Page 3 of 11
Re: Star Wars Rule
Posted: October 18th, 2010, 7:27 am
by Awesomeness
Okay, we now have good screen possibilities.
Now, we need to use them.
What the cell will do, in pseudo code is:
Code: Select all
if cell is on {
if has three neighbors {
(do nothing)
} else {
turn off
}
} else {
if cell has 2 or 3 neighbors {
turn on
}
}
But I need someone experienced with logic gates to help me out. How would this be designed?
Re: Star Wars Rule
Posted: October 18th, 2010, 6:48 pm
by p46beth
You got that backwards. You essentially wrote the rule B23/S2. I think you meant B3/S23
Re: Star Wars Rule
Posted: October 18th, 2010, 8:50 pm
by Awesomeness
I don't think I got it backwards. ...I hope I didn't do it backwards...
Could someone verify it for me? Thanks.
Using components from most of the posts since the project begun, I have created a controllable on/off screen. It uses a p25 gun that I engineered, (which took a half an hour...
) the toggle gun, and an array of fanouts to create the screen. Period 25 is the minimum period for the fanout.
Code: Select all
x = 760, y = 2044, rule = 345/2/4
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5.A7.A3.2A8.A5.A7.A3.2A8.A5.A7.A3.2A8.A5.A7.A3.2A8.A5.A7.A3.2A$13.A5.
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8.9A.C2B.6A$12.3A3.A28.A.A10.A2.A2.A2.C2B2.A2.A10.A2.A2.A2.C2B2.A2.A
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2B26.2B26.2B26.2B$11.3A5.A2.A2.A2.A32.2B26.2B26.2B26.2B26.2B26.2B26.
2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B26.2B
26.2B26.2B26.2B26.2B26.2B$12.A341$62.A27.A27.A27.A27.A27.A27.A27.A27.
A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A27.A$61.
3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A
25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A25.3A$62.A27.A27.A
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27.A27.A27.A27.A27.A!
If someone else has a fully implementable example of a screen, (as in one glider can turn it on or off) which I'm sure exists, post it! I'd love to see different designs, so that we have more options.
The problem remains that I need someone to help me out with logic gates for the metacell. I know there's a bunch of people here who qualify for this! Please reply!
Re: Star Wars Rule
Posted: October 19th, 2010, 2:23 am
by apg
The problem remains that I need someone to help me out with logic gates for the metacell.
Well, I've made a metacell before, so I suppose I qualify.
The rule to be simulated is B3/S23, which can be expressed as "3 OR (c AND 2)". In other words, either the cell has three neighbours, or it is on and has two.
The condition for having three neighbours is equal to "b0 AND b1 AND NOT(b2)", where b0, b1, b2, b3 are the binary digits of the sum of live neighbours, with b0 being the least significant digit.
The condition for having two neighbours is equal to "NOT(b0) AND b1 AND NOT(b2)".
So, Life can be re-expressed as: "c' = (b0 AND b1 AND NOT(b2)) OR (c AND NOT(b0) AND b1 AND NOT(b2))".
This simplifies to
"c' = b1 AND NOT(b2) AND (b0 OR c)", which is surprisingly simple and elegant.
As for calculating b0, b1, and b2, this requires a binary counter circuit.
Re: Star Wars Rule
Posted: October 19th, 2010, 7:48 am
by Awesomeness
I understood everything you said until you got into binary with b0, b1, etc...
Okay, so we need to make a binary counter circuit to make this work? Does each digit have to be readable? I assume so...
I'll get to work.
Re: Star Wars Rule
Posted: October 22nd, 2010, 5:16 pm
by p46beth
The b0, b1, and b2 was a way to express how many neighbors were on. Basically, if X neighbors are on, write X in binary, and each bit corresponds to one of b0, b1, b2, or b3. For example, if 3 neighbors are live, that is 0011, so b0=1, b1=1, b2=0, and b3=0. If a relatively small binary counter exists, this would be a simpler way to track the inputs than an 8 variable logic function (the most straightforward way would be (a&b&)|(a&b&d)|... through every combination of three neighbors. But this would require 56 sets of three inputs, which means that each of 8 inputs would need to be duplicated 28 times, and then the result of 168 signals would have to be sent through a whopping 112 AND gates, plus 55 OR gates. The AND gates are very small, but 55 or gates would be huge, and time consuming.) If, however, we can find a binary counter, then far less computation needs to be done each generation.
Code: Select all
x = 14, y = 18, rule = 345/2/4
$5.2C$5.2B$5.2A5$5.2C$5.2B$5.2A$9.A$5.A2.3A$4.3A.2A$5.A3.A$8.3A$9.A!
This results in a p96 double gun, which fires spaceships far larger than the gun itself.
There are a large number of similar reactions in which a few gliders and a small still life produce unusual results. This suggests that glider constructions can, in fact, be used for a huge range of objects in this rule, provided we can find syntheses for a few common still lives. Specifically, the important things that need to be constructable are the small reflector (the above pattern is two gliders fired at such a reflector, but too quickly for it to recover in time), the plus, and some method for constructing the "wires" (including a construction for a 90 degree turn in the wire). Actually, with these three things, it would be possible to build all of the logic gates, which would strongly suggest the existence of a universal constructor. Unfortunately, the important still lifes do not have simple constructions the way the do in life. However, there are fewer unique pieces to build than in life.
EDIT: and here is a simple pattern which results in a gun+backrake
Code: Select all
x = 17, y = 25, rule = 345/2/4
$3.2C$3.2B$3.2A9$3.2C$3.2B$3.2A$7.A$3.A2.3A$2.3A.2A$3.A3.A$6.3A$7.A!
On an unrelated note, here is a breeder:
Code: Select all
x = 105, y = 70, rule = 345/2/4
24$69.2A$68.C2.C$69.BCB$70.A$66.BA$53.2A8.ABCBC$53.2A6.ABC5.A.A$52.B
2A.BA2.BC2.BC.2A.B.B$51.AC.2ACB.A.C.AB5AC.AC4.C$50.AB.A2.C2.C2B2C3.A
3.2A.B4.B$48.AB2.2A.A.A6.CA.A.2A.B.C4.C$46.A.A.A.A.A.A.A.A3.A.A.A.A3.
