2o17bo23bo$104b2o3b2o293bo5b
o6bo7bo3bo281bo19b5o110b5o18bo24b3o$104bobobobo293bo3b2o7bo9bobo282b2o
16b2o3b2o110bobo33bo12bo$105b5o295bo7bo2bo294b2o18b5o15bo130b4o$106b3o
304b2o317b3o15b2o50bo44b3o31b2obobo$107bo625bo16bobo50bo76b3obo2bo2b2o
$784b2o15b3o77b2obobo3b2o$47b2o179bo195b2o359bo96b4o$46bobo177b3o194b
2o357b3o55b2o41bo$45bo6b2o171bo199bo55b2o235bobo13bo47bo57bobo20b2o$
36b2o7bo2bo2bo2bo171bo255bo236b2o10b2o102b2o6bo19b2o$36b2o7bo6b3o54b2o
112bo2bo252b3o4bo2bo4bo2bo221bo11b3o24b2o71b2obo2bo2bo2bo$46bobo5b3o
52bo112bo256bo4b3o2b6o2b3o232b2o23b2o51bo20b2o2b2o6bo9b2o12b2o3b2o$47b
2o6bobo52b3o109bobo261bo2bo4bo2bo234bo26bo48bobo29bobo10b2o$57bo54bo
110bo208bo68bo229bobo75b2o29b2o26bo3bo$57b2o372b2o67bobo228b2o99bobo
34b3o$372bobo56bobo65bo3bo195b2o24b2o105bo2bo33b3o$78b2o140b2o3b2o140b
o4bo2bo66bo57b3o196b2o122b2o10b2o6b2o$78b2o140bobobobo141b2o5b2o64bobo
54b2o3b2o215bo11b2obob2o27bo4b2o50b2o8bo3b2o4b2o$221b5o137b2o8bo3b2o
51bo8b2o3bo275b2o43b2o4b2o44bo10b2o5b2o25b3o$222b3o138b2o10b2o53b4o5b
2o3bo9b2o270bo5bo5bo26bobo50bo8bo4bo2bo25bo3bo$223bo148bo2bo6b2o47b4o
4b2o3bo9b2o268bobo89b3o13bobo25bo5bo2b2o$80b2o45b2o243bobo7bobo46bo2bo
6bobo281b2o6b2ob2o122bo5bo2b2o$127bo256bo46b4o7bo292bo127bo$116bobo6bo
bo256b2o36b2o6b4o427bo3bo$115bo2bo6b2o294bobo6bo268b3o160bo$106b2o6b2o
305bo276bo3bo27b2o5b2o34b2o88bo2bo$76b2o3b2o23b2o4b2o3bo302b2o76b2o
197bo5bo26bo6bo34b2o51bo40bo$77b5o32b2o107b2o274bo197b2obob2o27b3o4b3o
22b2o9bo9bo38bobo39bo$77b2ob2o33bo2bo104b2o271b3o234bo6bo21bobo17bobo
39b2o40b3o$77b2ob2o34bobo377bo265bo7b2o9bobo84bo$78b3o619bo60b2o7b3o7b
o2bo11b2o$699bobo70b2obo5bobo11b2o$699bobo70bo2bo6bobo$699b2o71b2obo8b
o47bo$698bo64b2o5b3o60bo$76b2o619b3o62bobo5b2o59b3o$77bo480bo87b2o48bo
3bo61bo$74b3o480b4o85b2o47bob3obo59b2o$74bo481b2obobo134b5o4bo$545b2o
8b3obo2bo143b2o4b2o$156b2o387b2o9b2obobo143b2o5b2o85b2o37b2o$156b2o
399b4o3b2o233b2o37bobo$558bo5bobo273bo$566bo273b2o$566b2o232bo$559b2o
150b2o86b3o$559b2o84b3o63bo86bo3bo$644bo3bo46b2o15b3o85bo$155b3o485bo
5bo46bo17bo82bo5bo$154bo3bo484bo5bo43b3o101bo5bo$646bo46bo104bo3bo$92b
2o59bo5bo484bo3bo150b3o$91bobo59b2o3b2o485b3o$90bo6b2o547bo$81b2o7bo2b
o2bo2bo541b2o$81b2o7bo6b3o56bo399b2obob2o76bo2bo177b2o$91bobo5b3o53bo
474b2o6bo7b2o154bo17b2o$92b2o6bobo52bo400bo5bo67b2o6bo6bo2bo$102bo535b
o7b2o$102b2o54b2o397b2ob2o77bo2bo159bo17bo$158bo400bo81b2o157bobo16b3o
$159b3o532b2o105b2o15bo3bo$161bo532bobo17b2o104bo$696bo18bo101bo5bo$
561b2o133b2o17bobo9bo84b2o3bo5bo$561bo154b2o8b4o49b2o14b2o3b2o10b2o4bo
3bo$534b2o26b3o160b2ob4o5b2o40bobo27bo9b3o$534b2o28bo159b3ob2o3bo3bo2b
o39b3o13bo3bo9bo$725b2ob2o3bo7bo39b2o14b3o8b3o$715b2o9b5o3bo6bo6b2o31b
2o14b3o$714bo2bo9bo3b3o7bo6b2o29bobo$534b3o177bo22bo2bo39bo$534b3o177b
o22b2o56b2o19bo$533bo3bo176bob2o78bo19bo$532bo5bo177b2o7bo51b2o3b2o9b
3o24bo$533bo3bo185b2o52b2o3b2o9bo26b2o$534b3o187b2o96bo$715b2o62b3o38b
2o$715b2o12b2o48b3o$728b2o50bo$730bo9bo59b2o13b2o3b2o$621b2o115bobo58b
obo$621bo104b2o9bobo11b2o45b3o15bo3bo$613bo5bobo104b3o7bo2bo11b2o45b2o
17b3o$612b4o3b2o79bob2ob2o21b2obo5bobo58b2o17b3o$532b2o66b2o9b2obobo
83b2obobobo20bo2bo6bobo41bo16bobo$533bo66b2o8b3obo2bo88bo21b2obo8bo42b
2o15bo$530b3o78b2obobo102b2o5b3o53b2o$530bo81b4o102bobo5b2o$613bo96bo
7bo58b3o12b2o3b2o3b2o13b2o$708b2o7b2o57bo3bo11b2o3b2o3b2o13b2o$709b2o
64bo5bo$775bo5bo17b3o$118b3o657bo10bobo7b3o$118bo657bo3bo9b2o8bo$119bo
659bo10bo$115b2o658bo2bo$114bobo658bo$116bo602b2o55bo23bo$719bobo51b3o
23bobo$719bo53bo25bobo4$90b2o705b3o$90b2o704bo3bo16bo$795bo5bo13b3o$
113bo681bo5bo12bo$111b3o19b3o662bo15b2o$110bo22bo581b2o79bo3bo$110b2o
22bo580b2o80b3o$89b3o8b2o696bo$88b2ob2o6bobo591bo$88b2ob2o8bo591b3o38b
