Federico Caramanica
Eledialab  DISI
Trento  Italy
Registered: Sep 2009
Posts: 2 
Problem: CA with Random Initial Condition
Hi.
My name is Federico Caramanica and I 'm a Phd student of the Department
of Information Engineering and Computer Science of the University of Trento, Italy.
My
main research interests are in antenna arrays, wave propagation in urban environment and inverse scattering.
Now, I'm facing the following problem with cellular automata:
 Framework
1) onedimensional, 2state cellular automata, with a neighbordhood of
k>=3 cells
2) the initial state of CA (the row at time t=0) is a random binary
array of black/white cells. The probability that a cell is "black/full" is denoted "p" (I call this probability "average density of the CA") and consequentely "q=1p" is the probability of a "white/empty"
cell.
3) the horizontal extension of the CA is infinite (I don't consider boundary conditions).
 Problem Statement:
my problem is to find out a generic statistical description (analytical or algorithmical) of the average density of black cells "p(t)" in function of the the time "t" given the description of the rule and an initial state probability "p(t=0)=p" (e.g. p=0.6).
I can't use additivity, simmetry, approximations... and, if possible, I need a accurate statistical description for any rule.
Could you please suggest me a way to solve this problem?
I need this result to control my numerical results.
If I don't explain correctly the problem, please tell me!
Thank you for your attention.
Best regards,
Federico Caramanica
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Federico
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