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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

I think I have a proof of the aperiodicity of the center column in Wolfram’s Rule 30 open question. Outline Instead of assigning ones and zeros, we’ll be using boolean algebra to represent cell values. This allows us to ratchet up the complexity of the system in a more understandable way. We let $k$ be […]

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 $a=1$, […]