Various kinds of universality

[BokaBB]

Hey ya. This is supposed to be a continuation of this discussion: viewtopic.php?f=12&t=5937#p157199

Feel free to join.

Quoting you so you see this, I'm really sorry, please!

Hey, I think I agree on this. Still, there are certainly exceptions, like the rule B/S.

[BokaBB]

Hey ya. I'm sorry, but do you think this rule by me, Building Plan, can be universal? It can't escape its bounding diamond but nevertheless there's really complex stuff going on inside.
FLASHING WARNING

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x = 516, y = 577, rule = 234-ceyz5a8/3-ae4-q5-ciy7c8/6
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A6.A40.2A3.2A6.A8.A5.2A11.A.A11.A35.A31.A6.A16.A20.A$199.2A48.2A2.A5.
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39.2A3.A14.A.A13.A5.2A5.A2.3A8.A2.A.A39.A31.A3.A17.A22.A$186.A51.2A4.
A4.A39.A4.A14.A3.A12.A4.3A5.A2.2A.A7.A2.A.A39.A31.A3.A17.A22.A$185.A
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A$168.A53.A7.A4.A29.3A3.2A9.2A.A17.A6.2A2.A2.2A2.A2.A2.A.A5.2A.2A.2A.
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A10.25A16.2A2.8A2.A3.2A3.4A.2A4.A2.3A.A5.2A34.A36.A2.A16.A24.A$165.A
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32.A36.A2.A16.A24.A$164.A50.A11.A.A25.4A5.2A4.4A2.A4.A16.A2.A17.A2.A
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161.A48.A13.2A16.3A3.6A5.A10.A7.A16.A3.A9.A7.A2.A3.A3.2A.A4.5A.A.A2.A
7.6A2.A16.A23.A34.A5.A14.A24.A$160.A48.A13.2A15.2A4.5A7.A10.A7.A17.A
2.A10.A7.A.A4.A3.4A5.3A.A2.A2.A7.8A.A16.2A21.A34.A5.A14.A24.A$160.A
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5.A14.A24.A$158.A46.A15.2A9.2A2.2A5.3A8.A11.A9.A16.A3.A13.A4.A.A4.A5.
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A$154.A44.A18.2A3.2A11.4A9.7A3.A12.A16.A4.8A11.4A4.A5.A4.4A.A.3A.A.2A
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152.A42.A20.2A2.A11.7A8.A7.2A14.A15.A5.2A11.2A5.2A.A3.A5.A6.3A3.2A2.A
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27.A$150.A41.A16.2A4.2A2.3A6.A2.2A2.A8.A7.A16.A15.A5.2A19.2A2.A2.A5.A
