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:
“Every word was once a poem. Every new relation is a new word.”
—Ralph Waldo Emerson (1803–1882)
“The great, the fundamental need of any nation, any race, is for heroism, devotion, sacrifice; and there cannot be heroism, devotion, or sacrifice in a primarily skeptical spirit.”
—Anna Julia Cooper (1859–1964)
“There are twenty ways of going to a point, and one is the shortest; but set out at once on one. A man who has that presence of mind which can bring to him on the instant all he knows, is worth for action a dozen men who know as much, but can only bring it to light slowly.”
—Ralph Waldo Emerson (1803–1882)
“The most attractive class of people are those who are powerful obliquely, and not by the direct stroke: men of genius, but not yet accredited: one gets the cheer of their light, without paying too great a tax.”
—Ralph Waldo Emerson (1803–1882)
“The poetic notion of infinity is far greater than that which is sponsored by any creed.”
—Joseph Brodsky (b. 1940)