Playing around with low-iteration count, binary decomposition, edge detection renderings of the Burning Ship. Maybe something to turn into a colouring book?
Does it make sense to just carry out a fixed number of iterations? I guess the edges you are drawing have to do with where in the complex plane points wind up when you stop?
A fixed number of iterations works for the "interior" of this shape, I used 15. But for the "exterior" (escaping to infinity) you really want to bail out early otherwise it looks like the first image attached.
The edges are between cells with different (n, u, v) where n is the iteration count, u is the number of times x>0, and v is the number of times y>0. If you just use the last iteration it looks like the second image attached.
@anne correction: iteration count was 10 (15 is way denser)