2o$88b5o603bo37bobo60b2o$87b2o3b2o601b2o37bo62b2o$99b2o708b2obob2o$99b
obo5b3o589bo$93bo5bo6bo3bo588bo109bo5bo$92bob2o9bo5bo601b2obob2o$92bo
12bo5bo596b3o99b2ob2o$695b2o3b2o6bo4bo5bo92bo$92b2obo9bo590b5o8bo$90bo
2bo11b2o41b3o186b2o358b3o14b2ob2o$90bobo12b2o41bo188bo360bo17bo$104b2o
2bo40bo178bo6bobo236bo127b3o$105bobo219b2o6b2o236bobo128bo107b2o$106b
2o208b2o8b2o4b2o238bo3b2o125bo10bo97b2o$316b2o7b3o4b2o227b2o9bo3b2o
135bobo33b2o$91b3o232b2o4b2o227b2o9bo3b2o134bo3bo32bobo$90bo3bo8b2o3b
2o217b2o244bobo4b2o130b5o32bo$89bo5bo7b2o3b2o218bo245bo5bobo128b2o3b2o
$90bo3bo487bo129b5o$91b3o11b3o474b2o115b3o11b3o$91b3o11b3o606bo$106bo
592bobo$698b5o$697b2o3b2o$92b2o69b3o531b2o3b2o$92b2o69bo$164bo$105b2o
593bo$105b2o591b2o$713b2o49b2o$697bo15b2o49bobo$764bo$698bo2bo$700b2o
6$178b3o$178bo$179bo$913bo$911b3o$779b2o129bo$779bobo128b2o$779bo$908b
o$907b3o$906bo3bo$908bo$905bo5bo$905bo5bo$906bo3bo$193b3o711b3o$193bo$
194bo335b2o$530bo$521bo6bobo$520b2o6b2o264b2o$509b2o8b2o4b2o267bobo$
509b2o7b3o4b2o267bo$519b2o4b2o$520b2o386b2o$521bo386b2o5$208b3o$208bo$
209bo$824b2o$824b2o$505bo303b2o$505b3o294bo6bobo$508bo293b3o4bo$507b2o
296bo$804b2o$511bo206b2o$511bo205bobo$510bo205bo6b2o$707b2o7bo2bo2bo2b
o91b2o$707b2o7bo6b3o91b2o5b3o$223b3o281b2o3b2o31bo171bobo5b3o76b2o3b2o
12bo3bo$223bo283bo5bo30bobo171b2o6bobo75b2o3b2o11bo5bo$224bo318bo3b2o
179bo94bo3bo$508bo3bo19b2o9bo3b2o179b2o76b3o3b3o9b3o$509b3o20b2o9bo3b
2o257b3o5bo8bo2bo$544bobo4b2o254bo5bo9b3o$545bo5bobo268bob2o$553bo268b
obo$553b2o179bo88bo$734b3o$737bo$509b2o225b2o70b3o9b2o3b2o$509b2o297b
3o9bobobobo$807bo3bo9b5o$822b3o$238b3o565b2o3b2o10bo$238bo$239bo516b2o
$726bo7bo21b2o$726b3o5b3o$729bo7bo$497b2o229b2o6b2o$497bo324b2o$254b2o
232bo6bobo324b2o$255bo231b2o6b2o$255bobo5b2o211b2o8b2o4b2o315b2o$256b
2o5b2o211b2o7b3o4b2o286bo28b2o$266b2o10bo207b2o4b2o284b3o$266b3o7bobo
208b2o288bo$266b2o6b2o212bo288b2o$253b3o7b2o9b2o12b2o584b2o$253bo9b2o
9b2o12b2o585bo$254bo21bobo596bobo7b2o$266bo11bo458b2o137b2o6bobo$266bo
bo468b2o144bo13bobo$266b2o502b2o111bo2bo6b2o2bo2bo$564bo204bo2bo110bo
8bobo5b2o$562b3o205b2o103b2o7bobo3bo3bo3bo3b2o4b2o$261b2o298bo220b2o
91b2o8b2o2b2ob3o5b2o6b2o$261b2o298b2o219bobo90b2o15b2o3bo2bo$784bo90bo
21bobo$274b2o464b2o42b2o88bobo$274bobo281b2o181bo132bob2o$264bo4b2o4b
3o7b2o451b3o36b2o104bo$263bobob2o2bo4b3o6b2o451bo38bo71b2o32bobo$251b
2o9bo3bob3o4b3o500b3o69bo24b2o6b2o3b2o$251b2o9bo3bob2o4bobo279b2o3b2o
217bo69bobo8bo13b2o11bobo$262bo3b2o6b2o280b2o3b2o288b2o8bobo24bo$263bo
bo596bobo4b2o28bo$264bo293b3o284b2o15bo2bo3b2o26b4o$558b3o284b2o15bobo
22bobo6bobob2o9b2o$559bo301bobo23bo3bo3bo2bob3o8b2o$861bo29bo4bobob2o$
887bo4bo4b4o$891bo7bo$846bo32b2o6bo3bo$844b2ob2o29bobo6bobo$559b2o317b
o$457bo101b2o282bo5bo17b2o8b2o$456bobo407bobo$455bo3b2o382b2obob2o17bo
$444b2o9bo3b2o416b2o$444b2o9bo3b2o416bobo$456bobo4b2o407b2o6bo$457bo5b
obo61bo343bo2bo2bo2bo7b2o$465bo60bobo318b2o18b3o2b2o6bo7b2o$465b2o58bo
3b2o336b3o7bobo$514b2o9bo3b2o309b2o24bo3bo6b2o$514b2o9bo3b2o309b2o19b
2o2bo5bo$526bobo4b2o302b2o22b2o3bo3bo$527bo5bobo293b2o5b3o22b2o4b3o$
535bo293b2o6b2o12b2o8bo$535b2o284b2o17b2o9b2o7bobo$822bo17b2o18bobo$
822bobo6bo29bo$823b2o4bobo$827b2o12b2o$827b2o12b2o15b2o3b2o$827b2o29bo
bobobo$779bo49bobo27b5o$777bobo51bo28b3o4b2o$776bobo82bo5b2o$770b2o3bo
2bo$770b2o4bobo$777bobo9b2o$779bo9bobo$791bo46b2o23b2o$791b2o45b2o23bo
$864b3o$852bo13bo$851b2o$850b2o4b2o$849b3o4b2o2b2o$850b2o4b2o2b2o$851b
2o$852bo$817bo15b2o$816b2o15b2o$815b2o4b2o$805b2o7b3o4b2o$805b2o8b2o4b
2o15b5o$816b2o6b2o11bob3obo$817bo6bobo11bo3bo$826bo12b3o$826b2o12bo$
832b3o$831bo3bo$830bo5bo$830b2obob2o2b2o$839b2o2$833bo$832bobo$832bobo
$833bo2$833b2o$833b2o!