A.A3.A$45.36A$19.A.CB2.BA.CA.CB2.BA.CA.CB2.A.A.A.A.A.A.A.A.A.A.A.A.A.
A.A.A.A.A$17.2ABA.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A
.A.A.A.A$17.64A2$18.ABC$18.ABC!
Re: Star Wars Rule
Posted: October 23rd, 2010, 6:41 am
by apg
All we need for a universal constructor is the ability to build a cross -- any logic component can be built from well-spaced copies of it:
Code: Select all
x = 48, y = 15, rule = 345/2/4
6.A$5.3A$6.A39.A$45.3A$46.A2$42.A$CBA38.3A$CBA39.A3$5.2A$5.2B32.2A$5.
2C32.2B$39.2C!
Re: Star Wars Rule
Posted: October 23rd, 2010, 7:04 am
by apg
And here's a method to build a cross:
Code: Select all
x = 72, y = 12, rule = 345/2/4
2C$2B$2A3$CBA66.ABC$CBA66.ABC3$.2A$.2B$.2C!
Re: Star Wars Rule
Posted: October 23rd, 2010, 8:17 am
by apg
And here's a binary counter built entirely from crosses:
Code: Select all
x = 1158, y = 298, rule = 345/2/4
129.A84.A170.A84.A170.A84.A170.A84.A$128.3A82.3A168.3A82.3A168.3A82.
3A168.3A82.3A$129.A84.A170.A84.A170.A84.A170.A84.A2$133.A76.A178.A76.
A178.A76.A178.A76.A$132.3A74.3A176.3A74.3A176.3A74.3A176.3A74.3A$133.
A76.A178.A76.A178.A76.A178.A76.A58$119.A255.A255.A255.A$63.A54.3A126.
A71.A54.3A126.A71.A54.3A126.A71.A54.3A126.A$62.3A54.A126.3A69.3A54.A
126.3A69.3A54.A126.3A69.3A54.A126.3A$63.A183.A71.A183.A71.A183.A71.A
183.A2$67.A163.A11.A79.A163.A11.A79.A163.A11.A79.A163.A11.A$66.3A161.
3A9.3A77.3A161.3A9.3A77.3A161.3A9.3A77.3A161.3A9.3A$67.A163.A11.A29.A
49.A163.A11.A29.A49.A163.A11.A29.A49.A163.A11.A29.A$272.3A253.3A253.
3A253.3A$45.A10.A216.A27.A10.A216.A27.A10.A216.A27.A10.A216.A$44.3A8.
3A242.3A8.3A242.3A8.3A242.3A8.3A$45.A10.A62.A102.A46.A31.A10.A62.A
102.A46.A31.A10.A62.A102.A46.A31.A10.A62.A102.A46.A$118.3A100.3A44.3A
103.3A100.3A44.3A103.3A100.3A44.3A103.3A100.3A44.3A$119.A102.A46.A
105.A102.A46.A105.A102.A46.A105.A102.A46.A2$115.A255.A255.A255.A$104.
A9.3A243.A9.3A243.A9.3A243.A9.3A$103.3A9.A243.3A9.A243.3A9.A243.3A9.A
$104.A255.A255.A255.A2$100.A255.A255.A255.A$89.A9.3A243.A9.3A243.A9.
3A243.A9.3A$67.A20.3A9.A222.A20.3A9.A222.A20.3A9.A222.A20.3A9.A$66.3A
20.A25.A206.3A20.A25.A206.3A20.A25.A206.3A20.A25.A$67.A46.3A206.A46.
3A206.A46.3A206.A46.3A$85.A29.A225.A29.A225.A29.A225.A29.A$84.3A253.
3A253.3A253.3A$85.A255.A255.A255.A10$65.A13.A241.A13.A241.A13.A241.A
13.A$64.3A11.3A239.3A11.3A239.3A11.3A239.3A11.3A$65.A13.A241.A13.A
241.A13.A241.A13.A2$61.A21.A233.A21.A233.A21.A233.A21.A$60.3A19.3A15.
A215.3A19.3A15.A215.3A19.3A15.A215.3A19.3A15.A$61.A21.A15.3A215.A21.A
15.3A215.A21.A15.3A215.A21.A15.3A$100.A255.A255.A255.A2$104.A255.A
255.A255.A$103.3A253.3A253.3A253.3A$104.A255.A255.A255.A4$.A1154.A$3A
1152.3A$.A1154.A2$5.A1146.A$4.3A19.CBA57.A181.A73.A181.A73.A181.A73.A
181.A114.3A$5.A20.CBA56.3A179.3A71.3A179.3A71.3A179.3A71.3A179.3A114.
A$86.A181.A73.A181.A73.A181.A73.A181.A2$90.A173.A81.A173.A81.A173.A
81.A173.A$89.3A171.3A79.3A171.3A79.3A171.3A79.3A171.3A$90.A173.A81.A
173.A81.A173.A81.A173.A7$114.A255.A255.A255.A$113.3A253.3A253.3A253.
3A$114.A255.A255.A255.A2$118.A255.A255.A255.A$117.3A29.A87.A135.3A29.
A87.A135.3A29.A87.A135.3A29.A87.A$118.A29.3A85.3A135.A29.3A85.3A135.A
29.3A85.3A135.A29.3A85.3A$134.A14.A87.A152.A14.A87.A152.A14.A87.A152.
A14.A87.A$133.3A253.3A253.3A253.3A$134.A18.A79.A156.A18.A79.A156.A18.
A79.A156.A18.A79.A$152.3A77.3A173.3A77.3A173.3A77.3A173.3A77.3A$138.A
14.A79.A160.A14.A79.A160.A14.A79.A160.A14.A79.A$137.3A253.3A253.3A
253.3A$138.A255.A255.A255.A11$138.A30.A29.A194.A30.A29.A194.A30.A29.A
194.A30.A29.A$137.3A28.3A27.3A32.A159.3A28.3A27.3A32.A159.3A28.3A27.
3A32.A159.3A28.3A27.3A32.A$138.A15.A14.A29.A32.3A159.A15.A14.A29.A32.
