2.21 Peterson Variations
(type=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-1) * 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) 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=0/0/5", 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.