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IFS, Erzeugen eines Farns: Selbstähnliche Fraktale und das Barnsley Farn

IFS, Erzeugen eines Farns: Selbstähnliche Fraktale und das Barnsley Farn

          
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About the Book

Studienarbeit aus dem Jahr 2017 im Fachbereich Mathematik - Geometrie, Note: 1, Gymnasium Königsbrunn, Sprache: Deutsch, Abstract: Fraktale sind Formen, welche Strukturen beinhalten, die sich immer wieder in sich selbst wiederholen. Diese Formen lassen sich mathematisch erklären und berechnen. Solche Strukturen sind in der Natur weit verbreitet, aufgrund dessen sind Fraktale zur Modellierung und Simulation von Natur von wesentlicher Bedeutung. Mathematisch gesehen ist "[f]raktale Geometrie [. . . ] eine Erweiterung der klassischen Geometrie", die verwendet werden kann um präzise Strukturen zu erzeugen. Zur Erzeugung von Fraktalen gibt es viele verschiedene Methoden und Theorien. Eine Möglichkeit Fraktale zu erzeugen, ist IFS, dies ist eine Abkürzung für Iterated Function Systems oder in der deutschen Variante für Iterierte Funktionensysteme. Entwickelt wurde diese Theorie von Michael Barnsley im Jahr 1975. Dieses Verfahren nutzt die Selbstähnlichkeit der Fraktale aus, um diese dann zu erzeugen. Bei selbstähnlichen Fraktalen hat jede Vergrößerung eine Ähnlichkeit mit dem gesamten Fraktal. Es ist eine Art "Mehrfach-Verkleinerungs-Kopier-Maschine", besser gesagt, es ist "eine einfache Abbildungsmaschine, die mit einer Anzahl von n Linsen n verkleinerte und transformierte Abbildungen des Originals auf eine Kopie druckt". IFS kann aber auch verwendet werden, um plastische Objekte oder Formen, wie zum Beispiel einen Kreis, zu erzeugen. In weitestem Sinne sind diese Formen oder diese plastischen Objekte dennoch Fraktale. Diese sind dann nicht in allen Teilstücken komplett ähnlich, sondern gleichen nur in bestimmten Vergrößerungen dem gesamten Bild. Dieses Verfahren eignet sich nicht immer unbedingt optimal zur Erzeugung von allen Formen. Ein Kreis lässt sich beispielsweise nicht perfekt rund darstellen. Diese Methode eignet sich am besten zur Erzeugung von selbstähnlichen Fraktalen, wie zum Beispiel bei dem Barnsley Farn oder bei dem Sierpinski Dreieck. Aufgrund dessen be


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Product Details
  • ISBN-13: 9783668551275
  • Publisher: Grin Verlag
  • Publisher Imprint: Grin Verlag
  • Height: 210 mm
  • No of Pages: 54
  • Spine Width: 3 mm
  • Weight: 82 gr
  • ISBN-10: 3668551278
  • Publisher Date: 08 Nov 2017
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Sub Title: Selbstähnliche Fraktale und das Barnsley Farn
  • Width: 148 mm


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