Many shapes of natural objects such as clouds, trees, coastlines, lightning bolts, and waves have been extremely difficult to explain mathematically until the discovery of fractals.
Fractals are geometric shapes which repeat on an ever diminishing scale.
For example, fractular patterns look the same whether or not they are close and magnified or viewed from a distance. To further explore the concept of infinite repetition, we will examine the following scenario. Because mountains are some of the many occurrences in nature that are fractular, we will use them for our example. If you look at a mountain range from a distance, there appears to be large rugged areas with some smaller areas amongst them. Those variances in the shapes appear in many fractals, and are similar to Koch's snowflake.