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:
“The instincts of the ant are very unimportant, considered as the ant’s; but the moment a ray of relation is seen to extend from it to man, and the little drudge is seen to be a monitor, a little body with a mighty heart, then all its habits, even that said to be recently observed, that it never sleeps, become sublime.”
—Ralph Waldo Emerson (1803–1882)
“... the majority of colored men do not yet think it worth while that women aspire to higher education.... The three R’s, a little music and a good deal of dancing, a first rate dress-maker and a bottle of magnolia balm, are quite enough generally to render charming any woman possessed of tact and the capacity for worshipping masculinity.”
—Anna Julia Cooper (1859–1964)
“You have a row of dominoes set up; you knock over the first one, and what will happen to the last one is that it will go over very quickly.”
—Dwight D. Eisenhower (1890–1969)
“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)
“The poetic notion of infinity is far greater than that which is sponsored by any creed.”
—Joseph Brodsky (b. 1940)