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A2.A.A2.A2.2A.A.A.A2.A6.2A2.A.2A18.A.A10.A13.A3.A27.A9.A10.A27.A$145.
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12.A9.A4.A25.A9.A10.A28.A$142.A40.A4.2A6.2A2.A7.2A6.A.A6.A8.5A23.A8.
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8.A5.A24.A10.A9.A28.A$141.A41.A3.A6.2A3.A8.A6.A.A7.A4.5A.54A17.A5.A.A
2.3A.A.A2.A3.A4.A.4A.2A3.A5.A4.4A20.A3.A13.A7.A6.A23.A10.A9.A29.A$
141.A40.A3.A5.2A4.A8.2A5.A.A7.A.4A3.4A24.A2.3A9.A8.A.A2.2A15.A5.A.A2.
3A.A.A2.A2.2A4.2A3.2A.A3.A5.A4.A.2A20.A4.A13.2A5.A6.A23.A10.A9.A29.A$
140.A41.A.2A5.A4.2A9.A5.A.A7.3A3.4A.A25.4A11.A9.A.A4.2A12.A6.2A3.A.A.
2A2.A3.A.A3.2A3.4A3.A5.A4.A.2A21.A3.A15.A4.A7.A22.A10.A9.A29.A$139.A
41.A.A5.2A4.A10.2A5.2A6.3A2.3A2.A.A23.4A14.A8.A.A7.2A10.A5.A.A3.4A.A
2.A3.A2.A2.2A4.A.2A2.A5.A4.A.2A21.A4.A15.A4.A7.A21.A10.A9.A29.A$139.A
40.3A4.2A5.A11.A5.2A4.3A.4A4.A.A21.3A2.A14.A9.A.A9.2A7.2A5.A.A3.5A2.A
3.A3.A2.2A4.3A.2A6.A4.A.3A20.A5.A15.2A2.A8.A20.A11.A9.A28.A$138.A41.A
4.2A6.A11.2A4.2A3.2A.3A8.A.A17.4A5.A13.A9.A.A12.2A5.A5.A2.A3.A.3A2.A
3.A4.A.2A4.3A2.2A5.A3.A2.2A.A19.A5.A17.A.A8.A20.A11.A9.A28.A$137.A40.
2A4.A6.2A12.A5.A.6A.A8.A.A15.3A8.A14.A9.A.A14.2A3.A5.A.A4.A.2A2.A4.A
4.A.2A4.3A2.A.2A3.A3.A2.2A.A20.A5.A17.2A9.A19.A11.A9.A28.A$137.A39.2A
3.2A6.A13.2A4.5A5.A7.A2.A11.4A11.A13.A9.A2.A16.4A5.A.A4.A.2A2.A3.A6.
3A4.2A3.A3.A2.A3.A2.2A2.A19.A6.A17.A10.A18.A11.A9.A28.A$136.A39.A.A.
2A7.A14.A3.3A8.A7.A2.A9.3A14.A13.A10.A.A19.3A3.A2.A3.2A.2A.A4.A7.2A4.
3A2.A4.3A3.A2.2A2.A19.A6.A17.3A8.A18.A12.A8.A28.A$135.A38.2A.3A8.A14.
6A9.A8.A2.A6.3A17.A13.A10.A.A18.2A2.2A.A.A4.2A.2A.A4.A7.2A3.4A2.A6.A
3.A2.2A3.A18.A7.A16.A2.A8.A17.A12.A8.A28.A$135.A37.A2.2A8.2A12.5A2.2A
9.A7.A2.A3.4A19.A13.A10.A2.A18.2A4.2A.A4.6A4.A9.A3.4A2.A6.2A2.A2.2A3.
A19.A6.A16.A3.A8.A16.A12.A8.A27.A$134.A36.2A2.2A8.A11.6A3.2A9.A7.A2.A
2.2A23.A13.A10.A.A18.2A5.A.2A3.A.2A.2A4.A9.2A2.4A2.A6.A.3A2.2A4.A18.A
7.A15.A4.A8.A15.A12.A8.A27.A$134.A35.A2.3A8.A10.5A2.A2.2A9.A7.A3.3A
