Kam Torus

Nice Image Kamtorus type

(type=kamtorus, kamtorus3d)

This type is created by superimposing orbits generated by a set of equations, with a variable incremented each time.

           x(0) = y(0) = orbit/3;
           x(n+1) = x(n)*cos(a) + (x(n)*x(n)-y(n))*sin(a)
           y(n+1) = x(n)*sin(a) - (x(n)*x(n)-y(n))*cos(a)

After each orbit, 'orbit' is incremented by a step size. The parameters are angle "a", step size for incrementing 'orbit', stop value for 'orbit', and points per orbit. Try this with a stop value of 5 with sound=x for some weird fractal music (ok, ok, fractal noise)! You will also see the KAM Torus head into some chaotic territory that Scott Taylor wanted to hide from you by setting the defaults the way he did, but now we have revealed all!

The 3D variant is created by treating 'orbit' as the z coordinate.

With both variants, you can adjust the "maxiter" value ([X] options screen or parameter maxiter=) to change the number of orbits plotted.


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Noel Giffin,
noel@triumf.ca