Julia set (nonfiction): Difference between revisions
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The Julia set of a function f is commonly denoted J(f). | The Julia set of a function f is commonly denoted J(f). | ||
The Julia set is complementary to the [[Fatou set (nonfiction)]] (after [[Pierre Fatou (nonfiction)|Pierre Fatou]]), which consists of values with the property that all nearby values behave similarly under repeated iteration of the function. The Fatou set is commonly denoted F(f). | The Julia set is complementary to the [[Fatou set (nonfiction)|Fatou set]] (after [[Pierre Fatou (nonfiction)|Pierre Fatou]]), which consists of values with the property that all nearby values behave similarly under repeated iteration of the function. The Fatou set is commonly denoted F(f). | ||
The behavior the Julia set is chaotic, by contract with the Fatou set, which is regular. | The behavior the Julia set is chaotic, by contract with the Fatou set, which is regular. | ||
Revision as of 06:24, 3 February 2020
In complex dynamics, the Julia set is a set of values, defined by an iterated function, which has the property that an arbitrarily small perturbations in value can cause drastic changes.
The Julia set of a function f is commonly denoted J(f).
The Julia set is complementary to the Fatou set (after Pierre Fatou), which consists of values with the property that all nearby values behave similarly under repeated iteration of the function. The Fatou set is commonly denoted F(f).
The behavior the Julia set is chaotic, by contract with the Fatou set, which is regular.
Related concepts include Julia "laces" and Fatou "dusts", which are also defined by iterative functions with perturbation-related properties.
Both the Julia set and the Fatou set are related to the Mandelbrot set.