
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 email (dashlock@uoguelph.ca). This
site is joint work with my collaborator Liz Blankenship.

