Equivalent Descriptions of The Julia Set
- is the smallest closed set containing at least three points which is completely invariant under .
- is the closure of the set of repelling periodic points.
- For all but at most two points, the Julia set is the set of limit points of the full backwards orbit . (This suggests a simple algorithm for plotting Julia sets, see below.)
- If is an entire function - in particular, when is a polynomial, then is the boundary of the set of points which converge to infinity under iteration.
- If is a polynomial, then is the boundary of the filled Julia set; that is, those points whose orbits under iterations of remain bounded.
Read more about this topic: Julia Set
Famous quotes containing the words equivalent, descriptions, julia and/or set:
“Accountability in friendship is the equivalent of love without strategy.”
—Anita Brookner (b. 1938)
“The fundamental laws of physics do not describe true facts about reality. Rendered as descriptions of facts, they are false; amended to be true, they lose their explanatory force.”
—Nancy Cartwright (b. 1945)
“To-day ... when material prosperity and well earned ease and luxury are assured facts from a national standpoint, woman’s work and woman’s influence are needed as never before; needed to bring a heart power into this money getting, dollar-worshipping civilization; needed to bring a moral force into the utilitarian motives and interests of the time; needed to stand for God and Home and Native Land versus gain and greed and grasping selfishness.”
—Anna Julia Cooper (1859–1964)
“He turns agen and drives the noisy crowd
And beats the dogs in noises loud.
He drives away and beats them every one,
And then they loose them all and set them on.
He falls as dead and kicked by boys and men,
Then starts and grins and drives the crowd agen;
Till kicked and torn and beaten out he lies
And leaves his hold and cackles, groans, and dies.”
—John Clare (1793–1864)