Equivalent Descriptions of The Julia Set
- is the smallest closed set containing at least three points which is completely invariant under .
- is the closure of the set of repelling periodic points.
- For all but at most two points, the Julia set is the set of limit points of the full backwards orbit . (This suggests a simple algorithm for plotting Julia sets, see below.)
- If is an entire function - in particular, when is a polynomial, then is the boundary of the set of points which converge to infinity under iteration.
- If is a polynomial, then is the boundary of the filled Julia set; that is, those points whose orbits under iterations of remain bounded.
Read more about this topic: Julia Set
Famous quotes containing the words equivalent, descriptions, julia and/or set:
“For some men the power to destroy life becomes the equivalent to the female power to create life.”
—Myriam Miedzian, U.S. author. Boys Will Be Boys, ch. 4 (1991)
“Matter-of-fact descriptions make the improbable seem real.”
—Mason Cooley (b. 1927)
“Whenas in silks my Julia goes,
Then, then, methinks, how sweeetly flows
That liquefaction of her clothes.”
—Robert Herrick (1591–1674)
“It is ... despair at the mutability of all created things that links the Artist and the Ascetic—a desire to purify and preserve—to set oneself apart—somehow—from the river flowing onward to the grave.”
—Michele Murray (1933–1974)