3A159.A15.A14.A29.A32.3A159.A15.A14.A29.A32.3A$153.3A77.A175.3A77.A
175.3A77.A175.3A77.A$134.A19.A18.A21.A194.A19.A18.A21.A194.A19.A18.A
21.A194.A19.A18.A21.A$133.3A36.3A19.3A40.A151.3A36.3A19.3A40.A151.3A
36.3A19.3A40.A151.3A36.3A19.3A40.A$134.A23.A14.A21.A40.3A151.A23.A14.
A21.A40.3A151.A23.A14.A21.A40.3A151.A23.A14.A21.A40.3A$157.3A77.A175.
3A77.A175.3A77.A175.3A77.A$158.A255.A255.A255.A7$194.A255.A255.A255.A
$193.3A253.3A253.3A253.3A$194.A255.A255.A255.A2$158.A31.A223.A31.A
223.A31.A223.A31.A$157.3A29.3A221.3A29.3A221.3A29.3A221.3A29.3A$158.A
15.A15.A223.A15.A15.A223.A15.A15.A223.A15.A15.A$173.3A253.3A253.3A
253.3A$154.A19.A235.A19.A235.A19.A235.A19.A$153.3A253.3A253.3A253.3A$
154.A23.A231.A23.A231.A23.A231.A23.A$177.3A253.3A253.3A253.3A$178.A
255.A255.A255.A11$178.A31.A223.A31.A223.A31.A223.A31.A$177.3A29.3A
221.3A29.3A221.3A29.3A221.3A29.3A$178.A31.A223.A31.A223.A31.A223.A31.
A2$174.A39.A215.A39.A215.A39.A215.A39.A$173.3A37.3A213.3A37.3A213.3A
37.3A213.3A37.3A$174.A39.A215.A39.A215.A39.A215.A39.A3$243.A255.A255.
A255.A$242.3A253.3A253.3A253.3A$118.A124.A130.A124.A130.A124.A130.A
124.A$117.3A253.3A253.3A253.3A$118.A128.A126.A128.A126.A128.A126.A
128.A$246.3A253.3A253.3A253.3A$114.A132.A122.A132.A122.A132.A122.A
132.A$113.3A253.3A253.3A253.3A$114.A255.A255.A255.A58$111.A8.A9.A236.
A8.A9.A236.A8.A9.A236.A8.A9.A$110.3A6.3A7.3A234.3A6.3A7.3A234.3A6.3A
7.3A234.3A6.3A7.3A$111.A8.A9.A236.A8.A9.A236.A8.A9.A236.A8.A9.A2$107.
A26.A228.A26.A228.A26.A228.A26.A$5.A100.3A24.3A226.3A24.3A226.3A24.3A
226.3A24.3A248.A$4.3A100.A26.A228.A26.A228.A26.A228.A26.A248.3A$5.A
1146.A2$.A1154.A$3A1152.3A$.A1154.A9$104.A30.A224.A30.A224.A30.A224.A
30.A$103.3A28.3A222.3A28.3A222.3A28.3A222.3A28.3A$104.A30.A224.A30.A
224.A30.A224.A30.A2$100.A38.A216.A38.A216.A38.A216.A38.A$99.3A36.3A
214.3A36.3A214.3A36.3A214.3A36.3A$100.A38.A216.A38.A216.A38.A216.A38.
A!
Re: Star Wars Rule
Posted: October 23rd, 2010, 3:17 pm
by knightlife
Very nice. I especially like your merge circuit at the southern part of the binary counter which makes use of the symmetry of the splitter. At its core is a very small XOR gate with the correct output timing:
Code: Select all
x = 163, y = 16, rule = 345/2/4
45.A49.A49.A$44.3A47.3A47.3A$45.A49.A49.A3$CBA29.CBA47.CB48.CBA$CBA
29.CBA47.CBA47.CBA$45.A49.A49.A$44.3A47.3A47.3A$45.A49.A49.A2$49.A49.
A49.A$48.3A47.3A47.3A$49.A49.A49.A$61.BC47.ABC47.ABC$60.ABC47.ABC47.A
BC!
It can handle p32 glider streams.
I realize you probably already know about this, but I was impressed by how compact the XOR gate is.
I found ways to make a cross, but then I found that the cross could be moved 2x3 cells by hitting it with 3 simple gliders:
Code: Select all
x = 227, y = 107, rule = 345/2/4
10.2C28.2C28.2C28.2C28.2C28.2C28.2C28.2C$10.2B28.2B28.2B28.2B28.2B28.
2B28.2B28.2B$10.2A28.2A28.2A28.2A28.2A28.2A28.2A28.2A13$14.A29.A29.A
29.A29.A29.A29.A29.A$13.3A27.3A27.3A27.3A27.3A27.3A27.3A27.3A$14.A29.
A29.A29.A29.A29.A29.A29.A11$15.2A28.2A28.2A28.2A28.2A28.2A28.2A28.2A$
15.2B28.2B28.2B28.2B28.2B28.2B28.2B28.2B$15.2C28.2C28.2C28.2C28.2C28.
2C28.2C28.2C5$77.2A$43.2A32.2B24.2A$8.2A33.2B32.2C24.2B23.2A$8.2B33.
2C58.2C23.2B$8.2C118.2C28.2A$158.2B38.2A$158.2C38.2B$198.2C21.2A$221.
2B$221.2C16$190.2C28.2C$190.2B28.2B$190.2A28.2A4$9.2C28.2C28.2C$9.2B
28.2B28.2B$9.2A28.2A28.2A7$14.A29.A29.A119.A29.A$13.3A27.3A27.3A117.
3A27.3A$14.A29.A29.A119.A29.A8$9.2A28.2A28.2A$9.2B28.2B28.2B$9.2C28.
2C28.2C$195.2A28.2A$195.2B28.2B$195.2C28.2C2$2A$2B$2C24.2A30.2A$26.2B
30.2B$26.2C30.2C3$195.2A$195.2B$195.2C3$225.2A$225.2B$225.2C!
Two gliders make the new cross and the third is for clean up. The first three in the second row move the cross 3x2 instead of 2x3. The last two in the second row use only 2 tracks instead of 3 tracks.
