Julia set
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A Julia set is a fractal. It is a set defined given a rational function (written J(f)). The Fatou set of a rational function (F(f)) is the complementary set of the Julia set of f. The Fatou set of a function are the values such that all nearby values behave similarly when the function is repeatedly iterated.
Julia Set Media
The Julia set plotted with Matplotlib. The seed coordinates are (-0.512511498387847167, 0.521295573094847167), the same as for
- Julia set (red).png.
Zoom into a Julia set in the complex-valued z-plane with the complex-valued polynomial function of second degreep(z) = z^2 + cand the parameterscre = cim = -0.5251993
Three-dimensional slices through the (four-dimensional) Julia set of a function on the quaternions
Julia set (in white) for the rational function associated to Newton's method for f : z → z3−1. Coloring of Fatou set in red, green and blue tones according to the three attractors (the three roots of f).
The equipotential lines for iteration towards infinity
Field lines for an iteration of the form \frac{(1 - z^3/6)}{(z - z^{2}/2)^2} + c
Pictures in the field lines for an iteration of the form z^2 + c
Binary decomposition of interior in case of internal angle 0
A Julia set plot, generated using random IIM
A Julia set plot, generated using MIIM
A video of the Julia sets as left
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