ConwayLife.com

Posted: **September 8th, 2015, 8:58 am**

Has anybody realized that this is a knightship?

x = 6, y = 5, rule = B2o45/S2o45H
bo$b2o$b3o$ob2obo$bobobo!

There's many variations...

Code: Select all

x = 17, y = 27, rule = B2o45/S2o45H
4$3b3o$3b4o2$4b4o$3bob3obo$6b2o$7bo$7b2o$8bo$6b2o2b2o$7b2ob2o2$10bo$
10b2o$11bo!

Neat p3:

Code: Select all

x = 5, y = 8, rule = B2o45/S2o45H
o$2bo$bobo$b3o$bobo$2bo$4bo!

More p3s:

Code: Select all

x = 12, y = 14, rule = B2o45/S2o45H
2$5b2o2b2o$6b2ob2o3$4bo$3bo2bo$3b2ob2o2$4bobobo$6b2o!

Code: Select all

x = 20, y = 17, rule = B2o45/S2o45H
2$o2bo2bo$obo2bobo$2bobobo$4b2o$3bo3bo7bo$5b2o2bo4bo$11b3o$6b2o4b2o$
13bo2$14bo2$15bo!

And a (useful?) reaction:

Code: Select all

x = 38, y = 30, rule = B2o45/S2o45H
4$21bo$20bobo$20b4o$22b2obo$21b3obo$25bo2b3o$28b4o$29b3o$30b2o9$4bo$4b
2o$4b3o$3bob2obo$4bobobo!

Posted: **September 9th, 2015, 12:31 pm**

Saka wrote:Has anybody realized that this is a knightship?
Code: Select all
x = 6, y = 5, rule = B2o45/S2o45H
bo$b2o$b3o$ob2obo$bobobo!

I'm not sure that this type of ship is referred to as a knightship. It only appears to be a knightship because the hexagonal lattice is being simulated on a square lattice. Here is that ship oriented to the six directions it can travel in.

Code: Select all

x = 27, y = 27, rule = B2o45/S2o45H
8bo$8b2o$8b3o$7bob2obo$8bobobo4bo$17bob3o$19b3o$3bo15b3o$3obo$b3o17b2o
$2b3o2$3b2o2$22b2o2$22b3o$4b2o17b3o$22bob3o$5b3o15bo$5b3o$5b3obo$9bo4b
obobo$14bob2obo$16b3o$17b2o$18bo!

While I say this isn't classified as a knightship, it also can't be called orthogonal or diagonal - as it doesn't move in the direction of the nearest neighbours of a cell. If there's existing terminology for these directions on hexagonal lattices and the different types of ships that exist in hexagonal CA, then I'd sure appreciate someone pointing it out.

The first p3 oscillator you posted is part of the collection in the first post of this thread. The next two oscillators are p6, not p3.

Posted: **September 10th, 2015, 8:19 am**

Asymmetric p6:

Code: Select all

x = 5, y = 6, rule = B2o45/S2o45H
2o$2obo$4o$2b2o$bo$o2b2o!

A p6 that looks like the normal p6 hassling each other:

Code: Select all

x = 17, y = 14, rule = B2o45/S2o45H
2$b3o2$2b3o$2bo6bo$bobo4bobo$2bobo4bobo$3bo6bo$8b3o2$9b3o!

Posted: **September 20th, 2015, 2:02 pm**

Full-width speed-1 spaceship (is this the term?) on a torus:

Code: Select all

x = 13, y = 6, rule = B2o45/S2o45H:T0,6
4bobobobobo$4bobobobobo$o3bobobobobo$2bo3bobobobo$4bobobobobo$6bobobob
o!

Posted: **October 3rd, 2015, 4:32 pm**

This is really interesting.

Sad that there's no download for this. At least on this forum.

Posted: **October 12th, 2015, 9:34 pm**

Xenonquark wrote:Sad that there's no download for this.

Download for what?

Posted: **October 12th, 2015, 10:57 pm**

Xenonquark wrote:This is really interesting.
Sad that there's no download for this. At least on this forum.

If you're looking for the .rule file, it's in the first post of the thread.

Posted: **October 16th, 2015, 7:52 pm**

But I want a program that actually uses hexagons for cells.

Posted: **October 16th, 2015, 8:24 pm**

Golly can do this, if you click View->Show Cell Icons. It will still be on a square grid, but after a certain zoom level the cells will appear as sideways hexagons, if the rule is on a hexagonal neighborhood.

