Julia set

English: The Julia set is a fractal. It was first created by the French mathematician Gaston Julia. The set was then long forgotten until Benoît Mandelbrot (who was taught by Julia in the 40s), made a work about it in the early 1980s. See also: Mandelbrot set.

Slovenščina: Juliajeva množica je fraktal. Prvi ga je opisal francoski matematik Gaston Julia. Množica je nato dolgo časa ostala pozabljena, dokler ni o njej v zgodnjih 1980-ih napisal knjige (Juliajev učenec v 40-ih). Glejte tudi: Mandelbrotova množica.

Polski: Zbiór Julii to fraktal. Pierwszy opisał i stworzył go francuski matematyk Gaston Julia. Zobacz też: Zbiór Mandelbrota

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  Julia-Menge

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  From the escape-time function

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  Special colour-mapping

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  Detail of centerpart

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  Detail of centerpart

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  Highres image

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  Highres image

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  From the reversed formula.

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  From the reversed formula.

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  From the reversed formula.

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  From the reversed formula.

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  Quaternion set, (4D).

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  From the reversed formula.

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  Time escape Julia set from coordinate (phi-2, phi-1)

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  Time escape Julia set from coordinate (phi-2, 0)

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  Time escape Julia set from coordinate (-0.297491, -0.641051)

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  Image:Time escape Julia set from coordinate (0.285, 0)

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  Julia set for c=i made with IIM

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  Julia Set using z = z^2 + c, where c = -0.8+0.156i

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  Julia Set using z = z^10 + c where c = -0.925 + 0.19i

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  Julia Set using z = z^12 + c where c = -0.89511414 + 0.1i

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  Level curves of escape time

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  Filled-in Julia set

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  Binary decomposition of basin of attraction of infinity and finite attractor

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  Modified IIM

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  Fatou components

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  Modified IIM and critical orbit

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  Julia set of a cubic polynomial

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  z→z²-0.742+0.1i

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  Inner Structure of Julias: Cell-like

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  Inner Structure of Julias: Binary Fractal

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  Inner Structure of Julias: Similarity and Distortion

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  Inner Structure of Julias: Cell clusters

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  Inner Structure of Julias: Braids

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  Inner Structure of Julias: Coccid

Map of Julia sets

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  Map of the set.

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  Julia set for values of c ranging from -2.2-1.2i to 0.6+1.2i

3D

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  3D slice of a 4D Quaternion set

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Animations

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  animated zoom of z→z²+c for fixed c

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  Julia set fractal animation

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  JUlia set (white) for z→z²+c as c changes

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  Animated 3D slice of a 4D Quaternion set

Miscellaneous

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  a scenery render of a julia set.

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  Julia Set in Mandel: Fatou set

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  Julia set in Mandel: Structure, see above