A couple of questions about implementing perturbation for the Mandelbrot set

Question

I followed this thread on perturbation of the Mandelbrot set iterations: Perturbation of Mandelbrot set fractal

I was wondering what accuracy these different variables need to be calculated to (high accuracy or like normal floating point) i.e.

1. the original values of the reference point iterations, X_n in the link
2. the A, B and C coefficients
3. the approximated (perturbed) point

What do you do if the perturbed point requires more iterations than the reference point iterations? Do you always have to pick a reference point such that it has more iterations (before escaping) than the points you want to approximate?

Thanks

Answer 1

1. compute at high precision, store a low precision copy for series and pixels
2. low precision
3. low precision (this is the main point of the thing)
4. pick another reference (this also applies to "glitches")
5. pretty much, there's a few iterations of lee-way, but most interesting images have boundary points, so high iteration references are possible to find (escape iteration count can be made arbitrarily high close to the boundary)