Catalan numbers and power laws in cellular automaton rule 14

Details Catalan numbers and power laws in cellular automaton rule 14 Catalan numbers and power laws in cellular automaton rule 14

2007-11-08

arxiv.org/abs/0711.1338v1

Nonlinear Sciences

Cellular Automata and Lattice Gases

11 pages, 1 figure

Scientific paper

We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of iterations $n$. Using the fact that this rule conserves the number of blocks 10 and that preimages of some other blocks exhibit patterns closely related to patterns observed in rule 184, we derive expressions for the number of $n$-step preimages of all blocks of length 3. These expressions involve Catalan numbers, and together with basic properties of iterated probability measures they allow us to to compute the density of ones after $n$ iterations, as well as probabilities of occurrence of arbitrary block of length smaller or equal to 3.

Affiliated with

Also associated with

No associations

Rating

Catalan numbers and power laws in cellular automaton rule 14 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Catalan numbers and power laws in cellular automaton rule 14, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Catalan numbers and power laws in cellular automaton rule 14 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-377990