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:
“Hesitation increases in relation to risk in equal proportion to age.”
—Ernest Hemingway (1899–1961)
“Nothing natural can be wholly unworthy.”
—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)
“Military glory—the attractive rainbow that rises in showers of blood.”
—Abraham Lincoln (1809–1865)
“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)