I wonder how this technology could be used to create some sort of universal 32-bit programming language.
Polish notation with a reasonable set of arithmetic operations requires 32 bit constants, another variant with a limited set of registers... In all cases, the challenge would be a conditional jump in the program.
Compared to a Turing machine, this could have relatively small multiplicative constants.

otismo · Post by **otismo** » October 3rd, 2026, 9:35 pm

I could not resist making a small DEMO of EV2's Stable MWSS to HWSS Hammer RT2419

P2424 Glider Gun leaves five ticks to spare-but the interesting Hammer Reaction is a

Still Life "Hammer Reaction" (Pond and Boat) instead of the usual Glider Hammering

Code: Select all

x = 738, y = 422, rule = B3/S23
144b2o$127bo16b2o5b2o$127b3o21b2o$115b2o13bo$116bo12b2o$115bo33b2o$
115b2o32b2o$107bo47b2o$107b3o45b2o$110bo$109b2o2$118b2o$118b2o7$128b2o
$129bo28b2o$126b3o29bo$126bo29bobo$124bobo29b2o$124b2o3$100b2o$100bobo
b2o18b2o$102bob2o18bobo$101bo24bo$101b2ob2o20b2o$102bobo$102bobo$103b
2ob2o$105bobo47b2o$105bo33b2o14b2o$104b2o34bo22b2o$137b3o23bo$137bo23b
obo$161b2o$136bo$134b3o$133bo$133b2o8bo$143b3o$146bo$109bo35b2o$109b3o
$112bo$111b2o$133b2o2b2o$133bobo2bo$135b2o$135bo4b2o$110b2o18b2obobo5b
o$109bobo18b2ob2o6bobo$109bo32b2o$108b2o20b2ob2o$131bobo$131bobo22b2o$
128b2ob2o23bobo$128bobo27bo$130bo27b2o$130b2o2$138bob2o152b2o$138b2obo
142bo9bobob2o$284b3o9bobo$147b2o138bo7b2obo32bo290b2o$147b2o137b2o10bo
b2o28bobo290bo$281b2o7bo4b4o2bo26b3obo142bo11b2o133bo$280bobo6bobo3bo
3b2o5b2o19bo4bob2o138bobo10b2o133b2o11bo$106b2o170b3obobo4bo2bo3b3o7b
2o19bobobobobo130bo3b2o2bobo143b2o11b3o$105bobo169bo5b2o5b2o6bo23b2o4b
2obobo131bobo2bo2b2ob2o141bo2b2o8bo$105bo53b2o116b2o19bobo3b4o15bo8bob
o5b2o59b2o48b2o12bobo3bobo146bobo9b2o$104b2o53bo139b2o2bo3bo15bobo7bo
6b2o60bo25bo23bo13bob4o2bob2o141b2obobo4bo7b2o$157bobo94bo48bobo4b2o
12b2o76bobo21b3o23bobo13bo3bobob2o145b2o3bobo6bobo$157b2o95b3o47b3o3b
2o3b2o86b2o20bo27b2o12bo3bobo153bo2bo4bobob3o$257bo57bobob2obo102b2o
39bo3bobo155b2o5b2o5bo$247b2o7b2o23b2o21b3o10bobob2o12b2o129b2o3bo169b
2o$116b2o130bo32b2o20bo2bo10b2o15bo2bo107bo$116b2o130bobo52b2o30b2o51b
2o53b3o219bo$249b2o136bobo52bo123b2o95b3o$123bob2o252b2o7bo40b2o11b2o
35b2o85bobo93bo$123b2obo162bo90bo48b2o48b2o87bo4b2o62b2o23b2o7b2o$288b
obo84b2o3bobo111b2o68b4ob2o2bo2bo60b2o32bo$133b2o147b2o4bobo4b2o78bobo
3b2o110bo2bo67bo2bobobobob2o92bobo$105b2o27bo147bo2bo3bo3bo2bo15b2o13b
2o48bo116b2obo69bobobobo95b2o$106bo27bobo146b3o7b3o15bo2bo12bobo10b2o
29b2o4b2o118bo70b2obobo$106bobo23b2ob2o108bo23b2o41b2o14b2o10bobo27bob
o2b2o2bo117b2o73bo57bo$107b2o22bobo110bobo22bo11b7o3b7o40bobob3o17bo7b
obobo2b2o103b2o145bobo$131bobo111bo14b2o8b3o8bo6bobo6bo28b4o3b2o3b2o5b
o14b5o2b2obo2bobo107bo74b2o63b2o4bobo4b2o$130b2ob2o20b2o103bo11bo9bobo
b2o3b2obobo4b2o22bo2bo4b2o9b2o13bo5bo2bobo4b4o25b2o48b2o24b3o76bo7b2o
54bo2bo3bo3bo2bo$121b2o32bo105b3o19b2obo5bob2o4bobo7bo6b2o6b2o3bo11bo
2bobo12b3o2b2obob2o2bo3bo25b2o11b2o35b2o11b2o11bo78bobo5b2o55b3o7b3o$
121bobo6b2ob2o18bobo107bo24bobo9bo8bobo5b2o10b2o11b2o2b2o15bobo2bo5bob
2o39bo49bo92b2o35b2o50b2o23bo$123bo5bobob2o18b2o132b2ob2o7b2o4b2obobo
49b4o3b2o4b2obo41b3o47b3o126bo3b2o19b7o3b7o11bo22bobo$123b2o4bo117b2o
55bobobobobo42b2o3bo3bo11bo43bo49bo41bo80b2o4bo2bo19bo6bobo6bo8b3o8b2o
14bo$101b2o25b2o116bobo55bo4bob2o42b2o4b3obo7b3o134b3o38bo36b2o3b2o3b
4o21bobob2o3b2obobo9bo11bo$101b2o23bo2bobo114bo46b2o10b3obo53bob3o5bo
14b2o10b2o48b2o57bo41b3o28bob2obobo34b2obo5bob2o19b3o$126b2o2b2o113b2o
46bobo11bobo53bo4bo19bo11bo27b2o20bo58b2o11bo31bo27b2obobo10b2o29bobo
