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### Time for Langton's ant to cover a “square” torus

Langton's ant is a cellular automaton running as follows:
Squares on a plane are colored variously either black or white. We
arbitrarily identify one square as the "ant". The ant can travel ...

**11**

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333 views

### Does Langton's ant cover every n by 6 gridded torus?

This post follows this other post about times cover by Langton's ant of $n$ by $n$ gridded torus.
For $n$ by $n$ gridded torus, I've checked for $n \le 1000$ that the ant covers all. This fact needs ...

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244 views

### Infinite time game of life

Today in a talk with a friend of mine I had an idea of extending cellular automatons to transfinite working time. I know it has already been considered, but, as far as I can tell, GoL extended to ...

**8**

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310 views

### Distribution of digits of $pq$-adic idempotents (aka “automorphic numbers”)

Let $p$ and $q$ be distinct primes. By the ring of $pq$-adic integers I mean the ring $\mathbb{Z}_{pq} := \varprojlim \mathbb{Z}/(pq)^n\mathbb{Z}$ which is obviously isomorphic to $\mathbb{Z}_p ...

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87 views

### Periodic configurations for elementary cellular automata

Let $L$ be an elementary cellular automaton. Then $L$ acts on $\{0,1\}^{\mathbb{Z}}$. We say that a configuration $w\in\{0,1\}^{\mathbb{Z}}$ is periodic if $L^{(n)}(w)=w$ for some $n\in\mathbb{N}$.
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**0**

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41 views

### The orbit-structure of an automorphism of the full shift

My question concerns reversible cellular automaton rules on a one-dimensional wraparound universe consisting of $m$ sites each capable of being in any of $n$ states, or equivalently, the actions of ...

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213 views

### Recurrence relation with Hadamard Product

I've been drawn to a problem that requires ascertaining the existence of fixed points in the following recurrence relation, any ideas would be much appreciated. I seek neccessary conditions on $A,B$ ...