Posted: **October 16th, 2015, 9:06 pm**

gameoflifeboy wrote:Golly can do this, if you click View->Show Cell Icons. It will still be on a square grid, but after a certain zoom level the cells will appear as sideways hexagons, if the rule is on a hexagonal neighborhood.

I know that. But I want the actual grid to consist of hexagons.

Posted: **October 16th, 2015, 9:19 pm**

Xenonquark wrote:But I want the actual grid to consist of hexagons.

Download Ready if you want to see actual hexagons. After installing it, load Patterns/CellularAutomata/hex_B2oS2m34_gliders.vtu. It should be simple to modify the displayed kernel code to run other hex rules like B2o45/S2o45.

: hexgrid.png (6.28 KiB) Viewed 6620 times

Posted: **October 16th, 2015, 10:06 pm**

Andrew wrote:
Xenonquark wrote:But I want the actual grid to consist of hexagons.
Download Ready if you want to see actual hexagons. After installing it, load Patterns/CellularAutomata/hex_B2oS2m34_gliders.vtu. It should be simple to modify the displayed kernel code to run other hex rules like B2o45/S2o45.

Thank you. Now I can finally view cellular automata from the other side of the plane!

Posted: **March 13th, 2024, 9:57 pm**

This version of the p22 appeared in the b2o45s2o45h/D6_1o census:

Code: Select all

#C https://catagolue.hatsya.com/object/xp22_y3ggtgidbmczg0ggsgog273f2202y36mmkgzcqkcj3f22ya1049sotzw11w1yg31752zy2oo0g8yf4auoszy21307i0lusskgyab1jpig8zyb121x6lussk04gy12666zyl120970fe/b2o45s2o45h
x = 39, y = 39, rule = B2o45/S2o45H
9bo2b2o$11bob2o$9bo2bob2o$9bo2b2obo$7b5o2bo$9b3o$8b6obo7b3o$4bo4bobo11b4o$4bo
bo4bo$ob6o16b4o$4b3o16bo2bo2bo$bo2b5o$ob2o2bo18bobobo$2obo2bo19b4o$b2obo22b3o
$2b2o2bo20b4o$27bobobo$29b2o4$31b2o$30bobobo$6b2o2bo20b4o$6b2obo22b3o$6b2obo
2bo19b4o$7bob2o2bo18bobobo$9bo2b5o$13b3o16bo2bo2bo$10bob6o16b4o$15bobo4bo$16b
o4bobo11b4o$21b6obo7b3o$23b3o$22b5o2bo$25bo2b2obo$26bo2bob2o$29bob2o$28bo2b2o!
#C [[ THEME MCell ZOOM 10 GRID ]]

Posted: **August 20th, 2024, 3:50 pm**

p18

Code: Select all

x = 18, y = 20, rule = B2o45/S2o45H
4bo3bo$4bob2obo$4bobobobo$6bo2bo3$3o$8bo6bo$b3o4b2o4bobo$bo7b2o4bobo$
obo4b2o7bo$bobo4b2o4b3o$2bo6bo$15b3o3$8bo2bo$7bobobobo$8bob2obo$9bo3b
o!

Posted: **August 20th, 2024, 5:02 pm**

c0b0p0 wrote: January 24th, 2015, 10:20 pm Here is an SG (sparky glider) -> 2G reaction.
Code: Select all
x = 47, y = 47, rule = B2o45/S2o45H
41bo2$44bo$41bobo$38b3obo$40b2obo2bo$39b4o$40bobo$42bo32$o3bo$ob2obo$o
bobobo$2bo2bo$3b3o2$4b3o!

c0b0p0 wrote: January 26th, 2015, 9:00 pm Here is a G -> SG reaction.
Code: Select all
x = 28, y = 12, rule = B2o45/S2o45H
24b3o$24b4o$25b3o$26b2o5$o2b2o$2bob2o$5b2o$6bo!

Combined into a gunnable pattern.

Code: Select all

x = 219, y = 122, rule = B2o45/S2o45H
23$174b3o$176b2o$175b3o$176bobo$178bo3$154bo$153bo2bo$153b2ob2o2$29b3o
122bobobo$156b2o$30b3o$30bo2bo$29bobobobo$30bob2obo$31bo3bo5$151bo2$154b
o$151bobo$73bo74b3obo$72bo2bo74b2obo2bo$72b2ob2o72b4o$150bobo$73bobob
o74bo$75b2o31$110bo3bo$110bob2obo$110bobobobo$112bo2bo$113b3o2$114b3o
!

