There is no grammar school student who is not informed about what fractals are. They are special images created by computer programs with mathematical formulas behind. But what kind of formulas are they? Is it possible to make fractals at home by our own? Is it possible to understand the difficult rules behind these wonderful imaginary pictures?

Just start your favorite spreadsheet program and by clicking just a few, you can follow the easiest dynamics which lead to a chaotic behavior. Starting from the world of the real numbers, just a few steps are required to reach the the world of the complex numbers. This new world gives reasonable power to visually investigate the orbits of dynamical systems. It is widely known how the expression (a+b)² must be expanded – but did you know that this easy rule gives a very difficult geometry into the world of complex numbers?

The talk will introduce XaoS, the open source fractal exploration tool, and the audience will learn how the pocket calculator gives the answer if we about to find the cube root of an arbitrary number. But... why is the cube root mentioned here? Well... come and see!