ConwayLife.com

Conjecture: Every pattern has a glider destruction. This might be easy to prove, but I'm not sure if a pattern can survive all kinds of collisions with a glider, and with anything else.

Is there an eater that can eat a single glider wherever it comes from?
For example, Eater 1 can eat the glider in the left picture, but not in the right one, so it's not a solution.

This thread is for discussing elementary cellular automata, that operate in 1D Moore neighborhood with two states.

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In Rule 30, starting with a single black cell, the left part of the pattern appears ordered, while the right part appears chaotic:


x = 1, y = 1, rule = W30
o!


In ...

pipsqueek wrote: April 6th, 2023, 11:47 am I think you made a mistake, a line of 10 cells produces a p15 pentadecathlon.

Code: Select all

x = 10, y = 1, rule = B3/S23
10o!

Thanks! I've edited it.

The OEIS sequence https://oeis.org/A061342 is the period of the stationary component of the pattern which a row of n cells becomes in Conway's Game of Life.

Are the following conjectures right?


The periods are always 1, 2, 3, 6, 15 (I forgot this one at first) or 30;
There are finite odd terms ...

Btw, why are 1D CAs not popular in this forum? It seems that almost all of the threads are about 2D ones.

Hi there!

I'm recently interested in oscillators in n-range one-dimensional rules, especially with two states, 0 and 1. Only those with finite bounding box are considered.

One can prove that, when n=1, there only exist 1- and 2-period oscillators, where the latter only exist in Rule W108, for ...