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period54

Hello!

I have been exploring a certain large family of cellular automata that, in a sense, generalize order statistics. The core idea is that we can construct a cellular automaton in which the transition function is simply the minimum of the inputs. Such a minimum CA is not very interesting on its ...

period54

First oscillator with period 3 in this rule:

Code: Select all

x = 9, y = 11, rule = BTCA1
3.2B$3.2B2$4.A$2B.3A$2B2.A2.2B$3.3A.2B$4.A2$4.2B$4.2B!

period54

Six more new oscillators:

x = 175, y = 23, rule = BTCA1
63.2A26.3A7.A$35.3A61.3A$37.A24.5A25.A7.3A$37.A62.A$5.A22.2B33.4A$2.B
2.A21.2BAB108.A33.A$3B2.A22.BA2B93.B3.A7.3A31.3A$2.B.AB.A20.3A2B32.3B
55.B.B3.A8.3A31.3A$3.4A22.2BA2B30.B3AB29.2B25.B2.3A7.A33.A$4.3A2.B17.
4B3AB28.3B32.3B50.A$5.A2.2B16 ...

period54

Great patterns, knightlife. I really like the reflector.

Here is some more new stuff:

Gun that produces two gliders:

x = 40, y = 46, rule = BTCA1
7$29.A$27.3A$28.3A$28.A5$23.A$23.3A$22.3A$24.A6.B$29.B.B.B2$28.2B3.2B
2$29.B.B.B$31.B3$12.A$10.3A$11.3A$11.A2$3.A$3.3A10.B$2.3A9.B.B.B$4.A
26.A$13 ...

period54

4 new oscillators:

x = 64, y = 10, rule = BTCA1
3.A36.B3.B16.2B$2.3A12.A11.A10.B3.B12.2B2.2B$.4A12.3A7.3A8.3B3.3B10.
2B$4A12.3A2.5B2.3A10.3A16.4A$.2A15.A2.5B2.A12.3A15.4A$7.2A12.5B15.3A
12.2B.2AB$6.4A13.B14.3B3.3B9.2B.2A$5.4A31.B3.B14.A$5.3A32.B3.B$6.A!

A new puffer:

x = 15, y = 15, rule ...

period54

I've found a gun that produces small gliders.

Code: Select all

x = 32, y = 32, rule = BTCA1
26.A$26.3A$25.3A$27.A5$22.A$20.3A$21.3A$21.A$28.3B$27.2BA2B$27.BABAB$
27.2BA2B$28.3B4$9.A$9.3A$8.3A$10.A2$2.A23.A$3A22.2A$.3A9.3B11.A$.A10.
2BA2B$12.BABAB$12.2BA2B$13.3B!

period54

Some new patterns:

3 flotillas:
x = 52, y = 13, rule = BTCA1
$29.3B17.3B$8.3B17.3B17.3B$7.3B18.3B17.3B$7.3B18.B19.B$7.B16.4A19.A$
24.3A18.4A$6.3A15.3A18.2ABA$5.4A15.A19.2AB2A$.3B.3AB12.3B17.3B.3A$3B
2.2AB.2A9.3B17.3B6.A$3B5.A11.3B17.3B$B7.A11.B19.B!

4 oscillators:

x = 54, y = 9, rule = BTCA1 ...

period54

So, I made something similar to sliding block memory. It is extremely ugly and practically useless, but at least it works, and probably proves that this rule is Turing complete.

Construction:

x = 2815, y = 2943, rule = BTCA1
15.3B$14.3B$14.3B$14.B$11.3A5.3B$11.3A4.3B$11.3A4.3B$8.3B7.B$7.3B13.
3B ...

period54

Some glider-producing puffers (periods: 1024, 512, 256 and 128):

x = 1471, y = 2376, rule = BTCA1
1352.3B$1351.3B$1351.3B$1351.B$1348.3A5.3B$1348.3A4.3B$1348.3A4.3B$
1345.3B7.B$1344.3B13.3B$1344.3B12.3B$1344.B14.3B$1341.3A5.3B7.B$1341.
3A4.3B13.3B$1341.3A4.3B12.3B$1338.3B7.B14.3B$1337.3B13.3B7.B ...

