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GingerBread_Man iterated chaotic map with parameters. Attractor explorer.

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28 Jan 2012 (Updated )

This is the Gingerbreadman map with parameters to explore variations over the original attractor.

ginger.m
function ginger(a,b,numiterations)
% ginger Is a function for plot gingerBread map [1] [2] [3].
%
% The gingerbreadman map is given by the trnasformation:

%        (1)
%            x(i) = 1 - a*y(i-1) + b*abs(x(i-1));
%            y(i) = x(i-1);                              
%
%         In original form a=1 and b=1. here we can change these parameters
%         to explore diferent atractors.
% 
% INPUTS: 
%        a = This is the a parameter on ecuation (1)
%        b = This is the b parameter on ecuation (1)
%        numiterations = This set the number of iterations of ecuation (1)
%       
%
% Example (1):
%
%   ginger(1.40,1,10000)
%
%
% Example (2):
%
%   We can take frames and create a movie showing the evolution
%   
%  for i=1:1500
%    ginger(2*(i-1)/1500,1,2000)
%    axis([-20,20,-20,20])
%    M(i)=getframe(gcf)
%  end
% 
%  movie(M)
%
%  I uploaded that movie to youtube:
%  http://www.youtube.com/watch?v=5k18BuEES34
%
%
%  References:
%  [1] Loren on the Art of MATLAB, "Pretty 2-Dimensional Chaotic Maps",
%      http://blogs.mathworks.com/loren/2011/12/07/pretty-2-dimensional-cha
%      otic-maps/
%
%  [2] Wikipedia, "Gingerbread Map",
%      http://en.wikipedia.org/wiki/Gingerbreadman_map
%
%
%  [3] Adam Wachsman "Gingerbreadman chaotic 2D map",
%      http://www.mathworks.com/matlabcentral/fileexchange/34116
%
%This function was written by :
%                             Hctor Corte
%                             B.Sc. in physics 2010
%                             Battery Research Laboratory
%                             University of Oviedo
%                             Department of Electrical, Computer, and Systems Engineering
%                             Campus de Viesques, Edificio Departamental 3 - Office 3.2.05
%                             PC: 33204, Gijn (Spain)
%                             Phone: (+34) 985 182 559
%                             Fax: (+34) 985 182 138
%                             Email: cortehector@uniovi.es
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%This is just for security, you can change it to get better images, but
%carefully.
maxnumofiterations=10000;

if numiterations>maxnumofiterations  
   numiterations=maxnumofiterations;
   display('Number of iterations exceed max number of iterations')
end

%We are going to calculate simultaneusly the path of 100 randon points 
x=20*(rand(100,numiterations)-0.5);
y=20*(rand(100,numiterations)-0.5);

%This is the main loop, where iterations takes place
for i=1:numiterations
y(:,i+1)=x(:,i);
x(:,i+1)=1-b*y(:,i)+a*abs(x(:,i));
end

%Once we got all the points we have to plot them all.
for kj=1:100
plot(x(kj,:),y(kj,:),'.k','markersize',0.5)
hold on
end

title(['a=',num2str(a),';  b=',num2str(b)],'FontSize', 20);
hold off




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