Russell Walsmith wrote:
I believe that I can clarify the first part of this statement (and Osher Doctorow can correct me if it's wrong): What is being said here is that the Mset can be generated as easily from real numbers as from complex... Indeed, this is how Fractint does complex arithmetic internally. A complex number is represented as a pair of floating point numbers (reals), with suitable rules for combining them.
Recall that y=imag(pixel) is a real number (u da man Gerald) and so imaginary >numbers don't come into play in this formula. One virtue of this approach is >that it leads to interesting generalizations.
The broadest generalisation (while still keeping within the gambit of quadratic maps) would be Quadraticmap{ bailout=1000000 z=pixel: x=real(z) y=imag(z) nx=ca+(cb+cc*x+cd*y)*x+(ce+cf*y)*y ny=cg+(ch+ci*x+cj*y)*x+(ck+cl*y)*y z=nx+flip(ny) |z|<bailout } with ca .. cl real. Unfortunately Fractint doesn't supply enough user parameters to have a thorough play with this. Morgan L. Owens