2.33 Icon
(type=icon/icon3d)
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