inspired by tavis' deep field #nebulabrot #DeepZoom images on #fractal #fractals forums, I did a little shader that for each c in the complement of the #MandelbrotSet M, colours according to how often z <- z^2 + c hits a given small target disc , weighted by derivative (as a proxy for point density).
it looks as though the hit sources are distributed everywhere near the boundary of M, which i think i can prove for target discs outside a sufficiently large esape circle, but i'm not sure how for discs nearer M. intuitively, by the time any cell pair in binary decomposition of exterior escapes, it covers an annulus with radii R, R^2, so any disc outside R will be hit by some region in every cell pair.