24bo$101bo50b2o107b2o32bo4b2o6bo53b2o3b2o20b3o3b2o4b3o23bobo21b3o67bob
o7b2o20b2o31b2o10bobo27b2ob2o$100bobo32bo16bo108bobo27b4ob2o2bo2bo87bo
2bob3o4bo23bo25bo67bobo7b2o8b2o27b2o27b2o70b2o$100bo2bo29b2o18b3o107bo
27bo2bobobobob2o28b2o60bo4bo26b2o91bobob2o17bo27bo100bobo$101bo2bo13b
2o14b2o19bo98b2o7b2o29bobobobo32bo20b2o3b2o28b5ob2o2bo56bo62b2o3bo17bo
bo26b3o99bo$118bo135b2o39b2obobo30bo22bo4bo27bo2bo2bobobob2o54bobo39b
2o25bobo3b2o11b2o28bo99b2o$101bo2bo14b3o17bo159bo31b5o14b2o3b3obo27b2o
4bobobobo40b2o13bob3o37b2o26b2o2bo2bo32b2o90b2o$101b2o18bo8b2o6b4o194b
o13bobo4bob3o4b2o26b2obobo41bo10b2obo4bo69bobo2b2o28b2o51b2o36bobo$
131bo6bob2o143b2o46b3o12bobobo5bo3bo3b2o30bo42bobo8bobobobobo70bo3b2o
54b2o24bobo36bo$128b3o9bob2o142bo7b2o36bo15b2o2bob2o3b4o79b2o10bobob2o
4b2o124bo2bo17b2o4bo37b2o7b2o$128bo12b3o142bobo5b2o36b4o16bobo2bobo15b
2o7b2o60b2o5bobo8bo126b2o16bo2bo2b2ob4o42b2o$139bo3b2o142b2o41b2o3bo3b
2o10b2obob2o2b3o12bobo7bo7b2o51b2o6bo7bobo144b2obobobobo2bo$127bo10b2o
104b2o83bo2b3o4b2o13bo2bo5bo13bo7bobo5b2o67b2o36b2o110bobobobo$125b3o
11b4o102bo83b2obo21b2o2b5o14b2o7b2o25bo87bo60b2o38b2o8bobob2o$124bo15b
2o17b2o84bobo84bo27bo50b3o84b3o61bo23b2o6bo7bobo8bo$108b2o14b2o15bo17b
o86b2o84b2o76bo40b2o45bo64b3o20b2o5bobo8bo$108b2o47bobo225bo24b2o38bo
2bo53b2o56bo28bobob2o4b2o20b2o$157b2ob2o189bo31b3o65b2o50b2o2b2o46b2o
35bobobobobo16b2o7bo47b2o$160bobo134b2o41b2o8b2o30bo119bobo50b2o2b2o
31b2obo4bo16b2o5bobo47bo$160bobo134bo43bo8bobo29b2o34b2o82bo56bobo33bo
b3o24b2o46bobo$137b2o20b2ob2o100b2o32b3o37b3o55b2o21bo81b2o58bo33bobo
74b2o$138bo24bo100bo9b2o24bo37bo57bo22bob2o138b2o33bo$138bobo18b2obo
99bobo10bo121b3o11b2o4b3o2bo59bo52bo9b2o$139b2o18b2obobo97b2o9bo125bo
11b2o3bo3b2o37b2o19b3o32b2o17b3o3b2o2bo2bo$163b2o108b5o14b2o122b4o26b
2o10bobo18bo35bobo15b5o2bobo2b2o$278bo13bo109b2o15bo22b2obobo10b2o19b
2o36bo7b2o5b3ob2o5b2o109b2o$275b3o12bobo79b2o27bobo12b3o23bob2obobo67b
2o7bo5b2ob2o7bo69b2o39bo$139b2o133bo15b2o79bobo5b2o13bo6bo13bo32b2o3b
2o3b4o61b3o8bo6bo2bob2o67bo39bobo$107b2o29bobo133b4o93bo7b2o13b3o3b2o
14b5o32b2o4bo2bo24b2o34bo16bobob2obo64b3o41b2o$106bobo29bo133b2o3bo3b
2o87b2o25bo22bo36bo3b2o25bo52bobo68bo$106bo29b3o132bo2b3o4b2o106b2o5b
2o20bo38b2o29bob2o50bo2b2o$105b2o28bo135b2obo71b2o36bo5bo27b2o60b2o4b
3o2bo51b2ob3o$135b2o108b2o27bo71bobo2b2o27b2obobo2bo91b2o3bo3b2o58bo$
245b2o27b2o67bo4bo3bo26bobobobo2b2o56bo38b4o54b2ob3o$343b5ob3o24bo2bob
obob2obo56bobo23b2o15bo54b2obo95b2o$261b2o84bobo26b4ob2o2bo2bo54b3obo
22bobo12b3o154bo$261b2o19b2o52bo6b3obobo30bo4bo2b3o4b2o45bo4bob2o19bo
13bo50b2o66b2o39bo$269b2o8bo3bo50b3o5bo2bob2o29bobo5b2o3bo3b2o45bobobo
bobo18b2o14b5o36b2o7b2o66bo20b2o14b5o28b2o$246b2ob2o18bo9b4o30b2o18bo
8b2o34b2o8b4o45b2o4b2obobo40bo37bo72b2obo21bo13bo33b2o$145b2o100bob2o
16bobo39b2o2bobo17b2o53bo15b2o32bo8bobo5b2o30bo39bobo21b2o46bobob2o15b
2o3bobo12b3o$145b2o98bo21b2o10b2o28bobobo2bo2bo69b3o12bobo2b2o27bobo7b
o6b2o30b2o39b2o21bo12b2o33bo20b2o4b2o15bo13b2o$245b5obo26bobo2b2o4b2o
20bobob2o2b3o70bo13bo2bo29b2o20bo87bobo7b2o2bobo32b2o2b3o35b4o13b2o$
154b2o94b2o25bo2bobobo5bo19b2obo8bo64b5o14b3o2bo49b3o85b2o8bo3bo4bo30b
obo2bo30b2o3bo3b2o3b2o$154bo92b2o28b2obobo4b3o23bob6o2bo63bo21b3o52bo
95b3ob5o29bo2b2o32b2o4b3o2bo3bo18b2ob2o$108b2o45b3o89bo32bob2o3bo25bob
o5b2o66bo18bo41b2o11b2o97bobo33b2o43bob2o3bobo16b2obo$108b2o47bo90b3o
26b2obo27b2o4bo3b2o16b2o26b2o22b2o18b2o39bo2bo109bobob3o6bo67bo7b2o21b
o$114b2o32b2o100bo24bo2bobo26bo2bo7bo17b2o21b2o3bo85b2o111b2obo2bo5b3o
64b2o24bob5o$114b2o33bo100bobo22b2o2bo4b2o4b2o16b2o4bo5bo38bobo3b3o
