Posted November 20, 2020
dtgreene: If you zoom into the Mandelbrot set, you might find that parts of it appear disconnected, even though it's been proven that the set is, in fact, connected. So, if you were to render the at a higher resolution and average the pictures, might the connections that are otherwise not visible at that resolution appear?
clarry: If they appear by zooming in a bit, then they should also appear if you render at a higher resolution. Zooming in is functionally equivalent to increasing the resolution and then cropping the edges to bring you back to the original resolution. Of course averaging a huge number of samples into a single pixel means dimnishing returns. Chances are that at some point adding more samples doesn't change the resulting image anymore. But that also depends on the dynamic range of the picture. A "hot spot" could change the final pixel value by quite a bit even if its averaged together with lots of other samples.
(With that said, there's another parameter to worry about, and that's the number of iterations you check before determining whether the point you're checking has escaped the set.)
Edit: Having actually written code to render the Mandelbrot Set on the GPU, when zooming in I run into the limit of single float precision.
Post edited December 17, 2020 by dtgreene