Скачать или смотреть Mandelbrot animation #2: variable real exponent, full HD

Produced using my own rendering software, written for raw video output.

Technical info:
Fractal: Mandelbrot z -> z^a + c, with real parameter a
Algorithm: standard escape-time w/periodicity checking and 3-pass solid guessing, escape radius auto-calculated per frame
Inside coloring: black
Outside coloring: #iter
Max. iterations: 1000
Antialiasing: spatial: 4x grid supersampling; temporal: 100 FPS frame-blend downsampled to 29.97 FPS
Start: a = 1.5
End: a = 4
Rendering time: Didn't keep track fully, but an estimate based on one stretch of calculation is ~193 hours (or 8 days) total CPU time, although this was spread over more than 2 weeks.

Problem: the function, atan2, used to calculate the argument of a point has a branch cut on the negative real axis; that is, the range is -π/2 to π/2, so the angle you get is discontinuous as you cross the negative real axis. Unfortunately, with a non-integral exponent, it matters which value is chosen for the angle. If this is really about tracking the trajectory of a point under the above formula, it's arguable that one should eliminate the branch cut. Theoretically it's possible to track the angle under the assumption that the "c" term changes the angle by the minimum possible amount and to make a correction to the atan2 value each iteration. But this means the angle grows exponentially, resulting in (a) increasing inaccuracy each iteration and (b) the possibility of floating-point overflow. Is there a way to calculate it without getting such huge numbers? It could result in a picture without all of the discontinuities you see in this video.