200b2o8bo89b2o$134b2o12bo102b2o30bo2bo2bo2bo20bobo3b2o36bobob4o2bo209b
2o92b2o$134bo13b2o125b2o2bo4b2o4b2o21bob3o39b2o5bo227b2o40b2o36bo$112b
2o21b3o137bo2bobo29b2obo4b3o24bo3b2o12bo169bo58bo41bo34b3o$112b2o5b2o
16bo139b2obo30bobob2obo2bo22bobo3bo12b2o55bo52b2o57bobo54b2obo42b3o31b
o$119b2o159bob2o3bo21bobobo2bobobo22bobo3bo48b2o20b3o19b2o22b2o5bobo
56bobo53bo2bo33b2o10bo29bobo$277b2obobo3bobo20b2o2bobo3bo19b2obobo3bo
48bobo5b2o16bo18bobo10b2o9b2o7bo57bo55b2o34bo41b2o$44b2o201b2o28bo2bob
obo2bo25b2o24b2obo2b4obo46bo7b2o9bo5b2o19b2o10bobob2o14b2o53b3o13b2o
26b2o50b3o$44bobo2b2o197bo29bobo2bob2o56bobo3bobo44b2o17bobo35bobob2ob
o69bo16bo3b2o21b2o52bo$41bo4bo3bo197bobo28bobobo42b2o11b2ob2obob2o2bo
63bobo23b4o3b2o3b2obo3bobo81b3o3bobo52b2o$41b5ob3o199b2o30bobo19b2o22b
o12bobo2bobo3b2o57bo2b2obo23bo2bo4b2o6bob2obobob2o77bo2b4obobo51bo$45b
obo17b2o214b2o20bobo18b3o13bobob2o2bo51b2o4b2obobo2bo25b2o3bo10bo2bobo
bobobo79bo5b2o48b3o$41b3obobo13b2o2bobo237bo18bo2b3o11bobo2bobo50bo2bo
2bobobob2obo29b2o11bobobobobobo2bo77bo12b2o3bo35bo$40bo2bob2o14bobobo
2bo193b2o41b2o19bo3bo12bobo2b2o2b2o46b2o3bobobobo2b3o4b2o35bo2bo2b2ob
4o76b2o12bo3bobo35b3o23b2o$40b2o21bobob2o193bobo42bo17b2o2b2o11b2ob2ob
o2bo2bo47b4ob2o2bobo3bo3b2o36b3o4bo6bo88bo3bobo36b3o21bo31b2o$62b2obo
198bo14b2o23bobo39bobo3bobo12b2o33bo3bo4bo2b4o38b3o7bobo4b3o87bo3bobob
2o35bo18bobo31bo2bo$47bo17bob2o195b2o14bo21b3ob2o34b2obo2b4obo13bo35bo
2bob3obobo15b2o24bo2bo7b2o7bo84bob4o2bob2o34b2o18b2o10bo22b2obo$46bobo
16bobo2bo209bobo18bo40b2obobo3bo13bobo36bobobo3bo2b3o12bobo26b3o13b2o
83bobo3bobo70b3o23bo$45bo2bo11b2o4bo2b2o199bo10b2o18b2o43bobo3bo12b2o
38bo6bo5bo13bo29bo98bo2bobob2ob2o69bo13b2o2bo4bob2o$46b2o11bo2bo39b2o
146b2o16b3o76bobo3bo20b2o37b5o14b2o15b2o10b2o8b2o5b2o82b3obo2bobo36bo
32b2o12bob4o3b2ob2o$60b2o4bo2b2o31bobo146bo15bo80bo3b2o20bobo2b2o34bo
34bo20b2o4bobo79b3o3bobobobo35bobo45bo$43b2o20bobo2bo33bo4b2o137b3o16b
2o32bo69bo4bo3bo69bobo24b2o80bo2b2obobo2bo32b2o2bo2bo45b3o$42bobo20bob
2o31b4ob2o2bo2bo135bo4bo46bobo68b5ob3o60bo10b2o102b2o3bobo2bobo35b2o3b
2o43b3o2bo$42bo19b2obo34bo2bobobobob2o140b3o43bo2bo2b2o68bobo60b3o115b
o2b2obob2ob2o83bo2bo$41b2o4b2o14bobob2o34bobobobo146bo43b2o3b2o32b2o
30b3obobo59bo104b2o12bobo3bobo88b2o$48bo12bobobo2bo35b2obobo143b2o2bo
81b2o29bo2bob2o60b2o104bo13bob4o2bob2o40b2o27b2o$45b3o6b2o5b2o2bobo40b
o143bo2b2o67b2o44b2o50b2o119bobo13bo3bobob2o40b2o27b2o$45bo8b2o9b2o
185b2o16b2o27b2o22bo2bo96bo120b2o12bo3bobo$94b2o174b2o27b2o21bob2o97bo
b2o108b2o20bo3bobo$95bo7b2o217bo101bo2bo53bo48b2o2bobo20b2o3bo$95bobo
5b2o17bo198b2o102b2o53bobo47bo3bo4bo85b2o3bo$96b2o22b3o213b2o102b2o39b
o49b3ob5o64bo20bo3bobo$46bo72bo159bo3b2o51bo103b2o22b2o67bobo68b3o19bo
3bobo$46b3o70b2o157bobo3bo20bo31b3o24b2o26b2o70b2o67bobob3o30b2o35bo
19bo3bobob2o$49bo227bobo3bo19b3o33bo11b2o11b2o21b2o3bo67b2o72b2obo2bo
29b2o34b2o17bob4o2bob2o$48bobo222b2obobo3bo19bo49bo34bobo3b3o65bo77b2o
44b2o37bobo3bobo$49bo16b2o59b2o144b2obo2b4obo17b2o45b3o33bobob4o2bo53b
o3b2o3b3o17b2o104bo2bo36bobo2bo2b2ob2o$66bo61bo148bobo3bobo63bo35b2o5b
o55bobo3bo3bo19bobo104b2obo36bo3b2o2bobo$47bo16bobo39b2o20bob2o141b2ob
2o2bo2bobo105bo55bobo3bo26bo107bo44bobo10b2o$46bobobo13b2o40bo13b2o4b
3o2bo142bobo2b2o3bo83b2o21b2o50b2obobo3bo27b2o106b2o44bo11b2o$46bo2b2o
56b3o10b2o3bo3b2o131b2o10bobo92bo73b2obo2b4obo9b2o107b2o52b2o$45b2o62b
o15b4o133b2o11bo90b3o78bobo3bobo7bobo108bo52bo$109bob2o15bo152b2o83bo
76b2ob2o2bo2bobo7bo53b2o26b2o24b3o51bobo$107b2obobo12b3o154bo161bobo2b
2o3bo7b2o7b2o45bo3b2o21b2o11b2o11bo53b2o$107bo2bo13bo157bobo147b2o10bo
bo24b2o42b3o3bobo34bo$67b2o40b2o14b5o153b2o147b2o11bo69bo2b4obobo33b3o
