
tim's_error

    A serendipitous coding error in marksmandelpwr brings to life
    an ancient pterodactyl!  (Try setting fn to sqr.)

      z(0) = pixel, c = z(0) ^ (z(0) - 1):
      tmp = fn(z(n))
      real(tmp) = real(tmp) * real(c) - imag(tmp) * imag(c)
      imag(tmp) = real(tmp) * imag(c) - imag(tmp) * real(c)
      z(n+1) = tmp + pixel

    Parameters: real & imaginary perturbations of z(0) and function fn


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.