24.A13.A10.A2.A18.2A5.A.A.2A.A.2A.A5.A9.2A2.5A.A6.A3.A2.2A4.A18.A8.A
14.A5.2A6.A15.A12.A8.A27.A$133.A35.A.2A.A8.A9.4A4.A2.2A9.A7.A3.2A23.
14A2.A11.A2.A18.2A4.A2.A3.2A.2A.A4.A10.A.A.3A.A.A6.A2.A.A.2A5.A17.A8.
A14.A7.A6.A14.A13.A7.A27.A$132.A35.A.A3.A8.A7.4A6.A.A.A9.A7.A.27A2.A
11.3A11.A.A18.2A5.A2.A3.A.4A.A3.A10.A2.4A.A.A6.A2.A2.3A5.A18.A8.A13.A
8.A6.A13.A13.A7.A27.A$132.A34.3A3.A8.A6.4A7.A.A.A7.15A26.A13.A.3A7.A
2.A18.2A5.A.A4.A.2A.3A2.A10.2A2.4A.A.A6.A2.A3.2A6.A17.A9.A12.A9.2A4.A
13.A13.A7.A27.A$131.A34.2A4.A8.A5.4A9.2A.A6.2A.A7.2A3.A26.A12.A5.2A5.
A.A18.A.A4.A2.A3.A2.2A.A.2A.A10.2A3.A.A.3A6.A2.A3.3A5.A17.A9.A12.A11.
A4.A12.A13.A7.A27.A$130.A33.2A6.A8.A2.3A.A10.2A2.A4.2A3.A5.2A4.A26.A
13.A7.3A.A2.A18.2A5.A2.A3.A.A.2A2.A.2A10.2A3.A.A2.2A6.A2.A3.2A.2A3.A
17.A10.A11.A12.2A3.A11.A13.A7.A27.A$130.A32.2A6.A8.A.2A2.2A11.A2.A2.
3A4.A4.2A.A3.A27.A12.A11.3A.A18.2A4.A2.A3.A2.A.2A2.A.A.2A8.2A2.4A2.2A
6.A2.A3.2A3.A3.A17.A10.A10.A14.A3.A10.A14.A6.A27.A$129.A32.2A6.A8.3A
2.2A12.A2.A.2A6.A3.2A2.A4.A26.A13.A11.A2.3A16.2A5.A2.A3.A.A.2A3.A.A3.
2A6.2A2.4A2.2A5.A3.A3.2A4.A2.A17.A10.A10.A15.A2.A10.A14.A5.A28.A$128.
A32.2A7.A7.2A2.2A12.3A.3A8.A.2A3.A4.A27.A12.A12.A2.A2.3A13.2A5.A2.A2.
A2.A.2A4.2A5.2A4.A.A.4A2.2A5.A3.A3.2A4.A3.A16.A11.A9.A16.2A.A9.A14.A
5.A28.A$128.A31.2A7.A6.3A2.A13.A.4A9.3A4.A5.A26.A12.A13.A2.A5.3A9.A.A
4.A3.A2.A.A2.A5.A8.2A2.A.A.4A2.2A5.A2.A4.2A5.A2.A16.A11.A9.A18.2A9.A
14.A5.A28.A$127.A31.2A7.A5.2A.A.2A13.A.2A.A9.2A5.A5.A26.A13.A12.A2.A
9.2A7.2A5.A2.A3.A.A2.A5.A10.A.A.A.4A2.2A5.A2.A4.2A5.A3.A16.A11.A8.A
19.2A7.A15.A5.A28.A$127.A30.2A8.A2.3A3.2A14.4A.A8.2A7.A5.A26.A12.A13.
A2.A11.3A4.2A4.A3.A2.A.A2.2A5.A11.2A.A.4A2.3A3.A3.A4.2A6.A2.A16.A11.A
8.A20.2A6.A15.A5.A28.A$127.A29.2A8.A.2A5.A14.2A2.2A.A7.A.A6.A5.A26.A
13.A12.A3.A14.4A.A4.A3.A2.A.A2.2A4.2A12.A.A.A.2A2.3A3.A3.A4.2A6.A3.A
15.A11.A8.A20.A.2A4.A15.A5.A28.A$126.A30.A8.3A5.2A13.3A3.A.A6.2A.A6.A
5.A27.A12.A13.A2.A18.2A5.A2.A2.A.A2.3A4.2A12.3A.4A2.3A3.A3.A4.2A7.A2.
A15.A11.A8.A20.A3.A3.A15.A5.A28.A$126.A29.A8.2A5.2A.A10.3A.A3.3A5.2A
