Mandelbrot and transform

[element90]

I have seen how the Mandelbrot set has been altered by the use of abs and flip in UF. I've generalised these modifications by implementing Mandelbrot with transforms:

z = transform(z)
z = z^2 + c

The function transform applies a set of configured transforms such as unsign real, sign real, reverse sign real, circle fold in, circle fold out, circle reflect, log, exp, power, etc. In all I have 31 types of transform. The transforms can also be applied to the complex plane, the classic example of this is the inverse Mandelbrot where c is transformed using c = 1/c. If no transforms are configured then the standard Mandelbrot image is seen.

A second generalised form can also be explored:

z = transform(z^2) + c

The following pictures use the first generalised form as I haven't got round to exploring the second form yet.

1 complex plane transform: unsign real
3 iteration transforms: log(z), rotation, inverse fold on



1 iteration transform: inverse fold out



1 iteration transform: inverse fold out



2 iteration transforms: inverse fold in, square fold in