Elementry Cellular automata with a neighberhood of 5

For discussion of other cellular automata.
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Colonizor48
Posts: 30
Joined: October 16th, 2022, 4:45 pm

Elementry Cellular automata with a neighberhood of 5

Post by Colonizor48 » September 30th, 2023, 5:30 pm

I was experimenting with use of 1d cellular automata as a step in a PRNG algorithm, initially I used rule 30, combined with a majority function, Xor-shift and bit permutation step, but rule 30 proved to be insufficiently random. I was curious for alternatives, and I think I found one. These cellular automata are like wolfram's, but the next generation of each bit is determined by 2 bits to the either side of it. You can have rule numbers similarly. I made this thread to discuss these cellular automata. Each rule number is 32 bits, ranging from 0 to 4294967295(many of which are likely just inversions or complements of other rules) so there are 2^32 possible rule-strings. Most of which I conjecture are uninteresting based on looking at some randomly(if the chatGPT generated code I made is correct, I am to exhausted right now to code it on my own). But some could be useful. for example the rule 734828550_5(the 5 denoting a neighborhood size of 5) appears to be chaotic based off of the program I made. And far more random then rule 30. Many of these are likely Turing complete. I made this thread for searching for other interesting rules.

But for example, the truth table for rule 734828550 would be

11111 -1
11101- 0
11100 -1
11011 -0
11010 -1
11001 -1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
00001 - 1
00000 - 0

(I'll finish this later)

I found some code online that uses bit hacks that I don't understand to apply a normal elementary rule number to a neighborhood. I asked chatGPT to generalize it, and I cannot verify it right now, but it looks about right.(Note the code uses periodic boundary conditions).
Iterating a given rule-string on an odd numbered neighborhood, for any odd number seems to be computationally easy.
I will post the code later if anyone wants me to.

SOME OTHER INTERSTING RULES:
Rule 734928541, seems similar to 734828550, but more chaotic. And has some useful properties for making a random number generator. Generates random-ish looking outputs after enough time with periodic boundary, even on some inputs that don't look random. I could see running this and xoring bit shifted versions of some previous iterations could be a good PRNG, along with other steps such as a P-box, though it would likely need at least 2 iterations.
Rule 3141593 WIP

Colonizor48
Posts: 30
Joined: October 16th, 2022, 4:45 pm

Re: Elementry Cellular automata with a neighberhood of 5

Post by Colonizor48 » October 2nd, 2023, 3:05 pm

These rules apparently cannot be simulated in golly yet.

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