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Using computer graphics and visualization algorithms, we extend in this workthe results obtained analytically in [1], on the connectivity domains ofalternated Julia sets, defined by switching the dynamics of two quadratic Juliasets. As proved in [1], the alternated Julia sets exhibit, as for polynomialsof degree greater than two, the disconnectivity property in addition to theknown dichotomy property (connectedness and totally disconnectedness) whichcharacterizes the standard Julia sets. Via computer graphics, we unveil theseconnectivity domains which are four-dimensional fractals. The computer graphicsresults show here, without substituting the proof but serving as a researchguide, that for the alternated Julia sets, the Mandelbrot set consists of theset of all parameter values, for which each alternated Julia set is not onlyconnected, but also disconnected.

Graphical exploration of the connectivity sets of alternated Julia sets; M, the set of disconnected alternated Julia sets