Self-similar sets have the same jagged appearance under any magnification. Examples began to appear in the mathematical literature in the early part of the twentieth century. However, the advent of the computer has increased fascination with these objects. This is because they can now be created so easily using algorithms programmed on the computer. These sets have an allure of their own, but also show promising applications.
Fractals based on Brownian motion is the other focus.
Brownian motion is a natural phenomenon which has been shown to be intrinsically fractal based on the physical principles governing it. The theory of Brownian motion and fractional Brownian motion has led to algorithms that generate realistic landscapes which are used in high tech cinema. It is also being used to evaluate algorithms processing radar images which pick out the important objects in the display. This talk can be adapted to any level of audience from high school to graduate and research level. Even students with limited background will learn to calculate the Hausdorff dimension of some examples.