3.A5.A6.A26.A13.A12.A3.A17.A.2A3.A3.A2.A.A2.3A4.A.A11.3A.4A2.A.2A2.A
3.A4.2A7.A3.A15.A11.A7.A20.A4.A2.A15.A5.A27.A$126.A28.A7.3A4.2A2.A9.
2A3.A4.2A4.2A4.A6.A5.A27.A12.A13.A3.A17.A.A.2A.A3.A.A.A2.2A.A3.A2.A
11.A.2A.3A2.A.2A2.A3.A4.2A8.A2.A15.A11.A7.A20.A5.3A15.A5.A27.A$126.A
27.A6.2A.A4.A3.A8.2A4.A4.3A2.2A6.A5.A6.A26.A13.A13.A2.A18.2A4.A3.A2.A
.A2.2A.A3.A2.A11.A.3A.2A2.A.2A.A3.A5.2A8.A2.A15.A11.A7.A20.A6.2A15.A
5.A27.A$125.A27.A5.2A3.A2.2A4.A5.3A5.A5.2A.2A7.A5.A6.A27.A12.A13.A3.A
17.A.A4.2A2.A2.2A2.A.A.A3.A2.A10.A2.3A.A.A.A.2A.A3.A5.2A9.A2.A14.A11.
A7.A21.A5.A.2A13.A5.A27.A$125.A26.A6.A3.A.2A5.A4.2A7.A5.4A9.A4.A7.A
26.A13.A13.A2.A18.A.A4.A.A.A.A.A2.A.A.A2.A3.A10.A3.4A.A.A.A.2A3.A5.2A
9.A2.A15.A11.A6.A21.A5.A3.A12.A5.A27.A$125.A25.A7.A3.2A6.A3.2A8.A6.2A
11.A3.A7.A27.A12.A13.A3.A17.A.A4.A3.A2.2A2.A.A2.A2.A3.A10.A3.2A.A.A.A
2.3A3.A5.2A10.A2.A14.A11.A6.A21.A5.A4.2A10.A5.A27.A$125.A24.A8.A2.2A
7.4A9.A5.3A11.A4.A5.69A10.A.A4.A3.3A.A2.A.A2.A2.A4.A9.A3.A2.3A.A2.2A
4.A5.2A10.A2.A14.A11.A6.A21.A5.A6.2A8.A4.A28.A$124.A24.A10.3A7.2A11.A
4.2A.2A11.A3.A4.2A.A26.A14.A13.A2.A8.2A7.A2.A3.A4.A.2A2.A2.A2.A.A5.A
9.A3.A2.A.A.A2.3A3.A5.2A11.A2.A13.A11.A6.A21.A5.A8.A7.A4.A28.A$124.A
23.A11.2A5.3A12.A3.2A2.2A11.A3.A3.2A2.A27.A13.A13.A3.A10.2A5.A.A4.A3.
A.A.2A.A2.A2.A.A5.A9.A3.A2.A.3A2.3A3.A5.2A11.A2.A14.A11.A5.A21.A4.A
10.2A5.A4.A28.A$124.A22.A11.2A4.2A2.A11.A2.2A4.2A11.A2.A2.2A4.A26.A
14.A13.A3.A12.2A3.A.A4.A3.A.A.A.A2.A3.A.A5.A9.A2.2A2.A.3A3.2A3.A5.2A
12.A2.A13.A11.A5.A22.A3.A12.A4.A4.A28.A$124.A21.A11.3A2.2A3.A11.A.2A
5.3A11.A2.3A5.A27.A13.A13.A3.A15.3A.A4.A4.2A.A2.2A.A3.2A6.A9.A2.2A2.A
.A.A3.2A2.A5.A.A12.A2.A13.A11.A5.A22.A3.A13.2A2.A4.A28.A$123.A21.2A
10.A.A.2A4.A11.A.A6.A.2A10.A.3A7.A26.A14.A13.A3.A17.A.A4.A4.2A.A.A2.
2A3.2A6.A9.A2.2A2.A.2A.A.2A.A.A5.A.A13.A2.A12.A11.A5.A22.A3.A15.3A4.A
28.A$123.A20.2A10.A.3A.A4.A10.A.A7.2A.A10.3A8.A27.A13.A13.A4.A16.A.2A
4.A3.A.2A2.A2.A.A2.2A7.A7.A2.3A3.3A2.3A.A.A5.2A14.A2.A13.A11.A4.A22.A
3.A17.A4.A28.A$123.A19.2A10.A.2A3.A3.A11.2A7.A.2A9.2A.A8.A27.A14.A13.