Picking one of these ways, the following pattern shows how a flip flop or memory cell can be made that has complimentary outputs:
Code: Select all
x = 97, y = 67, rule = 345/2/4
66.2C$66.2B$66.2A14$66.2C$66.2B$66.2A10$89.A2.A2.A$88.9A$89.2A.A.2A$
89.A5.A$88.3A3.3A$89.A5.A$89.A5.A$88.3A3.3A$89.A5.A$89.2A.A.2A$88.9A$
68.A20.A2.A2.A$67.3A$CBA57.CBA5.A$CBA57.CBA2$92.A$91.3A$92.A$92.A$91.
3A$92.A$92.A$91.3A$92.A$92.A$91.3A$92.A9$71.2A$71.2B$71.2C!
The stable output objects are not necessary, but show when a 0 or 1 is read from the memory cell, just as a demo. A read, then flip, then another read is performed. To flip back, three gliders can perform the reverse move of the cross, but they use the same two tracks to do it, which is nice.
What I like about this arangement is that the memory cell can be used to make a glider take a different path in a passive manner, similar to a railroad switch.
Make an infinite memory bank:
Code: Select all
x = 55, y = 19, rule = 345/2/4
46.CBA$46.CBA$20.CA$19.B.B2AB25A$18.C.A.A.C.A.A.A.A.A.A.A.A.A.A.AB2A$
22.A3B2.A2.A.AC.A.C.AB2.BC.A$17.2C2.2C2.A.A.2A4.CB$6.AB11.BC2.B.C.5A
3.C$5.BC.C8.AC4.CA2B.A6.C$2.C3.AB2.ABA3.AB2A.A3.C.C.3C4.C$5.C.A.BC.CB
3.AC2AB4.BA2BABA$.A4.BAC5.C2.A2.2C10.B.3A3.2A$3A7.C2.C.C3A4.B3.ABABCA
C2B.B2.2BA.CBA$.A15.A.4AC2.C.AC.A.A.CAC.C.CA.A.A2.BC.A$AB2CBC10.AB.A.
B.A.A.A.A.A.A.A.A.A.A.A.A.A.A.AB2A$.ABABA10.AC37A$2.A.A12.B$15.C35.CB
A$51.CBA!
Re: Star Wars Rule
Posted: October 23rd, 2010, 5:43 pm
by p46beth
Ah, a plus puffer. Anyways, it was previously shown how a single plus could act as a memory cell , but this was p12, while you have made a stable memory cell!
Additionally, guns of all sufficiently high periods can be build with only pluses and a glider (reflectors and a signal-splitter). So all periods are constructable. The biggest bump I can see for future constructions is that all of the techniques you gave to move a plus require gliders from opposite sides. It would be a lot easier if it could be accomplished from only one direction like in life.
We have also found no way to build spaceships of arbitrarily high periods, or of any speed other than c. But this may be feasible with a UCC based spaceship, given how signals are even simpler to construct than a Herschel track.
Re: Star Wars Rule
Posted: October 23rd, 2010, 8:44 pm
by knightlife
137ben wrote:Anyways, it was previously shown how a single plus could act as a memory cell , but this was p12, while you have made a stable memory cell!
Calcyman used a stable memory cell in his binary counter, the cross is either there or not there to represent a bit. I am amazed his entire binary counter is using stable circuitry and is not dependent on any oscillator period. I would love to see a reaction that moves a cross with gliders from only one direction. So far, no luck finding a simple reaction to do that.
Found a bug!
Code: Select all
x = 84, y = 84, rule = 345/2/4
44.A$43.3A$42.2A.2A$41.2A.A.2A$40.2A.A.A.2A$39.2A.A.A.A.2A$38.2A.A.A.
A.A.2A$37.2A.A.A.A.A.A.2A$36.2A.A.A.A.A.A.A.2A$35.2A.A.A.5A.A.A.2A$
34.2A.A.A.2A3.2A.A.A.2A$33.2A.A.A.2A5.2A.A.A.2A$32.2A.A.A.2A7.2A.A.A.
2A$31.2A.A.A.2A9.2A.A.A.2A$30.2A.A.A.2A11.2A.A.A.2A$29.2A.A.A.2A13.2A
.A.A.2A$28.2A.A.A.2A15.2A.A.A.2A$27.2A.A.A.2A17.2A.A.A.2A$26.2A.A.A.
2A19.2A.A.A.2A$25.2A.A.A.2A21.2A.A.A.2A$24.2A.A.A.2A23.2A.A.A.2A$23.
2A.A.A.2A25.2A.A.A.2A$22.2A.A.A.2A27.2A.A.A.2A$21.2A.A.A.2A29.2A.A.A.
2A$20.2A.A.A.2A31.2A.A.A.2A$19.2A.A.A.2A33.2A.A.A.2A$18.2A.A.A.2A35.
2A.A.A.2A$17.2A.A.A.2A37.2A.A.A.2A$16.2A.A.A.2A39.2A.A.A.2A$15.2A.A.A
.2A41.2A.A.A.2A$14.2A.A.A.2A43.2A.A.A.2A$13.2A.A.A.2A45.2A.A.A.2A$12.
2A.A.A.2A47.2A.A.A.2A$11.2A.A.A.2A49.2A.A.A.2A$10.2A.A.A.2A35.2C14.2A
.A.A.2A$9.2A.A.A.2A36.2B15.2A.A.A.2A$8.2A.A.A.2A37.2A16.2A.A.A.2A$7.
2A.A.A.2A57.2A.A.A.2A$6.2A.A.A.2A59.2A.A.A.2A$5.2A.A.A.2A60.A.A.A.A.
2A$4.2A.A.A.2A61.2A.A.A.2A$3.2A.A.A.2A61.2A.A.A.2A$2.2A.A.A.2A61.2A.A
.A.2A$.2A.A.A.2A61.2A.A.A.2A$2A.A.A.A.A60.2A.A.A.2A$.2A.A.A.2A59.2A.A
.A.2A$2.2A.A.A.2A57.2A.A.A.2A$3.2A.A.A.2A55.2A.A.A.2A$4.2A.A.A.2A53.
2A.A.A.2A$5.2A.A.A.2A51.2A.A.A.2A$6.2A.A.A.2A49.2A.A.A.2A$7.2A.A.A.2A
47.2A.A.A.2A$8.2A.A.A.2A45.2A.A.A.2A$9.2A.A.A.2A43.2A.A.A.2A$10.2A.A.
