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 (1623–1662)
“The problem of the twentieth century is the problem of the color-line—the relation of the darker to the lighter races of men in Asia and Africa, in America and the islands of the sea. It was a phase of this problem that caused the Civil War.”
—W.E.B. (William Edward Burghardt)
“... peace produced by suppression is neither natural nor desirable.”
—Anna Julia Cooper (1859–1964)
“Well, most men have bound their eyes with one or another handkerchief, and attached themselves to some of these communities of opinion. This conformity makes them not false in a few particulars, authors of a few lies, but false in all particulars. Their every truth is not quite true. Their two is not the real two, their four not the real four; so that every word they say chagrins us and we know not where to set them right.”
—Ralph Waldo Emerson (1803–1882)
“Military glory—the attractive rainbow that rises in showers of blood.”
—Abraham Lincoln (1809–1865)
“As we begin to comprehend that the earth itself is a kind of manned spaceship hurtling through the infinity of space—it will seem increasingly absurd that we have not better organized the life of the human family.”
—Hubert H. Humphrey (1911–1978)