Timeline for Probabilistic 2D cellular automata with memory lifetime increasing like $e^{L^2}$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| May 21 at 23:58 | comment | added | Andi Bauer | Another vague argument that indicates my intuition might be wrong: The memory lifetime of any 1-dimensional simple (like local majority voting) CA does not increase with $L$ at all. Now if we consider the 2D CA on a $L_1\times L_2$ torus where we scale $L_2$ but leave $L_1$ constant, we get an effective 1D CA whose memory time does not grow with $L_2$. If $L_1$ relatively large then the memory life time will increase till $L_2\approx L_1$ and then become constant. I'd expect this constant to grow like $e^{L_1}$, so on an $L\times L$ torus the memory lifetime should grow like $e^L$. | |
| May 21 at 12:27 | answer | added | Ilmari Karonen | timeline score: 3 | |
| May 20 at 14:37 | history | asked | Andi Bauer | CC BY-SA 4.0 |