Julia Sets - Moving the seed

I've been at the fractals again. This time I made it morph:


This is a Julia set again, but instead I am tracing a path through the complex space with the seed value. The path taken in this video is a near-circle centred at 0.12 + 0.74i with an real radius of 0.11 and an imaginary radius of 0.10.

There were a number of other really cool ones, but the problem is that the path they take tends to go into areas which have lots of points that do not fly off into infinity, which means they take a long time to process. That means that I can't have a nice framerate like the video has.

One thing that was kinda neat was that if you flip the sign on the centre of the ellipse for the imaginary component, it flips the patterns displayed on the x-axis (or maybe it's the y-axis). So centred at 0.12 - 0.74i, those swirls are in the top-right and bottom-left instead of the top-left and bottom-right.

A thing I would like to try to make better animations would be to see where the framerates get low. I can probably do this by iterating between -1 and 1 in the real and imaginary components and spit out a time for each computation. My plan will be to spit that out into a greyscale image so that it is easy to see where the slow points are.