A.2A41.2A.A.A.2A$11.2A.A.A.2A39.2A.A.A.2A$12.2A.A.A.2A37.2A.A.A.2A$
13.2A.A.A.2A35.2A.A.A.2A$14.2A.A.A.2A33.2A.A.A.2A$15.2A.A.A.2A31.2A.A
.A.2A$16.2A.A.A.2A29.2A.A.A.2A$17.2A.A.A.2A27.2A.A.A.2A$18.2A.A.A.2A
25.2A.A.A.2A$19.2A.A.A.2A23.2A.A.A.2A$20.2A.A.A.2A21.2A.A.A.2A$21.2A.
A.A.2A19.2A.A.A.2A$22.2A.A.A.2A17.2A.A.A.2A$23.2A.A.A.2A15.2A.A.A.2A$
24.2A.A.A.2A13.2A.A.A.2A$25.2A.A.A.2A11.2A.A.A.2A$26.2A.A.A.2A9.2A.A.
A.2A$27.2A.A.A.2A7.2A.A.A.2A$28.2A.A.A.2A5.2A.A.A.2A$29.2A.A.A.2A3.2A
.A.A.2A$30.2A.A.A.5A.A.A.2A$31.2A.A.A.A.A.A.A.2A$32.2A.A.A.A.A.A.2A$
33.2A.A.A.A.A.2A$34.2A.A.A.A.2A$35.2A.A.A.2A$36.2A.A.2A$37.2A.2A$38.
3A$39.A!
Try moving the glider three or five cells to the right.
Re: Star Wars Rule
Posted: October 23rd, 2010, 10:22 pm
by Extrementhusiast
Duplicate a signal:
Code: Select all
x = 32, y = 32, rule = 345/2/4
15.2C10.C.A$15.2B9.B.3A$15.2A8.A.2A.2A$26.2A.2A$25.2A.2A$24.2A.2A$23.
2A.2A$22.2A.2A$21.2A.2A.C$20.2A.2A.B$19.2A.2A.A$18.2A.2A$17.2A.2A$16.
2A.2A$15.2A.2A$14.2A.2A$13.2A.2A$12.2A.2A$11.2A.2A$10.2A.2A$9.2A.2A$
8.2A.2A$7.2A.2A$6.2A.2A$5.2A.2A$4.2A.2A$3.2A.2A$2.2A.2A$.2A.2A$2A.2A$
.3A$2.A!
The original signal (coming from the top right) is undisturbed, as the lower signal comparison shows.
Re: Star Wars Rule
Posted: October 24th, 2010, 1:11 pm
by p46beth
Calcyman used a stable memory cell in his binary counter, the cross is either there or not there to represent a bit. I am amazed his entire binary counter is using stable circuitry and is not dependent on any oscillator period.
I was referring to the memory cell on the first page of this thread, which consists of only a single plus:
Code: Select all
x = 68, y = 79, rule = 345/2/4
6$8.2C8.2C$8.2B8.2B$8.2A8.2A14$8.2C8.2C$8.2B8.2B$8.2A8.2A5$54.2C$54.
2B$54.2A7$8.2C8.2C$8.2B8.2B33.A$8.2A8.2A32.3A$53.A8.ABC$62.ABC7$54.2C
$54.2B$54.2A3$8.2C8.2C$8.2B8.2B$8.2A8.2A2$52.CBA$9.CBA41.A$10.A9.A31.
3A$9.3A7.3A31.A8.ABC$10.A9.A41.ABC!
Calcyman's requires more space and more pluses, but has the advantage of being stable.
Anyways nice bug!
Extreme: the problem with using that reaction is that the duplicated signal moves along the original path. Actually, it could be used to half the period of a signal stream:
Code: Select all
x = 48, y = 45, rule = 345/2/4
3$39.C$38.B.A$37.A.3A$38.2A.2A$37.2A.2A$36.2A.2A$35.2A.2A$34.2A.2A$
26.2C3.C.2A.2A$26.2B2.B.2A.2A$26.2A.A.2A.2A$30.2A.2A$29.2A.2A$28.2A.
2A$27.2A.2A$26.2A.2A$25.2A.2A.C$24.2A.2A.B$23.2A.2A.A$22.2A.2A$21.2A.
2A$20.2A.2A$19.2A.2A$18.2A.2A$17.2A.2A$16.2A.2A$15.2A.2A$14.2A.2A$13.
2A.2A$12.2A.2A$11.2A.2A$12.3A$13.A!
Re: Star Wars Rule
Posted: October 24th, 2010, 8:16 pm
by knightlife
Move or duplicate a plus from one direction:
Code: Select all
x = 137, y = 82, rule = 345/2/4
128.A$113.CBA11.B.B$113.CBA10.2AC3A3.A$122.C.BC.AC3A2.3A$123.ABC.AB.A
4.A27$114.C4.A.A$117.C2AB2A12.A$CBA31.CBA31.CBA43.BCAB.AB2A11.3A$CBA
31.CBA31.CBA43.C.ABC.A14.A28$135.A$85.C48.3A$83.B4.A30.C4.A.A8.A$83.
2C.B4A31.C2AB2A$83.AB.AC3A28.BCAB.AB2A$80.C2.BC.AB.A29.C.ABC.A$48.CBA
$48.CBA11$27.CBA18.CBA$27.CBA18.CBA!
These techniques all "pull" on the plus to make a new one (2x3, 3x2, 7x2).
Not easy to make that p4 spaceship from gliders... Or is it?
EDIT:
These are the "pull by 2" versions:
Code: Select all
x = 109, y = 60, rule = 345/2/4
5.BC.ABC.A78.C.ABC.A$6.C2.A.AB2A76.BCAB.AB2A$8.2B.4A79.C2AB2A$8.AC.C.
A77.C4.A.A8.A$10.B95.3A$107.A7$5.CBA$5.CBA27$5.BC.ABC.A78.C.ABC.A$6.C
2.A.AB2A76.BCAB.AB2A$8.2B.4A79.C2AB2A$8.AC.C.A77.C4.A.A8.A$10.B95.3A$
107.A13$CBA$CBA!