A3.A17.A.A.2A.A4.2A.A2.A2.A2.A.A8.A7.A2.3A3.3A3.2A.A.A5.2A15.A2.A12.A
11.A4.A22.A3.A17.3A2.A28.A$123.A18.2A9.2A.2A5.A.A11.A8.A2.2A7.2A.2A9.
A27.A13.A14.A3.A17.A.A3.2A4.3A2.A3.A3.2A8.A7.A2.3A3.3A3.3A.2A5.2A15.A
2.A12.A11.A4.A22.A2.A18.A2.A.A28.A$122.A18.2A9.A.3A7.A11.2A7.A3.2A4.
3A3.2A8.A27.A14.A13.A3.A17.A2.A3.A.2A.2A.A2.A3.A3.2A8.A7.A2.A2.A2.3A
2.A2.A.2A5.2A15.A2.A12.A12.A3.A23.A.A18.A3.2A28.A$122.A18.A9.A.A.A8.
2A9.2A8.A2.A.A2.2A5.2A9.A27.A14.A13.A3.A17.A.A4.A3.4A2.A3.A4.A.2A6.A
6.A2.2A2.A2.A.A2.A2.4A5.2A16.A2.A12.A11.A3.A23.A.A18.A4.3A25.A$122.A
17.A9.3A2.A7.A2.A7.2A8.A3.2A.2A7.A9.A27.A14.A13.A4.A16.A2.A4.A4.3A2.A
3.A4.A3.A5.A6.A2.A3.A2.A.A2.A2.A.2A5.2A16.A2.A12.A11.A3.A23.A.A18.A4.
A2.A24.A$122.A16.A9.2A3.A7.A4.A4.2A.A7.A4.3A8.A10.A26.A15.A13.A3.A17.
A2.A3.A4.6A4.A4.A4.A4.A6.A2.A3.A2.A.A2.A3.3A5.2A16.A3.A11.A11.A3.A23.
A.A18.A4.A3.2A22.A$122.A15.2A7.2A4.A8.A4.A3.A2.A7.A4.3A9.A9.A27.A14.A
13.A4.A17.A.A4.A4.3A2.2A3.A3.2A5.A3.A6.A.2A3.A2.A.A2.A3.3A5.2A17.A2.A
11.A12.A2.A23.A.A18.A3.A6.A21.A$121.A15.2A7.2A5.A7.A6.A.A2.A8.A.4A.A
8.2A8.A27.A15.A13.A4.A16.A2.A3.A5.2A2.A2.3A4.2A6.A2.A6.A.A4.A2.A.A.A
4.4A4.2A17.A3.A11.A11.A2.A23.A.A18.A3.A7.2A19.A$121.A14.2A6.2A6.A7.A
8.A3.A7.3A3.A.A7.2A9.A27.A14.A14.A3.A17.A2.A3.A4.3A2.A4.A3.2A7.A2.A5.
A2.A4.A2.A.A.A4.2A.2A3.2A17.A3.A11.A11.A2.A24.A19.A3.A9.A18.A$121.A
13.A.A5.2A6.A8.A6.2A.A.A7.2A5.2A7.A.A8.A27.A15.A13.A4.A16.A2.A4.A4.2A
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A3.A10.A17.A$121.A13.2A4.3A7.A7.A6.A4.2A5.3A6.2A6.A2.A8.A27.A14.A14.A
4.A16.A2.A3.A5.2A2.A4.A3.3A9.A.A4.A.A5.A.A.2A.A4.2A.A2.A.2A18.A3.A10.
A12.A.A24.A19.A3.A11.2A15.A$120.A13.2A4.A.A7.A7.A6.A5.2A3.2A.A6.A.A6.
A.A8.A27.A15.A13.A4.A17.A2.A3.A4.2A2.A5.A3.A.2A9.2A4.A.A5.A.A.3A5.2A.
A3.3A18.A4.A10.A11.A.A24.A19.A3.A13.A14.A$120.A12.A.A2.2A2.A6.A8.A5.A
5.A.4A2.A7.A.A5.A2.A8.A27.A14.A14.A4.A16.A2.A3.A5.2A2.A5.A3.A.A.2A7.
2A4.2A7.2A.3A5.2A2.A3.2A18.A4.A10.A11.A.A24.A19.A3.A14.A13.A$120.A11.
A.A.2A3.A7.A7.A4.2A6.4A3.A8.A.A4.A2.A8.A27.A15.A14.A3.A17.A2.A3.A4.2A
