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:
“You know there are no secrets in America. Its quite different in England, where people think of a secret as a shared relation between two people.”
—W.H. (Wystan Hugh)
“Skepticism is unbelief in cause and effect. A man does not see, that, as he eats, so he thinks: as he deals, so he is, and so he appears; he does not see that his son is the son of his thoughts and of his actions; that fortunes are not exceptions but fruits; that relation and connection are not somewhere and sometimes, but everywhere and always; no miscellany, no exemption, no anomaly,but method, and an even web; and what comes out, that was put in.”
—Ralph Waldo Emerson (18031882)
“Her wrongs are ... indissolubly linked with all undefended woe, all helpless suffering, and the plenitude of her rights will mean the final triumph of all right over might, the supremacy of the moral forces of reason and justice and love in the government of the nation. God hasten the day.”
—Anna Julia Cooper (18591964)
“[My mother told me:] You must decide whether you want to get married someday, or have a career.... I set my sights on the career. I thought, what does any man really have to offer me?”
—Annie Elizabeth Delany (b. 1891)
“It is a tribute to the peculiar horror of contemporary life that it makes the worst features of earlier timesthe stupefaction of the masses, the obsessed and driven lives of the bourgeoisieseem attractive by comparison.”
—Christopher Lasch (b. 1932)
“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 (19041989)