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Results tagged with cellular-automata
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user 7742
3
votes
Probabilistic 2D cellular automata with memory lifetime increasing like $e^{L^2}$
Intuitively, I would expect a $e^{-L^2}$ scaling, since flipping from all-$0$ to all-$1$ means having a temporal domain wall in spacetime, which requires $O(L^2)$ local faults if every cluster of err …
- 1,299
1
vote
Local rule for the product of two cellular automata
Assuming that my edits to your question indeed reflect your intent correctly, the answer seems simple (and, indeed, was basically already sketched by Ville Salo in a comment above).
First, let's assum …
- 1,299
27
votes
Does Conway's game of life admit a notion of energy?
Conserved quantities like energy are characteristic of time-reversible dynamical systems. Conway's Game of Life is a dissipative, non-time-reversible system, and thus not likely to have any nontrivia …
- 1,299
32
votes
Accepted
The 1-step vanishing polyplets on Conway's game of life
Here are two more vanishing 12-plets similar to yours:
$$
\substack{
\displaystyle{◻◻◼◻◻◻} \cr
\displaystyle{◻◻◻◼◻◻} \cr
\displaystyle{◻◻◼◼◼◼} \cr
\displaystyle{◼◼◼◼◻◻} \cr
\displaystyle{◻◻◼◻◻◻} \cr
…
- 1,299
3
votes
Why do some linear cellular automata over $Z_{2}$ on the torus have small order?
Since nobody's posted a full answer yet, let me, for the record, provide my partial answer below. I originally started writing this draft confident that I had the answer, since I was quite familiar w …
- 1,299