$67bo61bo388bo5b2o35bo$48bo16bobo59bo391bo83bo$48b3o14b2o60b2o389b2o
21b2o59bobo34bo$51bo489bo61b2o32b3o$50b2o490b3o91bo$54bo489bo91b2o$53b
obo548b2o$53bo2bo210bo336b2o$20bo33b2o19bo191b3o215b2o157b2o$20b3o5b2o
43b3o16bo177bo214bo159bo$23bo4bo43bo19b3o174b2o26b2o184bobo159bob2o$7b
o9bo4bo3bobo43b2o21bo201b2o183bobo152b2o4b3o2bo$7b3o5b3o3bo3bobo66b2o
382b2o3bo153b2o3bo3b2o$10bo3bo6b2o3bo234b2o215b2o162b4o$9b2o3b2o245bo
366b2o15bo$86b2o170b2obo365bobo12b3o$86bo171bo2b3o4b2o357bo13bo$83b2ob
o172b2o3bo3b2o356b2o14b5o$62b2o19bo2b3o4b2o166b4o208b2o171bo$2o38b2o
19bobo5b2o13b2o3bo3b2o166bo15b2o194b2o169bo$bo38b2o19bo7b2o15b4o172b3o
12bobo2b2o360b2o$bobo56b2o24bo15b2o161bo13bo2bo$2b2o83b3o12bobo155b5o
14b3o2bo332bo$52bo21bo15bo13bo155bo21b3o332b3o$5bo45bobo16b2obobo9b5o
14b2o156bo18bo338bo$4bobo45b2o15bobobobo9bo175b2o18b2o336b2o$5b2o36b2o
21bo2bobobobob2o8bo401bo$23b2o19bo21b4ob2o2bo2bo7b2o399b3o$23bobo15b3o
26bo4b2o39bo369bo$25bo15bo26bobo43b3o369b2o$25b2o20b2o19b2o43bo$9b2o
32b2obobo9bo54b2o$8bobo33bobo9b3o212b2o356b2o$8b2o34bob2o7bo214bobo5b
2o342b2o5bobo$41b2obo10b2o31bo32b2ob2o144bo7b2o342b2o7bo$11b2o28bo2b4o
4bo7b2o13bo10b3o33bob2o143b2o360b2o$11bo30b2o3bo3bobo6bo5b2o5b3o9bo36b
o366b2o$12b3o29b3o3bo2bo4bobo6bo4bo12b2o27b2o4b3o160bo205bobo126bo$14b
o29bo6b2o5b2o7bobo3bo40b2o3bo3b2o154b2obobo206bo125bobob2o$42bobo23bob
o3bo44b4o2bo152bobobobo206b2o124bobobobo$42b2o25bo3b2o30b2o15bob2o149b
o2bobobobob2o326b2obobobobo2bo$104bobo12b3o2bo150b4ob2o2bo2bo326bo2bo
2b2ob4o$40b4o60bo13bo5bo154bo4b2o193b2o3b2o130b2o4bo$39bo3bo52b2o5b2o
14b5o153bobo199b2o3b2o136bobo$39b2o19b2o34bobo22bo155b2o344b2o$60b2o
36bo$98b2o351b3ob3o2$735b2o$53bo649b6o25bo2bo$52bobo647bo5bo25bo2bo$
29b2o15b2o4bobo4b2o647bo26b2o$28bobo5b2o8bo2bo3bo3bo2bo641bo4bo$28bo7b
2o9b3o7b3o25b2o617b2o$27b2o43b2o11b2o365b3ob3o275b2o$45b7o3b7o11bo660b
2o$41bo3bo6bobo6bo8b3o205b2o344b2o$37b2obobo3bobob2o3b2obobo9bo207bobo
199b2o3b2o136bobo$36bobobobo4b2obo5bob2o220bo4b2o193b2o3b2o130b2o4bo$
33bo2bobobob2o8bobo221b4ob2o2bo2bo326bo2bo2b2ob4o$33b4ob2o2bo8b2ob2o
220bo2bobobobob2o326b2obobobobo2bo$37bo4bobo234bobobobo206b2o124bobobo
bo$35bobo5b2o235b2obobo206bo125bobob2o$35b2o247bo205bobo126bo$490b2o$
270b2o360b2o$271bo7b2o342b2o7bo$271bobo5b2o342b2o5bobo$272b2o356b2o3$
487b2o$487bo$488b3o$490bo$262b2o18b2o336b2o$263bo18bo338bo$261bo21b3o
332b3o$261b5o14b3o2bo332bo$266bo13bo2bo$263b3o12bobo2b2o360b2o$262bo
15b2o194b2o169bo$262b4o208b2o171bo$260b2o3bo3b2o356b2o14b5o$259bo2b3o
4b2o357bo13bo$259b2obo365bobo12b3o$262bo366b2o15bo$262b2o215b2o162b4o$
479b2o3bo153b2o3bo3b2o$298b2o183bobo152b2o4b3o2bo$270b2o26b2o184bobo
159bob2o$271bo214bo159bo$268b3o215b2o157b2o$268bo336b2o$605b2o$545bo
91b2o$543b3o91bo$542bo61b2o32b3o$519b2o21b2o59bobo34bo$520bo83bo$519bo
5b2o35bo$284b2o147b2o11bo69bo2b4obobo33b3o$283bobo147b2o10bobo24b2o42b
3o3bobo34bo$283bo161bobo2b2o3bo7b2o7b2o45bo3b2o21b2o11b2o11bo53b2o$
282b2o83bo76b2ob2o2bo2bobo7bo53b2o26b2o24b3o51bobo$263b2o11bo90b3o78bo
bo3bobo7bobo108bo52bo$263b2o10bobo92bo73b2obo2b4obo9b2o107b2o52b2o$
275bobo2b2o3bo83b2o21b2o50b2obobo3bo27b2o106b2o44bo11b2o$274b2ob2o2bo
2bobo105bo55bobo3bo26bo107bo44bobo10b2o$278bobo3bobo63bo35b2o5bo55bobo
3bo3bo19bobo104b2obo36bo3b2o2bobo$274b2obo2b4obo17b2o45b3o33bobob4o2bo
53bo3b2o3b3o17b2o104bo2bo36bobo2bo2b2ob2o$274b2obobo3bo19bo49bo34bobo
3b3o65bo77b2o44b2o37bobo3bobo$278bobo3bo19b3o33bo11b2o11b2o21b2o3bo67b
2o72b2obo2bo29b2o34b2o17bob4o2bob2o$279bobo3bo20bo31b3o24b2o26b2o70b2o
67bobob3o30b2o35bo19bo3bobob2o$280bo3b2o51bo103b2o22b2o67bobo68b3o19bo
3bobo$337b2o102b2o39bo49b3ob5o64bo20bo3bobo$322b2o102b2o53bobo47bo3bo
