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:
“Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
—Ralph Waldo Emerson (1803–1882)
“... peace produced by suppression is neither natural nor desirable.”
—Anna Julia Cooper (1859–1964)
“And, in those offices, my doggerel
Was not set up in blunt ten-point, nor read
By a distinguished cousin of the mayor....”
—Philip Larkin (1922–1986)
“Mrs. Robinson: Do you find me undesirable?
Benjamin: Oh, no, Mrs. Robinson. I think you’re the most attractive of all my parents’ friends.”
—Calder Willingham (1923–1995)
“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)