Fractals

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

Random IFS with Memory runs iterated function systems on an initial point. The user can set allowed/disallowed sequences of transforms in 1-step or 2-step memory.

Box Dimension explores the idea of fractal dimension by counting boxes along geographical edges. Latest version allows user to supply his own pictures.

Mandelbrot-Julia Sets explores the famous Mandelbrot Set and its associated Julia Sets with paired plots. Each point of a Mandelbrot set generates a Julia set. Includes Julia orbits, several color schemes, and alternate functions besides the usual z2.

I also have a simpler Flash version. This was written as an ActionScript 3 performance test.

FracStats does R/S analysis and comparison to a normal distribution, on a time series, with or without difference processing on the input data. Also does multifractal analysis (f(alpha) curves) on time series or planar data, using either the method of moments or histogram method. Several data sets are supplied, but the main use is to paste in your own data to explore.

DrivenIFS explores data-driven Iterated Function Systems.

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.

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

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

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.