4bo85b2o3bo$323bo101bo2bo53bo48b2o2bobo20b2o3bo$271b2o27b2o21bob2o97bo
b2o108b2o20bo3bobo$253b2o16b2o27b2o22bo2bo96bo120b2o12bo3bobo$253bo2b
2o67b2o44b2o50b2o119bobo13bo3bobob2o40b2o27b2o$254b2o2bo81b2o29bo2bob
2o60b2o104bo13bob4o2bob2o40b2o27b2o$257bo43b2o3b2o32b2o30b3obobo59bo
104b2o12bobo3bobo88b2o$254b3o43bo2bo2b2o68bobo60b3o115bo2b2obob2ob2o
83bo2bo$249bo4bo46bobo68b5ob3o60bo10b2o102b2o3bobo2bobo35b2o3b2o43b3o
2bo$249b3o16b2o32bo69bo4bo3bo69bobo24b2o80bo2b2obobo2bo32b2o2bo2bo45b
3o$252bo15bo80bo3b2o20bobo2b2o34bo34bo20b2o4bobo79b3o3bobobobo35bobo
45bo$251b2o16b3o76bobo3bo20b2o37b5o14b2o15b2o10b2o8b2o5b2o82b3obo2bobo
36bo32b2o12bob4o3b2ob2o$271bo10b2o18b2o43bobo3bo12b2o38bo6bo5bo13bo29b
o98bo2bobob2ob2o69bo13b2o2bo4bob2o$281bobo18bo40b2obobo3bo13bobo36bobo
bo3bo2b3o12bobo26b3o13b2o83bobo3bobo70b3o23bo$265b2o14bo21b3ob2o34b2ob
o2b4obo13bo35bo2bob3obobo15b2o24bo2bo7b2o7bo84bob4o2bob2o34b2o18b2o10b
o22b2obo$265bo14b2o23bobo39bobo3bobo12b2o33bo3bo4bo2b4o38b3o7bobo4b3o
87bo3bobob2o35bo18bobo31bo2bo$263bobo42bo17b2o2b2o11b2ob2obo2bo2bo47b
4ob2o2bobo3bo3b2o36b3o4bo6bo88bo3bobo36b3o21bo31b2o$263b2o41b2o19bo3bo
12bobo2b2o2b2o46b2o3bobobobo2b3o4b2o35bo2bo2b2ob4o76b2o12bo3bobo35b3o
23b2o$306bo18bo2b3o11bobo2bobo50bo2bo2bobobob2obo43b2obobobobo2bo77bo
12b2o3bo35bo$282b2o20bobo18b3o13bobob2o2bo51b2o4b2obobo2bo46bobobobo
79bo5b2o48b3o$250b2o30bobo19b2o22bo12bobo2bobo3b2o57bo2b2obo44bobob2o
77bo2b4obobo51bo$249bobo28bobobo42b2o11b2ob2obob2o2bo63bobo44bo81b3o3b
obo52b2o$249bo29bobo2bob2o56bobo3bobo44b2o17bobo112bo16bo3b2o21b2o52bo
$248b2o28bo2bobobo2bo25b2o24b2obo2b4obo46bo7b2o9bo5b2o51b2o53b3o13b2o
26b2o50b3o$278b2obobo3bobo20b2o2bobo3bo19b2obobo3bo48bobo5b2o16bo42b2o
7bo57bo55b2o34bo41b2o$281bob2o3bo21bobobo2bobobo22bobo3bo48b2o20b3o43b
2o5bobo56bobo53bo2bo33b2o10bo29bobo$278b2obo30bobob2obo2bo22bobo3bo12b
2o55bo52b2o57bobo54b2obo42b3o31bo$276bo2bobo29b2obo4b3o24bo3b2o12bo
169bo58bo41bo34b3o$276b2o2bo4b2o4b2o21bob3o39b2o5bo227b2o40b2o36bo$
252b2o30bo2bo2bo2bo20bobo3b2o36bobob4o2bo79bo129b2o92b2o$251bobo22b2o
2bo4b2o4b2o16b2o4bo5bo38bobo3b3o79b3o118b2o8bo89b2o$251bo24bo2bobo26bo
2bo7bo17b2o21b2o3bo85bo112b2obo2bo5b3o64b2o24bob5o$249b3o26b2obo27b2o
4bo3b2o16b2o26b2o22b2o18b2o39b2o111bobob3o6bo67bo7b2o21bo$248bo32bob2o
3bo25bobo5b2o66bo18bo54b2o18b2o77bobo33b2o43bob2o3bobo16b2obo$248b2o
28b2obobo4b3o23bob6o2bo63bo21b3o52bo18bo76b3ob5o29bo2b2o32b2o4b3o2bo3b
o18b2ob2o$251b2o25bo2bobobo5bo19b2obo8bo64b5o14b3o2bo49b3o21bo63b2o8bo
3bo4bo30bobo2bo30b2o3bo3b2o3b2o$246b5obo26bobo2b2o4b2o20bobob2o2b3o70b
o13bo2bo51bo2b3o14b5o63bobo7b2o2bobo32b2o2b3o35b4o13b2o$246bo21b2o10b
2o28bobobo2bo2bo69b3o12bobo2b2o52bo2bo13bo47b2o21bo12b2o33bo20b2o4b2o
15bo13b2o$248bob2o16bobo39b2o2bobo17b2o53bo15b2o58bobobo12b3o43bobo21b
2o46bobob2o15b2o3bobo12b3o$247b2ob2o18bo9b4o30b2o18bo8b2o34b2o8b4o67b
2o2b2o2b2o15bo42bo72b2obo21bo13bo33b2o$270b2o8bo3bo50b3o5bo2bob2o29bob
o5b2o3bo3b2o55b2o5bobo2bo16b4o41b2o7b2o66bo20b2o14b5o28b2o$262b2o19b2o
52bo6b3obobo30bo4bo2b3o4b2o55b2o7bobo12b2o3bo3b2o48b2o66b2o39bo$262b2o
84bobo26b4ob2o2bo2bo72b2o13b2o4b3o2bo154bo$344b5ob3o24bo2bobobob2obo
95bob2o55b2obo95b2o$246b2o27b2o67bo4bo3bo26bobobobo2b2o58bo35bo58b2ob
3o$246b2o27bo71bobo2b2o27b2obobo2bo58bobob2o30b2o64bo$272b2obo71b2o36b
o5bo27b2o27bobobobo89b2ob3o$272bo2b3o4b2o106b2o5b2o20bo25b2obobobobo2b
o85bo2b2o$273b2o3bo3b2o87b2o25bo22bo23bo2bo2b2ob4o18b2o64bobo68bo$275b
4o93bo7b2o13b3o3b2o14b5o25b2o4bo22bo47bo16bobob2obo64b3o41b2o$275bo15b
2o79bobo5b2o13bo6bo13bo36bobo21b3o44b3o8b2o5bo2bob2o67bo39bobo$276b3o
12bobo79b2o27bobo12b3o34b2o23bo38b2o7bo6b3o8bo69b2o39bo$279bo13bo109b
