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:
“We shall never resolve the enigma of the relation between the negative foundations of greatness and that greatness itself.”
—Jean Baudrillard (b. 1929)
“To be a good enough parent one must be able to feel secure in one’s parenthood, and one’s relation to one’s child...The security of the parent about being a parent will eventually become the source of the child’s feeling secure about himself.”
—Bruno Bettelheim (20th century)
“Life must be something more than dilettante speculation.”
—Anna Julia Cooper (1859–1964)
“So far no actual revolutionary masses have come into view. This might be considered sufficient reason for reproaching someone who has set out to describe a revolution. But it is not our fault. This is, after all, a German revolution.”
—Alfred Döblin (1878–1957)
“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)
“We must not suppose that, because a man is a rational animal, he will, therefore, always act rationally; or, because he has such or such a predominant passion, that he will act invariably and consequentially in pursuit of it. No, we are complicated machines; and though we have one main spring that gives motion to the whole, we have an infinity of little wheels, which, in their turns, retard, precipitate, and sometime stop that motion.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)