dot

Classic Iterated Function Systems

Larry Riddle
Department of Mathematics
Agnes Scott College

Fractal Poem

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 by a constant ratio, and translations. For each example we give, where applicable,

  • 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 fractals, and
  • references.
Select a fractal from the following table.

Note: by its vary nature, the study of fractal geometry is graphics intensive. These pages use many graphic elements and animations. Therefore they will not make much sense if you are using a text based browser or have image loading turned off.

Sierpinski Triangle Sierpinski Carpet Sierpinski Pentagon
Sierpinski Gasket Sierpinski Carpet Sierpinski Pentagon
Heightway Dragon McWorter Pentigree pentadentrite
Heighway Dragon McWorter Pentigree Pentadentrite
Koch curve Koch snowflake Levy dragon
Koch Curve Koch Snowflake Levy Dragon

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.