The Julia Set

julia set“It is an approximation of the locus of connectedness for the Julia sets of the family of functions f(z) = z^2 + lambda/(z^2) (rotated by pi/2). This is analogous to the standard Mandelbrot set (which applies to the family f(z) = z^2 + c), but holds additional fascination because for lambda values which are in the interior of one of the subdomains of the connectedness locus, the Julia set is a Universal Curve. To me this represents the structure unifying chaos (since Julia sets are chaotic) and order (since Universal Curves act as a sort of catalog of all planar curves).” –Aaron

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