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.... It is extremely fast, but uses only 32-bit float. And finally, the fourth works on CPU, but uses arbitrary precision (OpenMP), so it hasn't limit for depth (except rendering time).

http://www.fractalforums.com/mandelbrot-and-julia-set/m-set-on-a-partialtotal-mobius-cylinder-looks-neat/ Use a bailout of 6 for complete fractal. This implemenent the three mobius types. Total wraps the real value if it exceeds 1 or is less than -1. Right wraps only when the real values exceeds 1, Left only when less than -1. Normal and smoothed iteration versions of each type are provided. My first attempt is also there called 'Bad' because I'd created a couple of pictures and need...