Fractals

Kelly Plot allows you to explore Kelly plots further than in FracDyn, by pasting in your own data, and applying a choice of processing and binning schemes.

In Circle Inversion, a user drawn picture is inverted over one or more circles.

Limit Sets of Circle Inversions generates fractals from a set of input circles.

Aristid Lindenmayer, a botanist, invented L-Systems to describe plant development. L-Systems generates 2-d fractal images, including plant-like branching structures, and familiar fractals such as the Koch curve and Sierpinski gasket.The user can alter the rules, colors, and specify error and variation in the rule application.

Deterministic IFS with Memory applies selected sequences of affine transforms to an ancestral dot, to generate fractal pictures. Sequence selection is in 2D or 3D.

Close Pairs looks for signs of pattern in a time series. This app was commissioned by Gene Hamilton of Washington College, instead of Michael Frame at Yale. Michael once had a Close Pairs simulator, but the software senesced, and Gene wanted it back for his teaching.

Fractal Music Composer is a powerful music editor. Students build their own musical phrases out of notes from their choice of multiple keys and musical scales. Compositions are built from notes and phrases playing on assorted instruments. Fractal editing operations create self-similar sequences across different time and sound scales. Students can save MIDI output of their creations, which can play their music on almost any computer.

Click to listen to a sample composition made by applying fractal operations on two phrases from Pachelbel's Canon.

Affine calculates the affine transformation to map three source points to three target points.

Deterministic IFS runs iterated function systems (affine transforms) on a user-drawn picture.

Random IFS shows how random traversals of iterated function systems converge to the deterministic shape of the system.