Title: Mandelbrot and transform Post by: element90 on August 28, 2011, 01:22:49 PM 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 (http://nocache-nocookies.digitalgott.com/gallery/8/5522_27_08_11_5_13_53.jpeg) 1 iteration transform: inverse fold out (http://nocache-nocookies.digitalgott.com/gallery/8/5522_28_08_11_12_21_17.jpeg) 1 iteration transform: inverse fold out (http://nocache-nocookies.digitalgott.com/gallery/8/5522_28_08_11_12_23_04.jpeg) 2 iteration transforms: inverse fold in, square fold in (http://nocache-nocookies.digitalgott.com/gallery/8/5522_28_08_11_12_29_07.jpeg) |