Dynamical systems are systems whose state changes over time as in the case of erosion and growth. Fractals are generally self-similar and independent of scale. While classical geometry deals with objects of integer dimensions, fractal geometry describes non-integer dimensions. Zero dimensional points, one dimensional lines and curves, two dimensional plane figures like squares and circles, and three dimensional solids such as cubes and spheres make up the world as we have previously understood it. A less complex definition of a fractal is simply a shape in which an identical motif repeats itself over and over in a diminishing scale.
Fractals are self similar under magnification or reduction.
Explain to the students that this lesson will only scratch the surface to the vastness of fractal mathematics. Before you start the first activity you may want to show your students some pictures of fractals. An Eye for Fractals , by M. McGuire Jurassic Park by Michael Crichton. This is a picture of the spleenwort fern. It is a fractal that is infinitely complex.