An attempted proof sketch for the total aperiodicity of the Rule 30 elementary cellular automaton.
More art? Rule 22 Rule 37 …and more.
Factor pushing is an idea I came up with when trying to establish an easy proof of the existence of a prime in $(n,n^2)$. I haven’t managed that yet, but it’s still on my bucket list. To do it, you take some set of numbers, write them out in a row, and then generate new […]
1. horizontal union 2. vertical union
When $b=1$, the center column must be periodic. This means that all cells not dependent on $b$ must be periodic regardless of anything else. When $b=0$, then $a$ controls whether the left or center column behaves as the typical center column. If $a=0$, then the center is the center and must be periodic; if $a=1$, […]