Also, how do I rotate a pattern on a hexagonal plane?

Posted: **September 14th, 2024, 12:24 pm**

An 'interesting' property of this cellular automaton is that the conditions for birth match the conditions for survival; a cell does not participate in its subsequent state in the next generation. (The same is true for 3/4 Life.)

For two-state cellular automata with honeycomb neighbourhood, this property allows to express the set of rules as a 6-input Boolean function (instead of a 7-input function in the general case) so it may be easier to find an efficient Boolean circuit that implements the function. (See also a related forum thread.) A 6-input function can be reduced to a pair of 5-input functions:

Code: Select all

f(n,e,h,s,w,l) := (f1(n,e,h,s,w) and l) or (f0(n,e,h,s,w) and not l);

5-input functions were investigated, and every such function can be implemented with at most 12 two-input gates.
This gives an upper bound of (27 = 12 x 2 + 3) gates.

For B2o45/S2o45H, I think each of two needed 5-input functions can be implemented with only 10 gates.
This leads to an upper bound of (23 = 10 x 2 + 3) gates:

Code: Select all

// neighbourhood (r, v are ignored for the honeycomb neighbourhood):
//   l n r
//   w c e
//   v s h
// Reference for the single-letter notation for neighbours:
// https://web.archive.org/web/20240907235728/https://conwaylife.com/forums/viewtopic.php?f=7&t=2036&start=625#p51158
q1     := n xor h;                                                                      // 1 gate
q2     := e xor q1;                                                                     // 1 gate
r0     := (s or e) and not ((q2 and not h) or (((q2 xor s) or (w and not q1)) xor w));  // 8 gates
q3     := e xor h;                                                                      // 1 gate
q4     := (h xor s) or q3;                                                              // 2 gates
r1     := ((((n or w) xor q4) or (q3 xor s)) and not (n and w)) xor q4;                 // 7 gates
result := (r1 and l) or (r0 and not l);                                                 // 3 gates

Intermediate results can be shared between the two 5-input 1-output computations.
I can get an upper bound of (21 = 18 + 3) gates this way:

Code: Select all

q1     := n xor e;                                                    // 1 gate
q2     := s xor q1;                                                   // 1 gate
q3     := w xor q2;                                                   // 1 gate
q4     := h xor q3;                                                   // 1 gate
q5     := h and s;                                                    // 1 gate
q6     := q1 and not q3;                                              // 1 gate
q7     := n and not q6;                                               // 1 gate
r0     := (e or s) and not (q6 or (q4 and not (n and q5)));           // 5 gates
r1     := ((q5 xor not w) and (h xor q2 xor q7)) xor (q4 or q7);      // 6 gates
result := (r1 and l) or (r0 and not l);                               // 3 gates

It may be possible to get a better upper bound, either by solving the 5-input 2-output circuit in at most 17 gates, or by directly solving the 6-input 1-output circuit in at most 20 gates.
Is it feasible to determine the lowest possible cost (in 2-input 1-output gates) for this CA?

Posted: **October 11th, 2024, 6:30 pm**

WhiteHawk wrote: August 20th, 2024, 5:02 pm
c0b0p0 wrote: January 24th, 2015, 10:20 pm Here is an SG (sparky glider) -> 2G reaction.
Code: Select all
x = 47, y = 47, rule = B2o45/S2o45H
41bo2$44bo$41bobo$38b3obo$40b2obo2bo$39b4o$40bobo$42bo32$o3bo$ob2obo$o
bobobo$2bo2bo$3b3o2$4b3o!
c0b0p0 wrote: January 26th, 2015, 9:00 pm Here is a G -> SG reaction.
Code: Select all
x = 28, y = 12, rule = B2o45/S2o45H
24b3o$24b4o$25b3o$26b2o5$o2b2o$2bob2o$5b2o$6bo!
Combined into a gunnable pattern.
Code: Select all
x = 219, y = 122, rule = B2o45/S2o45H
23$174b3o$176b2o$175b3o$176bobo$178bo3$154bo$153bo2bo$153b2ob2o2$29b3o
122bobobo$156b2o$30b3o$30bo2bo$29bobobobo$30bob2obo$31bo3bo5$151bo2$154b
o$151bobo$73bo74b3obo$72bo2bo74b2obo2bo$72b2ob2o72b4o$150bobo$73bobob
o74bo$75b2o31$110bo3bo$110bob2obo$110bobobobo$112bo2bo$113b3o2$114b3o
!
Also, how do I rotate a pattern on a hexagonal plane?

