2.20 Pickover Popcorn
(type=popcorn/popcornjul)
Here is another Pickover idea. This one computes and plots the orbits of
the dynamic system defined by:
x(n+1) = x(n) - real(h * fn1( y(n) + fn2(C * y(n) ))
- imag(h * fn3( x(n) + fn4(C * x(n) ))
y(n+1) = y(n) - real(h * fn3( x(n) + fn4(C * x(n) ))
- imag(h * fn1( y(n) + fn2(C * y(n) ))
In the original the functions were: sin, tan, sin, tan, and C was 3.
The initializers x(0) and y(0) equal to ALL the complex values within
the "corners" values, and h=.01. ALL these orbits are superimposed,
resulting in "popcorn" effect. You may want to use a maxiter value less
than normal - Pickover recommends a value of 50. Although you can zoom
and rotate popcorn, the results may not be what you'd expect, due to the
superimposing of orbits and arbitrary use of color. The orbits
frequently occur outside of the screen boundaries. To view the fractal
in its entirety, set the preview display to "yes" using the "V" command.
As a bonus, type=popcornjul shows the Julia set generated by these same
equations with the usual escape-time coloring. Turn on orbit viewing
with the "O" command, and as you watch the orbit pattern you may get
some insight as to where the popcorn comes from.