In 1623, Galileo proposed that mathematics is the language that we should use to understand the universe. In his time, this meant using traditional Euclidean geometry to describe the seemingly complex natural shapes around us. However, this type of geometry proves to be an inadequate way to understand natural structures. After all, mountains are not cones, rivers are not straight lines, and clouds are not spheres.

Fractals were discovered at the turn of the last century. They were viewed as curious images of intrigue but of limited use until Mandlebrot pioneered the field of fractal geometry in the early 1900s. They can model and describe certain seemingly complex forms and phenomena that occur in the world. Myriads of natural fractals exist: galaxies, landscapes, and clouds. On a smaller scale, consider proteins and polymers; fractals can even be found within our bodies—our lungs and blood vessels.