In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. Thus the behavior of the function on the Fatou set is 'regular', while on the Julia set its behavior is 'chaotic'.
The Julia set of a function ƒ is commonly denoted J(ƒ), and the Fatou set is denoted F(ƒ). These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century.
Read more about Julia Set: Formal Definition, Equivalent Descriptions of The Julia Set, Properties of The Julia Set and Fatou Set, Examples, Quadratic Polynomials, Generalizations, The Potential Function and The Real Iteration Number, Field Lines, Distance Estimation
Famous quotes containing the words julia and/or set:
“The old, subjective, stagnant, indolent and wretched life for woman has gone. She has as many resources as men, as many activities beckon her on. As large possibilities swell and inspire her heart.”
—Anna Julia Cooper (1859–1964)
“The poverty of our century is unlike that of any other. It is not, as poverty was before, the result of natural scarcity, but of a set of priorities imposed upon the rest of the world by the rich. Consequently, the modern poor are not pitied ... but written off as trash. The twentieth-century consumer economy has produced the first culture for which a beggar is a reminder of nothing.”
—John Berger (b. 1926)