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The Lorenz Attractor

by Alain Busser

This notebook computes the famous Lorenz attractor, an unstable iteration.

Press Ctrl-R to run all commands at once.

>function compute () ...
 global pts,n,s,b,r,dt,M;
 for i=1 to n;
 x=M[1];
 y=M[2];
 z=M[3];
 pts[1,i]=(s*(y-x))*dt+x;
 pts[2,i]=(r*x-y-x*z)*dt+y;
 pts[3,i]=(x*y-b*z)*dt+z;
 M[1]=pts[1,i];
 M[2]=pts[2,i];
 M[3]=pts[3,i];
 end;
 return 0;
 endfunction

>n=10000; ...
 pts=ones(3,n); ...
 s=10; b=8/3; r=27; dt=0.01; M=normal(1,3)/1000000; ...
 compute();

Zoom now with +/-, or use the cursor keys to turn. You need red/green glasses to see this properly.

>plot3d(pts[1],pts[2],pts[3],>wire,linewidth=0.5,>anaglyph,<frame, ...
   angle=30°,scale=1.5):

The same in simple 3D.

>plot3d(pts[1],pts[2],pts[3],>wire,wirecolor=red,linewidth=0.2, ...
    zoom=3,height=40°):

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