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Brusselator_space.gif (125 × 125 pixels, file size: 1.44 MB, MIME type: image/gif, looped, 200 frames, 20 s)

Summary

Description
English: some frames from a simulation of the brusselator model in 2D
Date
Source Own work
Author Jkrieger
GIF development
InfoField
 
This diagram was created with MATLAB.
Source code
InfoField

MATLAB code

clear;
% timestep
DeltaT=0.1;
% diffusion coefficients
DX=0.2;
DY=0.02;
% reaction constants
k1=1;
k2=1;
k3=1;
k4=1;
% initial concentrations
X0=1;
Y0=1;
% constant concentrations
A=1;
B=3;
% sigma of the random initial distortion
initRandomSigma=2;
% width/height of the simulation grid
width=100;
% number of iterations before display
iterationsPre=3000;
% number of visible iterations after pre
iterations=300;
iterationsDT=6;
% number of visible iterations before pre
iterationsStart=300;
% number of visible iterations before pre
iterationsInit=300;
% number of invisible iterations before iterationsStart
iterationsStartPre=600;
% number of visible iterations after pre
iterationsPre1=6000;
% number of visible iterations after pre
iterations1=300;
 
 
% laplace operator
laplace=0.25*[0 1 0; 1 -4 1; 0 1 0];
 
% initialize reaction variables
X(1:width,1:width)=X0+(rand(width,width)-0.5)*2*initRandomSigma;
Y(1:width,1:width)=Y0+(rand(width,width)-0.5)*2*initRandomSigma;
X(X<0)=0;
Y(Y<0)=0;
X(X>4.5)=4.5;
Y(Y>4.5)=4.5;
 
Xi=X;
Yi=Y;
 
% colormap
rbmap(1:100,1:3)=0;
rbmap(:,1)=((length(rbmap)-1)-(0:(length(rbmap)-1)))/(length(rbmap)-1);
rbmap(:,3)=(0:(length(rbmap)-1))/(length(rbmap)-1);
 
 
figure(1)
s=get(gcf, 'Position');
s(3)=250;
s(4)=200;
set(gcf, 'Position', s);
mf=1;
for it=1:(iterationsInit+iterationsStartPre+iterationsStart+iterationsPre+iterations+iterationsPre1+iterations1)
    lapX=conv2(X, laplace, 'same');
    lapY=conv2(Y, laplace, 'same');
    vX=k1*A+k2*X.^2.*Y-k3*B*X-k4*X+DX.*lapX;
    vY=k3*B*X-k2*X.^2.*Y+DY.*lapY;
 
    % leave border as distrotion centers
    vX(1:width,[1 width])=0;
    vX([1 width],1:width)=0;
    vY(1:width,[1 width])=0;
    vY([1 width],1:width)=0;
 
    if ((it<=iterationsInit) ...

Licensing

w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
Attribution: Jan Krieger
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.


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3 August 2012

image/gif

d4e6c595dfd0671268202f6c17def14540cfb977

1,506,406 byte

20.000000000000014 second

125 pixel

125 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current09:23, 8 August 2012Thumbnail for version as of 09:23, 8 August 2012125 × 125 (1.44 MB)Jkriegermore regions
18:56, 4 August 2012Thumbnail for version as of 18:56, 4 August 2012163 × 163 (2.33 MB)Jkriegernow shows the first some intermediate and late simulation states
15:43, 3 August 2012Thumbnail for version as of 15:43, 3 August 2012176 × 176 (1.45 MB)Jkriegermore frames
15:16, 3 August 2012Thumbnail for version as of 15:16, 3 August 2012195 × 195 (886 KB)Jkriegerlonger
15:07, 3 August 2012Thumbnail for version as of 15:07, 3 August 2012222 × 222 (1.06 MB)Jkrieger{{Information |Description ={{en|1=some frames from a simulation of the brusselator model in 2D}} |Source ={{own}} |Author =Jkrieger |Date =2012-08-03 |Permission = |other_versions = }} [[Category:Com...

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