Coloring methods

From XaoS:

iter+real: This mode colors the boundaries by adding the real part of the last orbit to the number of iterations.

iter+imag: Similar to iter+real, the only difference is that it uses the imaginary part of the last orbit.

iter+real/imag: This mode colors the boundaries by adding the number of iterations to the real part of the last orbit divided by the imaginary part.

iter+real+imag+real/imag : It is the sum of all the previous coloring modes.

Binary Decomposition: When the imaginary part is greater than zero, this mode uses the number of iterations; otherwise it uses the maximal number of iterations minus the number of iterations of binary decomposition.

Biomorphs: This coloring mode is so called since it makes some fractals look like one-celled animals.

Potential: This coloring mode looks very good in true-color for unzoomed images.

Color decomposition: In this mode, the color is calculated from the angle of the last orbit. It is similar to binary decomposition but interpolates colors smoothly.

Fractals:

Partial and Total Mobius Mandelbrots (left, right and both), research in progress...

SimonBrot 8th and 10th : z = z^n (|x| + i |y|)^n + c, where n are respectively 4 (Simonbrot 8th) and 5 (Simonbrot 10th)

Nova fractals (hard to implement, due to them converging rather than escape to infinity)

Magnet fractals (Types I and II) - also difficult to implement, same reason as for the Nova fractals, although Karl Runmo previously attempted to implement Magnets in Kalles Fraktaler.

Simon100A,B,C from simon.snake, Burning Ship, Celtic and Buffalo variants (plugin for Fractal eXtreme), also known as SimonBrot abs() variants

realflow100's Mandelbrot/Burning Ship hybrid, powers 2 - 5. Implemented in claude's "et" fractal program. Update: experimenting in progress...

Extending the Burning Ship, Celtic, Buffalo and Mandelbar fractals up to power 10.

Update: most of the fractals can be reproduced with the hybrid formula system in Kalles Fraktaler 2.15!

Zooming:

Halley's method for zooming (cubic convergence, more effective than the Newton-Raphson method, but requires a second derivative)