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15.2A11.A$120.A10.A.A.A4.A7.A7.A4.A7.2A3.A2.A8.2A4.A3.A7.A28.A15.A13.
A4.A16.A2.A4.A4.2A2.A5.A3.A.A5.A6.2A2.A.A7.A2.3A4.A2.A.A3.3A18.A4.A9.
A12.2A23.A.A18.A3.A17.A10.A$119.A10.A2.2A4.A7.A8.A3.A6.2A6.2A8.A.A4.A
3.A7.A27.A15.A14.A4.A16.A2.A3.A5.A2.A6.A3.A.A6.A5.A.A.3A7.A.A.2A4.A2.
A2.A2.3A18.A4.A9.A12.A24.A.A18.A3.A18.A9.A$119.A9.A.2A5.A8.A7.A3.A4.
3A.A6.2A8.A.A3.A3.A7.A27.A16.A13.A4.A17.A2.A3.A4.2A2.A6.A3.A.A7.A4.A.
A.2A8.A.A.2A4.A2.A2.A2.A2.A18.A4.A8.A12.A24.A.A18.A3.A19.2A7.A$119.A
8.A.2A5.A8.A7.A3.A3.2A3.A7.A.2A6.A.A2.A4.A7.A27.A15.A14.A4.A16.A2.A4.
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A18.A3.A21.A6.A$119.A7.3A.A5.A8.A7.A.2A2.2A5.A6.A4.A5.2A3.A3.A7.A27.A
16.A13.A5.A16.A2.A3.A4.2A2.A6.A3.A2.A9.A2.A2.3A7.2A.A.2A3.A3.A2.A2.A
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$70.A46.2A46.A12.A19.3A16.A2.A4.2A43.A114.A24.A$71.A47.A45.A13.A16.2A
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77.A86.A19.A17.2A4.A2.A20.2A10.3A131.A21.A$78.A85.A20.A15.A5.A4.A21.
2A6.2A134.A20.A$79.A84.A21.A13.A4.2A6.A22.2A2.2A135.A20.A$79.A84.A21.
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A$89.A74.A17.A3.A8.A29.A144.A17.A$90.A73.A16.A2.2A10.A29.A143.A16.A$
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93.A70.A12.A2.A17.A30.A137.A17.A$94.2A68.A11.A.2A18.A31.A136.A16.A$
96.A67.A9.2A.A21.A31.A134.A16.A$97.A66.A8.A2.A23.A31.A132.A16.A$98.A
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2A$217.A42.A87.A2.A$218.A42.2A84.A2.A$219.A43.A82.A.2A$220.A43.2A80.
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224.A49.3A63.3A$225.A51.2A60.A.A$226.A52.2A57.3A$227.A53.2A53.3A$228.
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231.A60.2A15.7A14.2A$232.A61.2A5.8A20.A$233.2A61.5A26.2A$235.A90.A$
236.A87.2A$237.2A84.A$239.A82.A$240.A79.2A$241.2A76.A$243.A73.2A$244.
2A70.A$246.A67.2A$247.A65.A$248.2A61.2A$250.2A58.A$252.3A53.2A$255.3A
47.3A$258.3A38.6A$261.4A29.5A$265.3A21.5A$268.3A12.6A$271.3A4.5A$274.
4A!

