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Julia set

Fractal sets in complex dynamics of mathematicsA map of behavior of initial points z{\displaystyle z} in the complex plane, by iterating the quadratic map f(z)=z2+c{\displaystyle f(z)=z^{2}+c} where c is approximately -0.5125 + 0.5213i. The green and blue regions are the Fatou set, and the Julia set consists of the central yellow pointsZoom into a Julia set in the complex-valued z-plane with the complex-valued polynomial function of second degreep(z)=z2+c{\displaystyle p(z)=z^{2}+c}and the parameterscre = cim = -0.5251993Three-dimensional slices through the (four-dimensional) Julia set of a function on the quaternionsIn complex dynamics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function.

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