Code: Select all

x = 540, y = 351, rule = B2o45/S2o45H
7$439b2o$440b2o$441b2o$442bo$441bo2$442bo36$397b2o$398b2o$399b2o$400b
o$399bo2$400bo23$202b3o$202b4o2$206bo$208bo9$63b2o2bo287b2o$63b2obo289b
2o$63b2o292b2o$64bo293bo$357bo2$358bo14$229bo2$230bo2$231bo$231b2o$231b
3o$230bo4bo$229bo7bo14$147b2o2bo57bo2b2o99b2o$147b2obo60bob2o99b2o$147b
2o62b2ob2o99b2o$148bo58bo3b3obo100bo$207b2ob5o100bo$208bob2o44b2o2b2o
$215bo41b2ob2o54bo$207b2ob2o54bo$180bo7bo18b2o2b2o47bob2o$182bo4bo26b
o3bo41b2ob5o$184b3o27bob2obo41bo3b3obo$185b2o27bobobobo45b2ob2o$186bo
29bo2bo40b3o4bob2o$217b3o46bo2b2o$187bo73b3o$218b3o40bo2bo$188bo71bob
obobo$261bob2obo$262bo3bo9$300bo7bo$302bo4bo$304b3o$305b2o$306bo2$307b
o2$308bo11$202b3o$202b4o2$203b4o$202bob3obo2b3o$205b2o$206bo5b3o$206b
2o4bo2bo$207bo3bobobobo90bo$205b2o2b2obob2obo90b2o$206b2ob2o2bo3bo91b
o2$209bo91bo3bo2b2ob2o$209b2o90bob2obob2o2b2o$210bo90bobobobo3bo$303b
o2bo4b2o$304b3o5bo$312b2o$305b3o2bob3obo$312b4o2$313b4o$314b3o11$210b
o2$211bo2$212bo$212b2o$212b3o$211bo4bo$210bo7bo9$252bo3bo$252bob2obo$
252bobobobo71bo$254bo2bo40b3o$255b3o73bo$248b2o2bo46b3o$248b2obo4b3o40b
o2bo29bo$248b2ob2o45bobobobo27b2o$249bob3o3bo41bob2obo27b3o$251b5ob2o
41bo3bo26bo4bo$255b2obo47b2o2b2o18bo7bo$252bo54b2ob2o$202bo54b2ob2o41b
o$257b2o2b2o44b2obo$203bo100b5ob2o$202bo100bob3o3bo58bo$202b2o99b2ob2o
62b2o$203b2o99b2obo60bob2o$204b2o99b2o2bo57bo2b2o14$281bo7bo$283bo4bo
$285b3o$286b2o$287bo2$288bo2$289bo14$160bo2$161bo$160bo293bo$160b2o292b
2o$161b2o289bob2o$162b2o287bo2b2o9$310bo$312bo2$313b4o$314b3o23$118bo
2$119bo$118bo419bo$118b2o418b2o$119b2o415bob2o$120b2o413bo2b2o!

Posted: **October 13th, 2024, 1:51 am**

This similar rule is really abundant with natural guns. It largely consists of them!

Code: Select all

x = 16, y = 16, rule = B2o3p45/S2o3p45H
boooobooobbobbbo$
obobbbobbbooobob$
bbbbobbobbbobobo$
oobboooobobooobb$
ooboooobbboobboo$
oobbboboooobobob$
ooobboobboboobbb$
bbboobbobbbobbob$
oobbboooobobbobb$
oobooboboooboobb$
oboboooooboboboo$
bobbobobobobbooo$
booobobbbbooobob$
ooobbobbooboobob$
bbooobboobobbbbb$
ooboobbobobboobo!

ConwayLife.com

Hex rule B2o45/S2o45H

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45H

Re: Hex rule B2o45/S2o45

Re: B2o45/S2o45H

Re: Hex rule B2o45/S2o45

Re: Hex rule B2o45/S2o45H