We are all familiar with Euclidean geometry. This means we understand circles, square, rectangle... shapes that are easily defined using conventional mathematics. Fractal geometry addresses those shapes that are not so conventional. Lets talk about coastlines. These are not regular shapes. In the past the coast line of England (for example) has been measured by outlining the coast and then assigning an amount to that outline. To be truly accurate one needs to measure ALL parts of the coast line. Than means every nook and cranny, every irregular twist and turn. The conventional measurement lists the length of England's coastline at about 1,000 miles. Include all the nooks and crannies and the actual coast is closer to 3.000 miles. Fractal geometry can be much more precise.
The image above shows conventional measurement on the left and fractal measuring on the right.