<p>Is there a way to compute the limit of the ratio (number of black cells)/(number of white cells), in the <a href="http://mathworld.wolfram.com/Rule110.html" rel="nofollow">rule 110</a> or rule 30 automaton? With initial state = 1 black cell.</p>

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

CC BY-SA 3.0
2012-01-21T14:15:22.510Z
http://math.stackexchange.com/questions/100876/density-of-black-cells-in-rule-110
Tsuyoshi Ito
CC BY-SA 3.0
2012-01-22T11:43:26.863Z
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?
Yoshio Okamoto
CC BY-SA 3.0
2012-01-22T18:32:13.207Z
I am looking at the limit of the left right-angled-triangle with height n (ie n rows) and base n ( n columns)
sture
CC BY-SA 3.0
2012-01-23T00:09:53.503Z
[Simultaneous cross-posting is discouraged](http://meta.cstheory.stackexchange.com/questions/225/official-faq-for-theoretical-computer-science/231#231). I am closing the post for now, wait a week and if you don't get an answer on [math.se] then flag the post and we will reopen it. Next time please wait a few days before cross-posting your question.
Kaveh
<co.combinatorics><automata-theory><cellular-automata>
Density of black cells in rule 110 cellular automata
sture
# Density of black cells in rule 110 cellular automata

(Asked by: username_0 on 2012-01-21)

Is there a way to compute the limit of the ratio (number of black cells)/(number of white cells), in the [rule 110](http://mathworld.wolfram.com/Rule110.html) 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...

**Tags:** co.combinatorics, automata-theory, cellular-automata

> **Comments:**
> **username_1**: http://math.stackexchange.com/questions/100876/density-of-black-cells-in-rule-110  
> **username_2**: 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?  
> **username_0**: I am looking at the limit of the left right-angled-triangle with height n (ie n rows) and base n ( n columns)  
> **username_3**: [Simultaneous cross-posting is discouraged](http://meta.cstheory.stackexchange.com/questions/225/official-faq-for-theoretical-computer-science/231#231). I am closing the post for now, wait a week and if you don't get an answer on [math.se] then flag the post and we will reopen it. Next time please wait a few days before cross-posting your question.  

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## 0 answers

