Welcome to my collection of Mandelbrot-looking fractals.

There are many functions which can be iterated and yield a fractal structure but only very few of them are really nice like the Mandelbrot set. The formula for the Mandelbrot set is: $$z_0 = c$$ $$z\to z^2 + c$$ The iterative formulae generally have two parts. The first is a function of c, which refers to the point on screen. The second is a function of z and c, where z is the output of the previous iteration. The iterating process is stopped after certain count of iterations or when it diverges too far from the origin.

When the second function is constant in c, the result is usually too regular. When it is set to an arbitrary function, the result is usually too chaotic and looks more like a distorted Mandelbrot set. There is a very small set of functions which yield something which resembles the Mandelbrot set. So far, there seems to be no rule how to predict whether a function yields such fractal or not, not even a way to generate all the functions which do so. But I can at least collect such functions.

I am a noob so the terminology is mostly made up. The offered information is based on what seems to hold from the generated pictures and I did not proove it mathematically.