Back in August last year I was experimenting with vector renditions of the Buddhabrot, reasoning that tracing the boundary of hyperbolic components and plotting those iterates would give a reasonable idea of what the limit of the Buddhabrot at infinite iterations would look like. It's not perfect (some straight lines instead of curves, due to problems with highly awkward behaviour near root points) and the level of detail could be a bit higher, but I think it looks quite ok.

The program expects a list of minibrot islands as input on stdin with lines like "period size cre cim", suitable values might be derived by regexp voodoo from my Mandelbrot set feature database. It then finds all child components recursively, down to a minimum size limit, and traces their boundaries and the iterates thereof (the image of a closed curve under the quadratic polynomial map is another loop). The colouring weight is adjusted by the amount of stretching involved in the transformations, as well as the period and size of the component it belongs to.

You can download the Haskell source: vector-buddhabrot.hs whose heaviest dependency is cairo, with other dependencies including strict, deepseq, parallel, and my mandelbrot-numerics library.