Hi Ron, good to hear from you. Ron wrote:
The first one involves MarksMandel. The error here is in the documentation.
The documentation has the formula as
z -> (c^exp-1)*z^2 + c
It should actually be
z -> c^(exp-1)*z^2 +c
You are correct. I know because I checked the actual code - comparing with ultrafractal (or any other program) isn't a reliable way to know what's right. (I run into this at my work at NASA all the time.) We'll fix the docs.
If cj = 0.1 or ck = 0.1 the image agrees with what I get in my UF formula using your hypercomplex code. If BOTH cj = 0.1 and ck = 0.1, the images are different. The built-in Fractint formula forces symmetry around the x axis, and the correct image is not symmetrical.
Forcing symmetry is an attempt to save a lot of processing tgime, but is not guaranteed to be correct. There are a number of fractals with parameter combinations that break the symmetry. I'd say "it's a feature". The only sure way to get the correct image is to turn off symmetry. I'm sure this disclaimer is documented somewhere, but if not, we should add it Tim