ConwayLife.com

A rule satisfying the following properties:

2 state cellular automata that is 2d
The rule can be non isotropic or isotropic.
On a kxk toridial universe, given a random initial configuration and random time t, the probability that a given cell is alive should be exactly 50%
The rule explodes ...

A rule satisfying the following properties:

2 state cellular automata that is 2d
The rule does not have to be isotropic(and as a result can either be totalistic or non totalistic)
On a kxk toridial universe, given a random initial configuration and random time t, the probability that a given cell ...

B2kn34ekz/S2-ek457
This rule is a few transitions away from a rule that does explode. B2kn34ekz/S2457(This rule already is on the more stable end of explosive rules.)

Candidates:B2kn34ekz/S2457(found by randomly looking)(this automaton interestingly seems to be on the boundary between class 2, class 3, class 4. Slight changes to its transitions result in class 4 or 2 automata. For example, B2kn34ekz/S247 seems to be just barely class 4, with patterns that ...

But I am interested in looking at the space of all cellular automata and trying to determine if there is any sort of pattern or continuity between adjacent cellular automata. I want to eventually define the space of all Isotropic rules as a metric space with a well defined notion of distance ...

A high-period oscillator in a small torus might work as a PRNG for some purposes. But few patterns I ran to completion all settled into low-period result (at most p2).
This takes over 4.5 megaticks to settle into empty 10x10 torus:
x = 10, y = 10, rule = B2kn34ekz/S2457:T10,10
4ob4o$2b3o2b2o ...

This rule is interesting. It seems to be smack in the middle of a phase transition between class 1, class 2, class 3, and class 4. And minor changes to it can result in all 3 even though the rule itself is seemingly class 3. Most small changes result in a class 1 or class 2 rule. The rule itself is ...

I'll just cut to the chase. I need help finding a cellular automation that satisfies the following properties:
1 or 2 dimensional
Type 3
2 state
Given a random input, a random t value, and a random cell coordinate in closed space, there should be a 50/50 chance that a cell is alive or dead.
Not ...

These rules apparently cannot be simulated in golly yet.

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 ...

The least Baile-PSW pseudoprime(one probably exists, the known lower bound is 2^64, I would say there is probably one between 2^64 and 2^1000, but I have nothing to back that up)


The smallest odd perfect number


This is i'll defined, as odd perfect numbers are not known to exist or not ...

(using BEAF notation)
let f_0(n) = 0
f_1(n) = {n} = 1
f_2(n) = {n, n(1)n, n}
f_3(n) = {n, n, n(1)n, n, n(1)n, n, n(1)(2)n, n, n(1)n, n, n(1)n, n, n(1)(2)n, n, n(1)n, n, n(1)n, n, n}(i think this is right, if it is not correct me please, it is supposed to be a 3x3x3 3d array filled with n
f_k(n ...

The least Baile-PSW pseudoprime(one probably exists, the known lower bound is 2^64, I would say there is probably one between 2^64 and 2^1000, but I have nothing to back that up)

I wonder if this rule is Turing complete.

yujh wrote: October 17th, 2022, 9:56 pm

Colonizor48 wrote: October 17th, 2022, 8:37 pm g4b2s345/C1 and g4b2s345/D
g4b2s345 is turing complete but explosive

You can not use a normal version of apgsearch on explosive rules, but you can try to install apgspaceinvaders.

Where can I find apgspaceinvaders?

This leaves the open question of is it possible for a rule without b0 b1 b2 or b3 is Strongly Turing complete. I suspect the answer of this is negative(it can never get larger then it's bounding box), but I very well could be wrong. You were almost there! If a rule cannot expand beyond its ...

Does a list of such rules exist? It is trivial that any totalistic rule without b0 b1 b2 or b3 is not strongly Turing complete(not turing complete unless you allow infinity large initial conditions). As no pattern can grow beyond it's initial bounding box and must return to its initial condition ...

I have thought of a potential angle of attack for determining if a given rule has Spaceships. Somehow converting the decision problem of "Given a life rule-string, does it have any spaceships?" into a SAT problem and solving that. SAT while worst case hard as far as we know, does have efficent ...

If you are allowed an infinite periodic grid, B57/S01234 is Turing-complete. Here is an OR gate:
x = 190, y = 69, rule = B57/S01234
26bobo62bobo69bobo$26bobo62bobo69bobo$26bobo62bobo69bobo$26bobo62bobo
69bobo2$26bobo62bobo69bobo$24bobobobo58bobobobo65bobobobo$26bobo62bobo
69bobo ...

A W110 simulator in B5678/S0123456-ac78:

this example is trivial due to not being a life like rule. (if "life like rule" implies it must be totalistic)


Yes I met totalistic rules. None of what I have conjectured includes non-totalistic rules. By life like rules I just mean totalistic ...

Also I conjecture that no rule without b0 b1 b2 or b3 is turing complete(this can probably be proven trivially)

A W110 simulator in B5678/S0123456-ac78:

this example is trivial due to not being a life like rule. (if "life like rule" implies it must be totalistic)


Yes i met totalistic ...

g4b2s345/C1 and g4b2s345/D
g4b2s345 is turing complete but explosive

This 5c/37o (according to a Catagolue comment, it is known as Eppstein's glider 8214) appeared in the D4_+2 census.
x = 9, y = 9, rule = B35/S238
b3o$ob2o4bo$b2o4b2o$bo5bo2$bo5bo$b2o4b2o$ob2o4bo$b3o!
This c/2o (Eppstein's glider 4716, also works in B35/S23) appeared in D2_+1 :
x = 7, y = 7 ...

this is a good point, in most cases spaceships allow for the construction of basic logic circuits. plenty of life like rules have at least one spaceship.
but this does not always mean the rule is Turing complete, a rule could be explosive and have a simple spaceship. one could construct a basic ...

This 5c/37o (according to a Catagolue comment, it is known as Eppstein's glider 8214) appeared in the D4_+2 census.
x = 9, y = 9, rule = B35/S238
b3o$ob2o4bo$b2o4b2o$bo5bo2$bo5bo$b2o4b2o$ob2o4bo$b3o!
This c/2o (Eppstein's glider 4716, also works in B35/S23) appeared in D2_+1 :
x = 7, y = 7 ...