[pcallahan]

Hey ya. I'm sorry, but do you think this rule by me, Building Plan, can be universal? It can't escape its bounding diamond but nevertheless there's really complex stuff going on inside.

I would be very surprised if it's not universal (with a caveat), but I don't have any proof.

The caveat is that if you start with a finite pattern surrounded by empty cells, its memory space is limited by its bounding diamond, so it may be complete for some space-limited complexity class (quadratic in the size of a skinny starting pattern), but not universal. There are a limited number of states and it is bound to repeat at some point.

However, the requirement of a "finite" starting pattern is misleading. There's no particular reason that empty space consists of just a particular cell value. Let the starting universe consist of a periodic pattern or periodic on a narrow band with 0-value cells around it. This will not have the bounding diamond limitation.

Update: looking at this more closely, I see a lot of moving bands. What I would do is start by wrapping the universal on one coordinate (or equivalently, extending cells into periodic lines). From that, you can reduce it to a 1D CA that might have a simpler universality proof (again, it has to be infinite in at least one dimension and will need some extension other than 0-value cells).

[BokaBB]

There are a limited number of states and it is bound to repeat at some point.

Does this mean every bounding diamond of the rule is likely a very high-period oscillator or likely to turn into one?

[pcallahan]

Does this mean every bounding diamond of the rule is likely a very high-period oscillator or likely to turn into one?

I just updated my previous reply as follows:

Looking at this more closely, I see a lot of moving bands. What I would do is start by wrapping the universe on one coordinate (or equivalently, extending cells into periodic lines). From that, you can reduce it to a 1D CA that might have a simpler universality proof (again, it has to be infinite in at least one dimension and will need some extension other than 0-value cells).

I don't know the longterm expectations for this. Maybe it turns into a simpler oscillator, e.g. with just bands traveling predictably in one dimension. Have you tried it in Golly?

[BokaBB]

L

Does this mean every bounding diamond of the rule is likely a very high-period oscillator or likely to turn into one?

I just updated my previous reply as follows:

Looking at this more closely, I see a lot of moving bands. What I would do is start by wrapping the universal on one coordinate (or equivalently, extending cells into periodic lines). From that, you can reduce it to a 1D CA that might have a simpler universality proof (again, it has to be infinite in at least one dimension and will need some extension other than 0-value cells).

I don't know the longterm expectations for this. Maybe it turns into a simpler oscillator, e.g. with just bands traveling predictably in one dimension. Have you tried it in Golly?

Yes. It ended up the moving bands can occasionally essentially take over it all. However, they're definitely not universally present and there's occasions on which they can hardly even arise and occasions on which the bands do take over nearly entirely, but chaos takes them down again at some point. I have no idea though what could arise after a million generations or so, and I assume you have a better computer than me, so I'd like to ask you to run a scribble for marathon lengths once to check what happens with it if possible, please!

[pcallahan]

To be honest, I don't have the time. However, if I were only interested in a universality proof and not some other understanding of the dynamics, I would begin by restricting starting conditions to make the behavior as orderly as possible without being completely uninteresting (as I suggest above, with one-dimensional restrictions).

[BokaBB]

No problem.

[pipsqueek]

I have an idea to how the non-universality of a rule could be proved (using 1d cellular automaton as an example)

first of all, lets define a transformation as any function that takes a pattern and outputs another pattern. the function must also not map any two different patterns to the same pattern.

if you wanted to prove the universality of a rule, such as rule 137, you would easily be able to run a pattern and apply a transformation that switches the 1's and 0's for some of the phases of its evolution. then you would notice it looks exactly like rule 110. which is universal. so you know that rule 137 is too.

then you could prove that no reversible function could map the generations of a pattern of the rule to the generations of a pattern in a universal rule.

Though the last part doesn't sound easy.