Peterson Variations

Nice Image cmplxmarsjul type

(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.

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