
Peterson Variations

formulas: marksmandel, marksjulia, cmplxmarksmand,
          cmplxmarksjul, marksmandelpwr, tim's_error


These fractal types are contributions of Mark Peterson. MarksMandel and
MarksJulia are two families of fractal types that are linked in the same
manner as the classic Mandelbrot/Julia sets: each MarksMandel set can be
considered as a mapping into the MarksJulia sets, and is linked with the
spacebar toggle. The basic equation for these sets is:

      Z(n+1) = ((lambda^exp) * Z(n)^2) + lambda

where Z(0) = 0.0 and lambda is (x + iy) for MarksMandel. For MarksJulia,
Z(0) = (x + iy) and lambda is a constant (taken from the MarksMandel
spacebar toggle, if that method is used). The exponent is a positive
integer or a complex number. We call these "families" because each value
of the exponent yields a different MarksMandel set, which turns out to be
a kinda-polygon with (exponent+1) sides. The exponent value is the third
parameter, after the "initialization warping" values. Typically one would
use null warping values, and specify the exponent with something like
"params=0/0/4", which creates an unwarped, pentagonal MarksMandel set.

In the process of coding MarksMandelPwr formula type, Tim Wegner
created the type "tim's_error" after making an interesting coding mistake.