Re: Star Wars Rule
Posted: October 25th, 2010, 7:30 pm
by Extrementhusiast
Alternate reader:
Code: Select all
x = 14, y = 14, rule = 345/2/4
3.2C$3.2B$3.2A7$C$B.A$4A$2.A8.ABC$11.ABC!
Or:
Code: Select all
x = 13, y = 14, rule = 345/2/4
2.2C$2.2B$2.2A8$.A$3A$.A.A6.ABC$.CB7.ABC!
They use the same two gliders in the same two positions as in the set/reset mechanism. BTW, the set reaction makes a counterclockwise orbiter, while the reset reaction destroys a
clockwise orbiter. Here is a fix:
Code: Select all
x = 14, y = 14, rule = 345/2/4
3.2C$3.2B$3.2A8$C.A$B3A$A.A8.ABC$11.ABC!
Or, if you don't need/want the spark:
Code: Select all
x = 14, y = 14, rule = 345/2/4
3.2C$3.2B$3.2A8$2.A$C3A$B.A8.ABC$.A9.ABC!
Yet another way:
Code: Select all
x = 14, y = 14, rule = 345/2/4
3.2C$3.2B$3.2A8$2.A$.3[code]
A$C.A8.ABC$.BA8.ABC!
[/code]
And another:
Code: Select all
x = 13, y = 14, rule = 345/2/4
2.2C$2.2B$2.2A8$.A$3A$.A8.ABC$CBA7.ABC!
"Re-periods" the oscillator:
Code: Select all
x = 13, y = 14, rule = 345/2/4
2.2C$2.2B$2.2A8$.A$4A$.A.B6.ABC$2.C7.ABC!
Note that all of these use the same two gliders in the same position relative to the cross! Only the orbiter is in a different position. Here is a single-glider reflector that advances the orbiter by two generations:
Code: Select all
x = 13, y = 5, rule = 345/2/4
.AB$.A.C$3A$.A8.ABC$10.ABC!
This advances the orbiter one generation cleanly:
Code: Select all
x = 13, y = 5, rule = 345/2/4
ABC$.A$3A$.A8.ABC$10.ABC!
This retreats the orbiter one generation cleanly:
Code: Select all
x = 14, y = 5, rule = 345/2/4
.C$B.A$4A$2.A8.ABC$11.ABC!
Re: Star Wars Rule
Posted: October 25th, 2010, 8:43 pm
by ssaamm
180 degree reflector:
Code: Select all
x = 9, y = 21, rule = 345/2/4
4.A.BA$2.C.3A$2.B2A.2AC$2.A.3A.B$3.A.A.A$4.BC13$2A$2B$2C!
Re: Star Wars Rule
Posted: October 26th, 2010, 12:24 am
by Extrementhusiast
137ben wrote:
Extreme: the problem with using that reaction is that the duplicated signal moves along the original path. Actually, it could be used to half the period of a signal stream:
(pattern)
It could be used for more than that. If we can make a memory cell, we can make the inverse of that data with that reaction.
Re: Star Wars Rule
Posted: October 26th, 2010, 7:39 am
by Awesomeness
Okay, I get b0, b1, and b2 now. I understand c as well. We require a binary counter to find b0, b1, and b2. Can we read it as of now? Can we clear it? And can we make it count up x times and stop? That's what I assume we'll need.
But what about c' = b1 AND NOT(b2) AND (b0 OR c)? It seems to be missing parentheses to me. It's like saying p AND q AND r. Is the q being fed into both gates or something? It'd be easier if you'd fully parenthesize it even when it's unnecessary, because I'm incompetent.
Once I know exactly what it means I can get started right away.
Re: Star Wars Rule
Posted: October 26th, 2010, 8:02 am
by p46beth
AND is associative--p AND q AND r= (p AND q) AND r= p AND (q AND r)
so it doesn't matter that he left out those parenthesis.
Re: Star Wars Rule
Posted: October 26th, 2010, 11:17 am
by apg
Okay, that's:
c' = (b1 AND NOT(b2)) AND (b0 OR c)
or:
c' = b1 AND (NOT(b2) AND (b0 OR c))
And if that's not clear enough, I've made a Boolean logic-circuit diagram. c' is the final state of the cell; c is the initial state.
Re: Star Wars Rule
Posted: October 26th, 2010, 11:38 am
by apg
As for the b0, b1, b2, the following neighbour counts correspond to the following values:
Code: Select all
sigma(n) = 0, b0 = 0, b1 = 0, b2 = 0;
sigma(n) = 1, b0 = 1, b1 = 0, b2 = 0;
sigma(n) = 2, b0 = 0, b1 = 1, b2 = 0;
sigma(n) = 3, b0 = 1, b1 = 1, b2 = 0;
sigma(n) = 4, b0 = 0, b1 = 0, b2 = 1;
sigma(n) = 5, b0 = 1, b1 = 0, b2 = 1;
sigma(n) = 6, b0 = 0, b1 = 1, b2 = 1;
sigma(n) = 7, b0 = 1, b1 = 1, b2 = 1;
sigma(n) = 8, b0 = 0, b1 = 0, b2 = 0.
Clearly, b0 = (n1 XOR n2 XOR n3 XOR n4 XOR n5 XOR n6 XOR n7 XOR n8). The expressions for the other binary digits are not so compact, and a binary counter would be more efficient than using purely Boolean logic gates.
Re: Star Wars Rule
Posted: October 26th, 2010, 6:22 pm
by Awesomeness
Is this correct?
Code: Select all
x = 106, y = 121, rule = 345/2/4
64.C4.4C$64.C7.C$64.C7.C$64.4C.4C$64.C2.C.C$57.2C5.C2.C.C$57.2B5.4C.
4C$57.2B7$50.C4.2C$50.C5.C$42.2C6.C5.C$42.2B6.4C2.C$42.2B6.C2.C2.C$
50.C2.C2.C$50.4C2.C25$13.C4.4C$13.C4.C2.C$13.C4.C2.C$13.4C.C2.C$13.C
2.C.C2.C$13.C2.C.C2.C$13.4C.4C9$16.2C$16.2B$16.2B2$3C$C$C$3C18.A$20.
3A$21.A3$4.C2B$4.C2B$20.A2.A2.A2.A2.A2.A$19.18A$20.A2.A2.A2.A2.A2.A$
20.A2.A2.A2.A2.A2.A$19.18A$20.A14.A42.A25.A$77.3A2.A2.A2.A2.A2.A2.A2.
