An algorithmic taxonomy of fractals.

Copyright Dan Ashlock and Liz Blakenship, 2005

A fractal is an object whose dimension is not a whole number. A line segment has a dimension of 1, a square has a dimension of 2, and a cube has a dimension of 3. A fractal may have a dimension that is in between 1 and 2 or 2 and 3. The decorations to the left and right are depictions of objects that have outlines with dimensions between 1 and 2. Fractals have mathematical definitions but are often fairly good models of natural objects like trees, clouds, or coastlines.
An algorithm is a precise set of directions for performing a computation or symbolic manipulation. Algorithms are the abstract form of computer programs, before you actually start writing code. The directions for sorting a list may be a type of algorithm that's familiar to you. There are several ways to sort a list. Some are easier to code while others are harder to code but run faster.
A taxonomy is a classification according to some set of characteristics of a category of objects. If you've taken a biology course you've probably seen the "tree of life" which summarizes our current best understanding of how all living creatures on earth are related. The tree of life is a huge taxonomy, part of which can be found on a web site with the same name.
This web site contains an algorithmic taxonomy of fractals. In other words its a classification of fractals by the algorithms that generate them. The taxonomy only includes some algorithms; if we've missed a cool one, tell us. You're welcome to use the text, images, and code on on this site for your personal web page or any educational venture. If you want anything for another reason contact Dr. Ashlock by e-mail ( This site is joint work with my collaborator Liz Blankenship.