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. It’s quite different in England, where people think of a secret as a shared relation between two people.”
—W.H. (Wystan Hugh)
“There is a constant in the average American imagination and taste, for which the past must be preserved and celebrated in full-scale authentic copy; a philosophy of immortality as duplication. It dominates the relation with the self, with the past, not infrequently with the present, always with History and, even, with the European tradition.”
—Umberto Eco (b. 1932)
“Whenas in silks my Julia goes,
Then, then, methinks, how sweeetly flows
That liquefaction of her clothes.”
—Robert Herrick (1591–1674)
“And that enquiring man John Synge comes next,
That dying chose the living world for text
And never could have rested in the tomb
But that, long travelling, he had come
Towards nightfall upon certain set apart
In a most desolate stony place....”
—William Butler Yeats (1865–1939)
“One of the most attractive things about the flowers is their beautiful reserve.”
—Henry David Thoreau (1817–1862)
“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)