Team:LCG-UNAM-Mexico:CA

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Revision as of 04:28, 16 October 2009

Contents

  • Cellular Automata
  • The Algorithm
  • Simulations


Cellular Automata

A cellular automaton is discrete dynamical system: a grid in a n-dimensional space in which each cell has one of a finite number of states, say on and off. The state for a given cell at time t is a function of it’s own state and the states of its neighbours at time t-1.
As time advances in discrete steps, the system evolves according to universal laws. Every time the clock ticks, the cells update their states simultaneously.
Cellular Automaton can simulate continuous physical systems described by Partial Differential Equations (PDE) .

The evolution in time depends on the rules that you define, in fact you can define any rule you want and you will get amazing and funny patterns.

It has been proved that a CA can be a Universal Turing Machine, in fact different CA are used to make a wide variety of computations. You can simulate a lot of different complex systems using a CA and you can also see emergence of complex behaviour by defining simple rules in a CA REFERENCE GAME OF LIFE.

If we think of the cells in the grid as if they were biological cells we can simulate a population of bacteria, tissue growth, swarming etc.


Example.jpg



The Algorithm


This pseudo code is a simplified version of the Matlab script we implemented which is available at request.
To implement the algorithm we used two CA data structures but for simplicity we present here all the operations on a single CA object.




Comments start with     //


For each cell in the CA sampled at random*:

//Infection

       if   np>0 and runif(0,1)<infectionProb

               //bacteria becomes infected.

i = 1;     

               bs= sampleBurstSizeDistribution();

               lt = sampleLysisTimeDistribution();

                //bacterium cannot duplicate or move anymore.

               r = l = NULL;

               continue;


       //For Infected Bacteria:

       elseif i==1

               if lt==0  //Is time for lysis?.

                       //number of phages at t-1 plus those produced by

//the bacterium.

np += bs;   

s=0; //bacterium death.

               else

                       lt--;

               

               continue;


//Duplication.

elseif r ==0

               if checkForAvailableSpace(neighbourhood_ij) == TRUE

                       duplicate;

               sampleDuplicationTimeDistribution();

               set r for the new bacteria;

               continue;


       //Change Direction

       elseif l==0

               d=randomSample([1,2,..,8]);

               r=r-1;   l =persistence_time;

               

       //Movement.        

       else                

//check if the space the bacterium is moving towards //is empty.

               (New_i  New_j) = checkForSpace(i.j,d)

               r--; l--;

               //move bacterium

CA[New_i, New_j ]= CA[i ,j];

//Bacterium left an empty space in the CA.

CA[i,j]= [ 0 ];



end


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