2o15bo97bo7b2o6bo2bo6b2o109b2o$274b5o14b2o122b4o95bobo16b3o3bobo2b2o$
263b2o9bo125bo11b2o3bo3b2o29bo63b2o17b3o3b2o2bo2bo$263bobo10bo121b3o
11b2o4b3o2bo26b3o93b2o$265bo9b2o24bo37bo57bo22bob2o25bo112b2o33bo$265b
2o32b3o37b3o11bo43b2o21bo28b2o51b2o58bo33bobo74b2o$298bo43bo8b2o30b2o
34b2o82bo56bobo33bob3o24b2o46bobo$298b2o41b2o9b2o29bo119bobo50b2o2b2o
31b2obo4bo16b2o5bobo47bo$384b3o117b2o2b2o46b2o35bobobobobo16b2o7bo47b
2o$386bo24b2o95b2o56bo28bobob2o4b2o20b2o$247b2o84b2o76bo87bo64b3o20b2o
5bobo8bo$246bobo84bo27bo50b3o84b3o61bo23b2o6bo7bobo8bo$246bo83b2obo21b
2o2b5o14b2o7b2o25bo24b2o61bo60b2o38b2o8bobob2o$245b2o83bo2b3o4b2o13bo
2bo5bo13bo7bobo5b2o42bobo5b2o53b2o110bobobobo$288b2o41b2o3bo3b2o10b2ob
ob2o2b3o12bobo7bo7b2o42bo7b2o162b2obobobobo2bo$287bobo5b2o36b4o16bobo
2bobo15b2o7b2o50b2o153b2o16bo2bo2b2ob4o42b2o$287bo7b2o36bo15b2o2bob2o
3b4o227bo2bo17b2o4bo37b2o7b2o$286b2o46b3o12bobobo5bo3bo3b2o30bo51bo80b
o3b2o54b2o24bobo36bo$337bo13bobo4bob3o4b2o26b2obobo46b2obobo78bobo2b2o
28b2o51b2o36bobo$300bo31b5o14b2o3b3obo27b2o4bobobobo45bobobobo45b2o26b
2o2bo2bo32b2o90b2o$255b2o39b2obobo30bo22bo4bo27bo2bo2bobobob2o41bo2bob
obobob2o42b2o25bobo3b2o11b2o28bo99b2o$255b2o7b2o29bobobobo32bo20b2o3b
2o28b5ob2o2bo42b4ob2o2bo2bo64b2o3bo17bobo26b3o99bo$264bo27bo2bobobobob
2o28b2o60bo4bo26b2o18bo4b2o66bobob2o17bo27bo100bobo$262bobo27b4ob2o2bo
2bo87bo2bob3o4bo23bo16bobo74bobo7b2o8b2o27b2o27b2o70b2o$262b2o32bo4b2o
6bo53b2o3b2o20b3o3b2o4b3o23bobo14b2o5b4o66bobo7b2o20b2o31b2o10bobo27b
2ob2o$246b2o46bobo11bobo53bo4bo19bo11bo27b2o20bo3bo54b2o11bo31bo27b2ob
obo10b2o29bobo24bo$247bo46b2o10b3obo53bob3o5bo14b2o10b2o48b2o57bo41b3o
28bob2obobo34b2obo5bob2o19b3o$247bobo55bo4bob2o42b2o4b3obo7b3o134b3o
38bo36b2o3b2o3b4o21bobob2o3b2obobo9bo11bo$248b2o55bobobobobo42b2o3bo3b
o11bo43bo49bo41bo80b2o4bo2bo19bo6bobo6bo8b3o8b2o14bo$288b2ob2o7b2o4b2o
bobo49b4o3b2o4b2obo41b3o47b3o126bo3b2o19b7o3b7o11bo22bobo$264bo24bobo
9bo8bobo5b2o10b2o11b2o2b2o15bobo2bo5bob2o39bo49bo92b2o35b2o50b2o23bo$
262b3o19b2obo5bob2o4bobo7bo6b2o6b2o3bo11bo2bobo12b3o2b2obob2o2bo3bo25b
2o11b2o35b2o11b2o11bo78bobo5b2o55b3o7b3o$261bo11bo9bobob2o3b2obobo4b2o
22bo2bo4b2o9b2o13bo5bo2bobo4b4o25b2o48b2o24b3o76bo7b2o54bo2bo3bo3bo2bo
$246bo14b2o8b3o8bo6bobo6bo28b4o3b2o3b2o5bo14b5o2b2obo2bobo107bo74b2o
63b2o4bobo4b2o$245bobo22bo11b7o3b7o40bobob3o17bo7bobobo2b2o103b2o145bo
bo$246bo23b2o41b2o14b2o10bobo27bobo2b2o2bo117b2o73bo57bo$284b3o7b3o15b
o2bo12bobo10b2o29b2o4b2o118bo70b2obobo$283bo2bo3bo3bo2bo15b2o13b2o48bo
116b2obo69bobobobo95b2o$283b2o4bobo4b2o78bobo3b2o110bo2bo67bo2bobobobo
b2o92bobo$289bobo84b2o3bobo111b2o68b4ob2o2bo2bo60b2o32bo$290bo90bo48b
2o48b2o87bo4b2o62b2o23b2o7b2o$380b2o7bo40b2o11b2o35b2o85bobo93bo$250b
2o136bobo52bo123b2o95b3o$249bobo52b2o30b2o51b2o53b3o219bo$249bo32b2o
20bo2bo10b2o15bo2bo107bo$248b2o7b2o23b2o21b3o10bobob2o12b2o129b2o3bo
169b2o$258bo57bobob2obo102b2o39bo3bobo155b2o5b2o5bo$255b3o47b3o3b2o3b
2o86b2o20bo27b2o12bo3bobo153bo2bo4bobob3o$255bo48bobo4b2o12b2o76bobo
21b3o23bobo13bo3bobob2o145b2o3bobo6bobo$300b2o2bo3bo15bobo7bo6b2o60bo
25bo23bo13bob4o2bob2o141b2obobo4bo7b2o$278b2o19bobo3b4o15bo8bobo5b2o
59b2o48b2o12bobo3bobo146bobo9b2o$278bo5b2o5b2o6bo23b2o4b2obobo131bobo
2bo2b2ob2o141bo2b2o8bo$279b3obobo4bo2bo3b3o7b2o19bobobobobo130bo3b2o2b
obo143b2o11b3o$281bobo6bobo3bo3b2o5b2o19bo4bob2o138bobo10b2o133b2o11bo
$282b2o7bo4b4o2bo26b3obo142bo11b2o133bo$287b2o10bob2o28bobo290bo$288bo
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Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions

Re: Glider circuits: components and contraptions