Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Mandelbrot_set> ?p ?o. }
Showing items 1 to 58 of
58
with 100 items per page.
- Mandelbrot_set abstract "The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes) and is named after the mathematician Benoit Mandelbrot, who studied and popularized it.Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it. Treating the real and imaginary parts of each number as image coordinates, pixels are colored according to how rapidly the sequence diverges, if at all.More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomialremains bounded. That is, a complex number c is part of the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn remains bounded however large n gets.For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = −1 gives the sequence 0, −1, 0, −1, 0,…, which is bounded, and so −1 belongs to the Mandelbrot set.Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization.".
- Mandelbrot_set thumbnail Mandel_zoom_00_mandelbrot_set.jpg?width=300.
- Mandelbrot_set wikiPageExternalLink welcome.html.
- Mandelbrot_set wikiPageExternalLink -0.743643;0.131825;0.00003;5000.
- Mandelbrot_set wikiPageExternalLink 12185093.
- Mandelbrot_set wikiPageExternalLink mandalabeth.
- Mandelbrot_set wikiPageExternalLink 9201272.
- Mandelbrot_set wikiPageExternalLink preprints.html.
- Mandelbrot_set wikiPageID "19562".
- Mandelbrot_set wikiPageRevisionID "606401363".
- Mandelbrot_set caption "This image was rendered with the Escape Time Algorithm. Notice the very obvious "bands" of color.".
- Mandelbrot_set caption "This image was rendered with the Normalized Iteration Count Algorithm. Notice the bands of color have been replaced by a smooth gradient. Also, the colors take on the same pattern that would be observed if the Escape Time Algorithm were used.".
- Mandelbrot_set direction "vertical".
- Mandelbrot_set hasPhotoCollection Mandelbrot_set.
- Mandelbrot_set image "Escape Time Algorithm.png".
- Mandelbrot_set image "Normalized Iteration Count Algorithm.png".
- Mandelbrot_set width "180".
- Mandelbrot_set subject Category:Articles_containing_video_clips.
- Mandelbrot_set subject Category:Articles_with_example_pseudocode.
- Mandelbrot_set subject Category:Complex_dynamics.
- Mandelbrot_set subject Category:Fractals.
- Mandelbrot_set type Abstraction100002137.
- Mandelbrot_set type Cognition100023271.
- Mandelbrot_set type Form105930736.
- Mandelbrot_set type Fractal105931152.
- Mandelbrot_set type Fractals.
- Mandelbrot_set type PsychologicalFeature100023100.
- Mandelbrot_set type Structure105726345.
- Mandelbrot_set comment "The Mandelbrot set is a mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes) and is named after the mathematician Benoit Mandelbrot, who studied and popularized it.Mandelbrot set images are made by sampling complex numbers and determining for each whether the result tends towards infinity when a particular mathematical operation is iterated on it.".
- Mandelbrot_set label "Conjunto de Mandelbrot".
- Mandelbrot_set label "Conjunto de Mandelbrot".
- Mandelbrot_set label "Ensemble de Mandelbrot".
- Mandelbrot_set label "Insieme di Mandelbrot".
- Mandelbrot_set label "Mandelbrot set".
- Mandelbrot_set label "Mandelbrot-Menge".
- Mandelbrot_set label "Mandelbrotverzameling".
- Mandelbrot_set label "Zbiór Mandelbrota".
- Mandelbrot_set label "Множество Мандельброта".
- Mandelbrot_set label "مجموعة ماندلبرو".
- Mandelbrot_set label "マンデルブロ集合".
- Mandelbrot_set label "曼德博集合".
- Mandelbrot_set sameAs Mandelbrotova_množina.
- Mandelbrot_set sameAs Mandelbrot-Menge.
- Mandelbrot_set sameAs Conjunto_de_Mandelbrot.
- Mandelbrot_set sameAs Ensemble_de_Mandelbrot.
- Mandelbrot_set sameAs Insieme_di_Mandelbrot.
- Mandelbrot_set sameAs マンデルブロ集合.
- Mandelbrot_set sameAs 망델브로_집합.
- Mandelbrot_set sameAs Mandelbrotverzameling.
- Mandelbrot_set sameAs Zbiór_Mandelbrota.
- Mandelbrot_set sameAs Conjunto_de_Mandelbrot.
- Mandelbrot_set sameAs m.04y7v.
- Mandelbrot_set sameAs Q257.
- Mandelbrot_set sameAs Q257.
- Mandelbrot_set sameAs Mandelbrot_set.
- Mandelbrot_set wasDerivedFrom Mandelbrot_set?oldid=606401363.
- Mandelbrot_set depiction Mandel_zoom_00_mandelbrot_set.jpg.
- Mandelbrot_set isPrimaryTopicOf Mandelbrot_set.
