More art? Rule 22 Rule 37 …and more.
On the persistence of zeros in Rule 30
An attempted proof sketch for the total aperiodicity of the Rule 30 elementary cellular automaton.
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 $a=1$,…
Following my GUT
…in which I bounce ideas off GPT-4 until I get a big chunk of my G.U.T. worked out.
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…