Epicycloidal Ornaments

This Demonstration displays a program that can generate artistically appealing images. The basic elements are two formulas for curves that are mutually interconvertible using the control "misch" (meaning mix). Further variations in the images can be achieved by adjusting the other controls.
Das Programm ist ein Bildgenerator für den Bereich der Kunst. Die Basis bilden zwei Formeln für Kurven, die (mit dem Parameter ‚misch‘) gegenseitig ineinander überführbar sind. Zur erwünschten Vielfalt der Variationen tragen mehrere vom Benutzer verstellbare Parameter bei.


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The Wolfram Demonstrations Project can be used to your advantage to produce graphics that can be considered works of art—images both kinetic and interactive. Mathematica's programming capability enables pixels to be organized by specified rules for aesthetic appeal, including symmetry, homothety (conformal transformations), and continuity. The Demonstrations can themselves be considered as completed works of art, but can also serve as raw material for further experimentation. They have proven themselves to be useful in scientific investigations in the field of aesthetics. Also, in the classroom, they are suitable for mathematical visualizations and experiments. The images produced using digital technology are a significant contribution to currently popular attempts to make quantitative connections between Science and Art.
Die für das Wolfram-Demonstration-Projekt verwendete Methode für die Gestaltung von Grafiken eignet sich zur Herstellung von Kunstwerken besonderer Art: Bilder, variabel und interaktiv beeinflussbar. Die auf Mathematik gestützte Programmierung erlaubt es, die Bildelemente nach Regeln anzuordnen, die ästhetische Wirkung haben: Symmetrie, Homothetie (konforme Transformationen), Stetigkeit. Die vorführbereiten ‚Demonstrationen‘ können als fertige Kunstwerke gelten, aber auch als Rohmaterial für Experimente. Sie bewähren sich bei wissenschaftlichen Untersuchungen im Bereich der Ästhetik ebenso wie im Unterricht, eignen sich aber auch für mathematische Visualisierungen und Experimente. So werden die mit der digitalen Technik gefertigten und präsentierten Bilder zu einem beachtenswerten Beitrag zu den heute aktuellen Science-Art-Bestrebungen.
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