period54

I've found another very interesting rule:

@RULE Asymmetric11

# 000000++00--00000
# 000--00000-000000
# 00000000000000000

@COLORS
0 0 0 0
1 32 64 255
2 255 64 32

@TREE
num_states=3
num_neighbors=8
num_nodes=66
1 0 0 0
1 0 2 0
2 0 1 0
2 1 1 0
1 1 1 0
2 0 0 4
3 2 3 5
2 1 0 1
3 3 7 2
1 0 1 0
2 4 ...

period54

Yeah, also you can make huge and extremely messy puffers by combining "engines".

x = 684, y = 684, rule = BTCA1
673.3B$672.3B$672.3B$672.B$669.3A5.3B$669.3A4.3B$669.3A4.3B$666.3B7.B
$665.3B13.3B$665.3B12.3B$665.B14.3B$662.3A5.3B7.B$662.3A4.3B$662.3A4.
3B$659.3B7.B$658.3B$658.3B$658.B$655.3A5.3B ...

period54

And another puffer.

Code: Select all

x = 15, y = 19, rule = BTCA1
8.3B$7.3B$7.3B$7.B$4.3A5.3B$4.3A4.3B$4.3A4.3B$.3B7.B$3B$3B$B$5.3B$4.
3B$4.3B$4.B$9.3B$8.3B$8.3B$8.B!

period54

First puffer discovered in this rule!

Code: Select all

x = 12, y = 12, rule = BTCA1
10.B$9.3B$8.3BA$9.BA2$7.2A$6.4A$5.3A2B.A$2.B2.2AB2A$.3B2.AB2A$3BA$.BA
4.A!

period54

Yet another 10 cell methuselah. Lives 184420 generations, three times more than previous.

Code: Select all

x = 19, y = 16, rule = BTCA1
17.2A$17.2A$17.A$17.A10$A$.2A$.A!

period54

I have found a few more interesting rules:

A rule with a very common oblique puffer:

@RULE Asymmetric6

# 000+-00+000-000+0
# 000+00000--00----
# 000+0+--0-0--0-0-

@COLORS
0 0 0 0
1 32 64 255
2 255 64 32

@TREE
num_states=3
num_neighbors=8
num_nodes=74
1 0 0 0
1 0 2 1
1 1 0 1
2 0 1 2
1 0 0 1
2 1 ...

period54

There are lots of very interesting asymmetric rules in this family.

Here are few interesting examples:

@RULE Asymmetric1

# +000-0+00000000+-
# 000+00000-0-----0
# 0+0000-++00+0000-

@COLORS
0 0 0 0
1 32 64 255
2 255 64 32

@TREE
num_states=3
num_neighbors=8
num_nodes=74
1 0 0 2
1 1 0 0
2 0 0 1 ...

period54

And another: 10 cells, 59529 generations.

Code: Select all

x = 5, y = 6, rule = BTCA1
2.3B$3.B$.B$.B$2B$.2B!

period54

Another methuselah: 15 cells, stabilizes in 76708 generations. Curiously, it lacks symmetry.

x = 3, y = 6, rule = BTCA1
.B$3B$3B$3B$BAB$.2B!

It seems to be relatively common. My search program found three random soups that produce it.

Yeah, it looks tricky to put one glider that close behind ...

period54

A 23 cell pattern in this rule that takes 62087 generations to stabilize.

Code: Select all

x = 25, y = 10, rule = BTCA1
13B6$22.3B$21.3B$21.3B$21.B!

period54

When you say you can make a sliding block memory, does that mean you can hook up logic circuits to it to push, pull or check for zero location of the block?

No, that's my problem. Only way to push block I've found requires two gliders to be very close when colliding with it. I haven't found a way ...

period54

I have found a CA that can emulate any logic circuits using glider guns. I can make sliding block memory, but I haven't found a way to build a gun that produces stream of gliders needed to move a block.
Do I need to find a explicit way to build a block-moving gun to prove computational universality ...

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Metamaterial: 31 state Von Neumann neighborhood CA

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