Follow-up on my last post. I don't know why I never realized this before, but I now think that vulnerability at the left edge of a periodic region is inescapable: the left boundary of such a region always moves rightwards (encroaching on the periodic region) at the speed of light. This is because a change to the leftmost cell of a three-cell neighborhood always changes the fate of the center cell. I can't articulate why, but I am pretty sure that means you can't do much useful "engineering" in Rule 30. Such engineering always seems to involve "structures" of some sort moving around and interacting. How can you build anything like that with no stable regimes? On Tue, Oct 1, 2019 at 4:17 PM Allan Wechsler <acwacw@gmail.com> wrote:
Having played a bit with rule 30 in the past, I have what I think is a less ambitious question that Wolfram's very hard three.
Can a periodic regime take over territory leftward? In every example I have observed, periodic regimes are always vulnerable to incursion by chaos at their left borders. As one of Wolfram's figures shows, some periodic regimes can conquer chaos, but only in a rightward direction.
On Tue, Oct 1, 2019 at 3:31 PM James Propp <jamespropp@gmail.com> wrote:
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