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:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“... 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)
“If you set to work to believe everything, you will tire out the believing-muscles of your mind, and then you’ll be so weak you won’t be able to believe the simplest true things.”
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“The intellect,—that is miraculous! Who has it, has the talisman: his skin and bones, though they were of the color of night, are transparent, and the everlasting stars shine through, with attractive beams.”
—Ralph Waldo Emerson (1803–1882)
“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)