A2.3A$25.A2.A2.A46.A.23A.A$14.A9.9A46.2A.A2.A2.A2.A2.A2.A2.A.2A$13.3A
9.A5.A47.A12.CBA8.A$14.A10.A5.A46.3A21.3A$24.2A5.2A46.A23.A$18.A6.A4.
2A47.A23.A$17.3A2BC2.A3.2A47.3A21.3A$18.A.2BC.6A49.A23.A$25.A2.A50.A
23.A$18.2C22.2C34.3A21.3A$18.2B22.2B35.A23.A$18.2B22.2B35.A23.A$78.3A
21.3A$79.A23.A$64.A2.A2.A2.A5.A15.A2.A4.A$63.18A13.6A3.2A$64.A11.A2.A
13.2A3.A4.A$92.2A4.A4.A$20.A20.A49.2A5.2A3.2A$19.24A24.A2.A2.A18.A5.A
4.A$20.A2.A2.A2.A2.A2.A2.A2.A24.9A17.A5.A4.A$30.2C22.2C11.A5.A17.9A3.
2A$30.2B22.2B11.A5.A18.A2.A2.A4.A$30.2B22.2B10.2A5.2A28.A$67.A4.2A28.
3A$67.A3.2A7.A2.A2.A16.A$32.A20.A12.6A7.9A$31.24A12.A2.A9.A5.A$32.A2.
A2.A2.A2.A2.A2.A2.A26.A5.A$79.2A5.2A$80.2A4.A$81.2A3.A$82.6A$83.A2.A
5.A$91.3A$92.A$77.A11.A.2A$76.16A.A$77.A2.A2.A2.A5.3A$93.A!
I modeled it after (c OR b0) AND b1 And NOT(b2), which I believe is equivalent.
EDIT: I forgot to tell you it's p100 because of the NOT gate.
EDIT: I have confirmed this is correct. Now, we need to modify the binary counter to be readable after counting x times. We also need to establish a size for the metacell.
Re: Star Wars Rule
Posted: October 29th, 2010, 9:45 am
by knightlife
There is a smaller OR gate that I did not post yet. I use it here to shrink the set of gates. Also the separate NOT gate is not necessary:
Code: Select all
x = 60, y = 70, rule = 345/2/4
39.C4.2C$39.C5.C$39.C5.C$31.2C6.4C2.C$31.2B6.C2.C2.C$31.2A6.C2.C2.C$
39.4C2.C6$13.C4.4C$13.C4.C2.C$13.C4.C2.C$13.4C.C2.C$13.C2.C.C2.C$13.C
2.C.C2.C$13.4C.4C9$16.2C$16.2B$16.2A$51.C4.4C$3C48.C7.C$C43.2C5.C7.C$
C43.2B5.4C.4C$3C18.A22.2A5.C2.C.C$20.3A28.C2.C.C$21.A29.4C.4C3$4.CBA$
4.CBA$20.A2.A2.A$19.9A$20.A2.A2.A$23.A2.A$23.5A$23.2A.A$6.A16.A$5.3A
14.3A$6.A16.A2$10.A8.A$9.3A2BC3.3A$10.A.2BC4.A2$10.2C19.2C$10.2B19.2B
$10.2B19.2B6$45.A$12.A17.A13.3A$11.21A13.A$12.A2.A2.A2.A2.A2.A2.A$16.
2C31.A$16.2B30.3A$16.2B31.A!
The OR gate has the same input structure but the output is generated faster than the larger OR gate. Also note that the gun is not necessary since I made a true 3-input gate with the function A AND B AND (NOT C):
Code: Select all
x = 64, y = 17, rule = 345/2/4
.C6.2C27.C9.2C$C.C5.C.C25.C.C8.C.C$3C5.2C26.3C8.2C$C.C5.C.C25.C.C8.C.
C$C.C5.2C26.C.C8.2C2$.2C$.2B5.2C27.2C8.2C$.2A5.2B27.2B8.2B$8.2A27.2A
8.2A3$22.3C36.3C$2.A5.A13.C15.A8.A13.C$.9A7.ABC2.C14.12A7.ABC2.C$2.A
2.A2.A8.ABC2.C15.A2.A2.A2.A8.ABC2.C$22.3C36.3C!
The smaller one has a one cell offset in the A and B inputs.
Re: Star Wars Rule
Posted: November 7th, 2010, 7:23 am
by knightlife
This OR gate is small but still has a fairly slow recovery time. It can handle p32 glider streams:
Code: Select all
x = 23, y = 15, rule = 345/2/4
21.A$20.3A$21.A2$11.A2.A2.A$10.9A$CBA8.A5.A$CBA5$9.2A$9.2B$9.2C!
Then I found this one that fits in a 9x10 bounding box and can handle p23 glider streams:
Code: Select all
x = 139, y = 38, rule = 345/2/4
31.A49.A49.A$30.3A47.3A47.3A$31.A49.A49.A2$35.A49.A49.A$34.3A47.3A47.
3A$35.A49.A49.A$33.2A.2A45.2A.2A45.2A.2A$32.7A43.7A43.7A$CBA20.CBA7.A
3.A12.CBA20.CB8.A3.A12.CBA20.CBA7.A3.A$CBA20.CBA24.CBA20.CBA24.CBA20.
CBA2$32.A49.2A48.2A$32.2B48.2B48.2B$32.2C48.2C48.2C21$32.2A48.2A48.2A
$32.2B48.2B48.2B$32.2C48.2C48.2C!
This reaction I found is perfect for a T flip-flop:
Code: Select all
x = 25, y = 48, rule = 345/2/4
15.2C$15.2B$15.2A$10.CBA$10.CBA2$23.A$CBA19.3A$CBA20.A7$15.2A$15.2B$
15.2C13$15.2C$15.2B$15.2A$10.CBA$10.CBA2$23.A$CBA19.3A$CBA11.A8.A$13.
3A$14.A5$15.2A$15.2B$15.2C!
The top reaction creates a plus and the bottom reaction deletes it but with a carry out. However, the glider positions are identical!
