Pickover Popcorn

formulas: 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) - h*sin(y(n)+tan(3*y(n))
         y(n+1) = y(n) - h*sin(x(n)+tan(3*x(n))

with 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. 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. 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. Just for fun we added type popcornjul,
which is the plain old Julia set calculated from the same formula.