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 between, relation, julia, set, attractive and/or infinity:
“There is a certain standard of grace and beauty which consists in a certain relation between our nature, such as it is, weak or strong, and the thing which pleases us. Whatever is formed according to this standard pleases us, be it house, song, discourse, verse, prose, woman, birds, rivers, trees, room, dress, and so on. Whatever is not made according to this standard displeases those who have good taste.”
—Blaise Pascal (16231662)
“The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.”
—Sigmund Freud (18561939)
“... the majority of colored men do not yet think it worth while that women aspire to higher education.... The three Rs, 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 (18591964)
“The cunningest dissimulation is when a man pretends to be caught in the traps others set for him; and a man is never so easily over-reached as when he is contriving to over-reach others.”
—François, Duc De La Rochefoucauld (16131680)
“Mrs. Robinson: Do you find me undesirable?
Benjamin: Oh, no, Mrs. Robinson. I think youre the most attractive of all my parents friends.”
—Calder Willingham (19231995)
“The poetic notion of infinity is far greater than that which is sponsored by any creed.”
—Joseph Brodsky (b. 1940)