Noun
English Wikipedia has an article on:Julia setWikipedia
Julia set (plural Julia sets)
(mathematics) In complex dynamics, a set consisting of values generated by a mathematical function such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.
A better way to draw the Julia set in black and white is to estimate the distance of pixels (DEM) from the set and to color every pixel whose center is close to the set. Source: Internet
As it can happen that the two field lines of a pair do not end in the same point of the Julia set, our coloured field lines can ramify (endlessly) in their way towards the Julia set. Source: Internet
For example, Shishikura proves that, for a dense set of parameters in the boundary of the Mandelbrot set, the Julia set has Hausdorff dimension two, and then transfers this information to the parameter plane. citation. Source: Internet
Coloring of Fatou set according to attractor (the roots of f) For some functions f(z) we can say beforehand that the Julia set is a fractal and not a simple curve. Source: Internet
Each of the Fatou domains has the same boundary, which consequently is the Julia set. Source: Internet
For parameters outside the Mandelbrot set, the Julia set is a Cantor space : in this case it is sometimes referred to as Fatou dust. Source: Internet