a geometric description of how the fractal is constructed,

the IFS transformations,

the code for generating the fractal via a Lindenmayer system (L-system),

the similarity dimension of the fractal,

special properties and interesting facts about the fractal

variations of the fractal (see the Index for the complete list of fractals), and

references.

This site uses Javascript. It also uses MathJax (which requires Javascript) to display mathematical expressions. Please turn on JavaScript, then refresh the page.

One of the most common ways of generating fractals is as the fixed attractor set of an iterated function system. In these pages we investigate several of the classic iterated functions systems and their associated fractals. Each IFS consists of affine transformations involving rotations, scalings, and translations. For each example we give, where applicable,

If you want to experiment with drawing any of these fractals, or you want to draw your own, see my IFS Construction Kit (for Windows) which you may download and use for free. You can also view a gallery of images constructed with the IFS Construction Kit.

Read a Fractal Poem by Theoni Pappas.

[Note: Many pages use MathJax (which requires Javascript) to display mathematical expressions. There will be a slight delay as fonts are loaded and the expressions are typeset.]