Icon and Icon3d

Nice Image Icon type


This fractal type was inspired by the book "Symmetry in Chaos" by Michael Field and Martin Golubitsky (ISBN 0-19-853689-5, Oxford Press)

To quote from the book's jacket,

"Field and Golubitsky describe how a chaotic process eventually can lead to symmetric patterns (in a river, for instance, photographs of the turbulent movement of eddies, taken over time, often reveal patterns on the average."

The Icon type implemented here maps the classic population logistic map of bifurcation fractals onto the complex plane in Dn symmetry.

The initial points plotted are the more chaotic initial orbits, but as you wait, delicate webs will begin to form as the orbits settle into a more periodic pattern. Since pixels are colored by the number of times they are hit, the more periodic paths will become clarified with time. These fractals run continuously.

There are 6 parameters:

Lambda, Alpha, Beta, Gamma, Omega, and Degree

      Omega  0 = Dn, or dihedral (rotation + reflectional) symmetry
            !0 = Zn, or cyclic (rotational) symmetry
            Degree = n, or Degree of symmetry

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Noel Giffin,