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 majority of colored men do not yet think it worth while that women aspire to higher education.... The three R’s, a little music and a good deal of dancing, a first rate dress-maker and a bottle of magnolia balm, are quite enough generally to render charming any woman possessed of tact and the capacity for worshipping masculinity.”
—Anna Julia Cooper (1859–1964)
“Let us speak, though we show all our faults and weaknesses,—for it is a sign of strength to be weak, to know it, and out with it,—not in a set way and ostentatiously, though, but incidentally and without premeditation.”
—Herman Melville (1819–1891)