Is there a way to compute the limit of the ratio (number of black cells)/(number of white cells), in the rule 110 or rule 30 automaton? With initial state = 1 black cell.

Simulation of first 120000 rows of rule 110 shows a quite stable total density of 0.592..., and row-density 0.592...


closed as not constructive by Kaveh Jan 23 '12 at 0:10

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    $\begingroup$ math.stackexchange.com/questions/100876/… $\endgroup$ – Tsuyoshi Ito Jan 21 '12 at 14:15
  • $\begingroup$ The question is not clear to me. You look at the limit. This means you look at a sequence of numbers r0, r1, r2, ..., rn, ... (or some function). Then, what is n? And, is it clear that the limits really exist? $\endgroup$ – Yoshio Okamoto Jan 22 '12 at 11:43
  • $\begingroup$ I am looking at the limit of the left right-angled-triangle with height n (ie n rows) and base n ( n columns) $\endgroup$ – sture Jan 22 '12 at 18:32
  • $\begingroup$ Simultaneous cross-posting is discouraged. I am closing the post for now, wait a week and if you don't get an answer on Mathematics then flag the post and we will reopen it. Next time please wait a few days before cross-posting your question. $\endgroup$ – Kaveh Jan 23 '12 at 0:09