Relation Between Julia, Filled-in Julia Set and Attractive Basin of Infinity
The Julia set is the common boundary of the filled-in Julia set and the attractive basin of infinity
where :
denotes the attractive basin of infinity = exterior of filled-in Julia set = set of escaping points for
If the filled-in Julia set has no interior then the Julia set coincides with the filled-in Julia set. This happens when all the critical points of are pre-periodic. Such critical points are often called Misiurewicz points.
Read more about this topic: Filled Julia Set
Famous quotes containing the words relation, julia, set, attractive and/or infinity:
“To criticize is to appreciate, to appropriate, to take intellectual possession, to establish in fine a relation with the criticized thing and to make it one’s own.”
—Henry James (1843–1916)
“Life must be something more than dilettante speculation.”
—Anna Julia Cooper (1859–1964)
“There is nothing more mysterious than a TV set left on in an empty room. It is even stranger than a man talking to himself or a woman standing dreaming at her stove. It is as if another planet is communicating with you.”
—Jean Baudrillard (b. 1929)
“The men—the undergraduates of Yale and Princeton are cleaner, healthier, better-looking, better dressed, wealthier and more attractive than any undergraduate body in the country.”
—F. Scott Fitzgerald (1896–1940)
“New York, you are an Egypt! But an Egypt turned inside out. For she erected pyramids of slavery to death, and you erect pyramids of democracy with the vertical organ-pipes of your skyscrapers all meeting at the point of infinity of liberty!”
—Salvador Dali (1904–1989)