
Kam Torus Fractal Type

formulas: 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. You will 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.