Here is a 4-bit binary ripple counter making use of the reactions, counting each incoming glider:
Code: Select all
x = 1327, y = 98, rule = 345/2/4
1030.A30.A$1029.3A28.3A47.A30.A$1030.A30.A47.3A28.3A47.A30.A$1110.A
30.A47.3A28.3A47.A30.A$1007.A26.A22.A132.A30.A47.3A28.3A$1006.3A24.3A
20.3A28.A26.A22.A132.A30.A$1007.A26.A22.A28.3A24.3A20.3A28.A26.A22.A$
1087.A26.A22.A28.3A24.3A20.3A28.A26.A22.A$1011.A155.A26.A22.A28.3A24.
3A20.3A$1010.3A78.A155.A26.A22.A$1011.A78.3A78.A$1035.A55.A78.3A78.A$
1034.3A21.A56.A55.A78.3A$1035.A21.3A54.3A21.A56.A55.A$1058.A56.A21.3A
54.3A21.A56.A$1039.A98.A56.A21.3A54.3A21.A$1038.3A78.A98.A56.A21.3A$
1039.A78.3A78.A98.A$1119.A78.3A78.A$1199.A78.3A$1044.A234.A$1043.3A
78.A$1044.A78.3A78.A$1124.A78.3A78.A$1048.A155.A78.3A$1047.3A78.A155.
A$1048.A78.3A78.A$1128.A78.3A78.A$1208.A78.3A$1288.A3$1039.A9.A$1038.
3A7.3A68.A9.A$1039.A9.A68.3A7.3A68.A9.A$1119.A9.A68.3A7.3A68.A9.A$
1035.A17.A145.A9.A68.3A7.3A$1034.3A15.3A60.A17.A145.A9.A$1035.A17.A
60.3A15.3A60.A17.A$1115.A17.A60.3A15.3A60.A17.A$1195.A17.A60.3A15.3A$
1025.A249.A17.A$1004.A7.A11.3A78.A$1003.3A5.3A11.A58.A7.A11.3A78.A$
1004.A7.A70.3A5.3A11.A58.A7.A11.3A78.A$1084.A7.A70.3A5.3A11.A58.A7.A
11.3A$1016.A18.A128.A7.A70.3A5.3A11.A$CBA139.CBA139.CBA139.CBA139.CBA
139.CBA139.CBA139.CBA18.3A16.3A59.A18.A128.A7.A$CBA139.CBA139.CBA139.
CBA139.CBA139.CBA139.CBA139.CBA19.A18.A30.A7.C2B18.3A16.3A59.A18.A$
1025.A20.A18.3A6.C2B19.A18.A30.A7.C2B18.3A16.3A59.A18.A$1024.3A12.A5.
3A18.A38.A20.A18.3A6.C2B19.A18.A30.A7.C2B18.3A16.3A48.A$1025.A12.3A5.
A57.3A12.A5.3A18.A38.A20.A18.3A6.C2B19.A18.A30.A7.C2B7.3A$1039.A65.A
12.3A5.A57.3A12.A5.3A18.A38.A20.A18.3A6.C2B8.A$1029.A89.A65.A12.3A5.A
57.3A12.A5.3A18.A$1028.3A78.A89.A65.A12.3A5.A$1029.A78.3A78.A89.A$
1109.A78.3A78.A$1189.A78.3A$1269.A14$1029.A10.A$1028.3A8.3A67.A10.A$
1029.A10.A67.3A8.3A67.A10.A$1109.A10.A67.3A8.3A67.A10.A$1025.A18.A
144.A10.A67.3A8.3A$1024.3A16.3A59.A18.A144.A10.A$1025.A18.A59.3A16.3A
59.A18.A$1105.A18.A59.3A16.3A59.A18.A$1185.A18.A59.3A16.3A$1058.A206.
A18.A$1057.3A78.A$1058.A78.3A78.A$1138.A78.3A78.A$1218.A78.3A$1298.A
2$1016.A40.A$1015.3A38.3A37.A40.A$1016.A40.A37.3A38.3A37.A40.A$1096.A
40.A37.3A38.3A37.A40.A$1012.A48.A114.A40.A37.3A38.3A$1011.3A46.3A29.A
48.A114.A40.A$1012.A48.A29.3A46.3A29.A48.A$1092.A48.A29.3A46.3A29.A
48.A$1172.A48.A29.3A46.3A$1252.A48.A!
There are splitters and reflectors, but no merge circuits are needed. The same four gliders are produced by every input glider, simplifying construction quite a lot.
Input timing can be irregular because it is a stable design, although the example has even spacing for the input stream.
This counter still needs a readout, but is messy to implement. I like the previous idea of moving the plus because the read operation is almost completely independent.
So I went back to the "railroad switch" idea I posted earlier in this thread, having abandoned it when a simple flip-flop was quite a chore to implement. I made a flip-flop but it was not pretty. I think I found a way to move the plus that makes things easier, especially when a readout and a master reset are also needed to make a metacell. Still working on that one.
Just two spaceships from one direction can move the plus, but making use of this is difficult:
Code: Select all
x = 24, y = 5, rule = 345/2/4
10.ABC.AB.A4.A$9.C.BC.AC3A2.3A$CBA10.2AC3A3.A$CBA11.B.B$15.A!
One way to make that p4 spaceship with 5 gliders:
Code: Select all
x = 71, y = 13, rule = 345/2/4
CBA$CBA36.CBA$39.CBA3$45.CBA18.ABC$45.CBA18.ABC5$68.ABC$68.ABC!
Still too many gliders.
Can it be done with fewer gliders?
Curio:
Code: Select all
x = 30, y = 26, rule = 345/2/4
20.2C$20.2B$20.2A6$19.A2.A$18.6A$19.A2.A$16.A.2A2.2A.A$15.12A$16.A2.A
2.A2.A$13.A.2A2.A2.A2.2A.A$12.18A$CBA10.A2.A2.A2.A2.A2.A$CBA10.A2.A2.
A2.A2.A2.A$12.18A$13.A.2A2.A2.A2.2A.A$16.A2.A2.A2.A$15.12A$16.A.2A2.
2A.A$19.A2.A$18.6A$19.A2.A!
Doesn't quite have the right timing but can be made into a "delay by one tic" gate that can be controlled. Larger and smaller versions work also.