Fractals
- Classroom fractals
- The Mandelbrot set
- Julia sets
- Pascal's triangle
Fractals have captured the public imagination for a relatively short time, beginning with the work of Benoit Mandelbrot (1979), but their history and roots go back more than a century. The word "fractal" is derived from the latin word "frangere", which means "to break".
In the late 1800's, mathematicians were struggling with the notion of "dimension" and some of the rather unusual consequences of limits in calculus. Even today, "dimension" is not an obvious concept. We take it for granted that we can tell the difference between one-dimensional, two-dimensional and three-demensional, but exactly what is it that makes something two-dimensional?
What about a fractional dimension? Can you draw a figure that has dimension 3/2? Among many notions of dimension that mathematicians use, there is an idea called "self-similarity" dimension. Fractals are sets that (often through an iterative process) exhibit some degree of self-similarity or fractional dimension.