# Density of black cells in rule 110 cellular automata [closed]

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...

• math.stackexchange.com/questions/100876/… Jan 21, 2012 at 14:15
• 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? Jan 22, 2012 at 11:43
• I am looking at the limit of the left right-angled-triangle with height n (ie n rows) and base n ( n columns) Jan 22, 2012 at 18:32
• 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. Jan 23, 2012 at 0:09