Fractals: An Introduction
A fractal is a pattern that repeats itself on an increasingly smaller scale. Alternatively, one could say that a fractal is a set of self-similar patterns. If one were to cut off a piece of one of the fractal images on this site and then magnify it, one would see an image that would look exactly like the original image before the piece was cut off.
A more mathematical definition will be given in section 2.1. But, for the benefit of those who are not quite well-versed in mathematical theory, we will explore fractals first by actually looking at some basic examples. These two examples, the Sierpinski triangle and the Koch curve, are arguably the two most famous fractals. You have probably seen one or both of these patterns before, and not much theory is required to understand them.
However, it is necessary now to introduce one term that will be used throughout this site. That is the term iterated function system, or IFS for short. All fractal images are created by using mathematical functions and applying them as transformations on a pre-existing image (a line segment, a square, a triangle, etc.). Each fractal is created by applying a finite number of such transformations. The set of these functions, together, is an IFS.