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- Fractal_lake abstract "In geometry, and less formally, in most fractal art software, the fractal lake of an 'orbits' (or escape-time) fractal, is the part of the complex plane for which the orbit (a sequence of complex numbers) that is generated by iterating a given function does not \"escape\" from the unit circle. The lake may be connected or disjoint, and it may also have zero area.Orbits that are initialized inside the lake are either eventually captured by zero, captured by another point inside the unit circle, or may oscillate through a set of finite values indefinitely without ever converging to a fixed point. These points are described as being Inside the lake. Inside points are often detected for the purposes of using a different coloring method, in fractal rendering softwareBy this definition, the points of the Mandelbrot set form a \"fractal lake\", which is why the Mandelbrot set is also sometimes known as the \"Mandelbrot Lake\", or the \"lake of the Mandelbrot Fractal\".Many complex valued functions with an attractor at the origin define a fractal when this aspect of their orbits' behavior is categorized. Some of the orbits are attracted to the origin; some are periodic; some are attracted to other attractors, including possibly an attractor at infinity.For a given function there is a Julia fractal for each point on the complex plane. The Julia sets that correspond to points inside the Mandelbrot set are connected; those that correspond to points outside of the Mandelbrot set are disconnected.".
- Fractal_lake wikiPageID "17622181".
- Fractal_lake wikiPageLength "2396".
- Fractal_lake wikiPageOutDegree "26".
- Fractal_lake wikiPageRevisionID "601800803".
- Fractal_lake wikiPageWikiLink Area.
- Fractal_lake wikiPageWikiLink Attractor.
- Fractal_lake wikiPageWikiLink Category:Fractals.
- Fractal_lake wikiPageWikiLink Complex_number.
- Fractal_lake wikiPageWikiLink Complex_plane.
- Fractal_lake wikiPageWikiLink Connected_space.
- Fractal_lake wikiPageWikiLink Connectedness.
- Fractal_lake wikiPageWikiLink Connectedness_locus.
- Fractal_lake wikiPageWikiLink Disjoint_sets.
- Fractal_lake wikiPageWikiLink Filled_Julia_set.
- Fractal_lake wikiPageWikiLink Fractal.
- Fractal_lake wikiPageWikiLink Fractal_art.
- Fractal_lake wikiPageWikiLink Geometry.
- Fractal_lake wikiPageWikiLink Iteration.
- Fractal_lake wikiPageWikiLink Julia_set.
- Fractal_lake wikiPageWikiLink Lakes_of_Wada.
- Fractal_lake wikiPageWikiLink Mandelbrot_set.
- Fractal_lake wikiPageWikiLink Newton_fractal.
- Fractal_lake wikiPageWikiLink Orbit_(dynamics).
- Fractal_lake wikiPageWikiLink Oscillation.
- Fractal_lake wikiPageWikiLink Unit_circle.
- Fractal_lake wikiPageWikiLink Wikt:finite.
- Fractal_lake wikiPageUsesTemplate Template:Citation_needed.
- Fractal_lake wikiPageUsesTemplate Template:Geometry-stub.
- Fractal_lake wikiPageUsesTemplate Template:Orphan.
- Fractal_lake subject Category:Fractals.
- Fractal_lake hypernym Part.
- Fractal_lake type Function.
- Fractal_lake comment "In geometry, and less formally, in most fractal art software, the fractal lake of an 'orbits' (or escape-time) fractal, is the part of the complex plane for which the orbit (a sequence of complex numbers) that is generated by iterating a given function does not \"escape\" from the unit circle.".
- Fractal_lake label "Fractal lake".
- Fractal_lake sameAs Q5477493.
- Fractal_lake sameAs m.046603t.
- Fractal_lake sameAs Q5477493.
- Fractal_lake wasDerivedFrom Fractal_lake?oldid=601800803.
- Fractal_lake isPrimaryTopicOf Fractal_lake.