ECA matrices
More art? Rule 22 Rule 37 …and more.
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…
This is rule 30. The center column is highlighted, as we are interested in determining whether or not it’s possible for it to ever degenerate into a cyclic pattern. Today, I have a pretty good outline for how to show that it cannot. Rule 30 as boolean algebra We can always substitute variables in place…
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 $a=1$,…