Check for containment inside a Julia set?

Questions
1

I need a function that given a point p in the plane as argument, returns True whenever p lies in the interior of some Julia set, let’s say the Siegel Disk (Siegel Disk Fractal -- from Wolfram MathWorld). Could anyone provide some Mathematica code?

2

Have you looked at JuliaSetIterationCount? I am not an expert in this area but I believe that, with the default options, if the function returns 1001 that means the point appears to be in the Julia set or that, at least after 1000 iterations, it could not be determined that the point was not in the Julia set.

3

I guess this would check containment in the Julia set itself, but I would like to check containment in a filled Julia set, i.e. a Julia set and its interior.