Julia set

Julia sets, described by Gaston Julia, are fractal shapes defined on the complex number plane. Given an iterated map of the complex plane to itself, or a collection of such maps, the Julia set for this system can be defined (informally) as the set of points for which nearby points do not exhibit similar behaviour under repeated iterations of the map(s).

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Given two complex numbers, c and z0, we define the following recursion:

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:zn+1 = zn2 + c

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This is sometimes referred to as a quadratic map, and is a type of dynamical system. Given a specific choice of c and z_0, the above recursion leads to a sequence of complex numbers z_1, z_2, z_3... called the orbit of z_0.

Gaston Julia: Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularised by French mathematician Beno?t Mandelbrot, and the Julia and Mandelbrot fractals are closely related....

Fractal: A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be 'broken up' in a radical way. Some of the best examples can be divided into parts, each of which is similar to the original object. Fractals are said to possess infinite detail, and they ...

Complex number: In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying i^2 = -1. Every complex number can be written in the form x+iy, where x and y are real numbers called the real part and the imaginary part of the complex number, respectivel...

Julia set related Images and Photos (experimental)

Julia Ormond	Julia Ormond	Julia Keathberry	Julia Misbehaves
Being Julia	Smart Set (DVD)	Julia Ormond Print	Ready, Set, Green Book (Paperback)
House Set	Julia's Inspiration	Kekkaishi Set 1 (DVD)	Matching Set I