To make a connection between randomness and the order it constructs in chaos as well as the fascinating way Pascal's Triangle seems to pop up. To construct the fractal Siepinski's Triangle and look for patterns. In the late 1960s and early 1970s a researcher, Benoit Mandelbrot, invented a new geometry. It was a geometry that focused on broken, wrinkled, and uneven shapes. Fractals can be seen everywhere in nature and mathematics as they exist in dynamic systems, which are systems that are in a constant state of change or flux.
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.