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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+