The word fractal has become increasingly popular, although the concept started more than two centuries ago in the 17th century with prominent and prolific mathematician and philosopher Gottfried Wilhelm Leibnitz. Leibnitz is believed to have addressed for the first time the notion of recursive self-similarity, and it wasn’t until 1960 that the concept was formally stabilized both theoretically and practically, through the mathematical development and computerized visualizations by Benoit Mandelbrot, who settled on the name “fractal”.
Fractals are defined mainly by three characteristics:
- Self-similarity: identical or very similar shapes and forms at all scales.
- Iteration: a recursive relationship limited only by computer capacity. With sufficiently high performance, the iterations could be infinite. This allows for very detailed shapes at every scale, that modify with respect to the first iteration, manifesting the original shape at some levels of iteration. Because of this, fractals may have emergent properties, which make them a suitable tool for complex systems.
- Fractal dimension, or fractional dimensions: describes the counter-intuitive notion that a measured length changes with the length of the measuring stick used; it quantifies how the number of scaled measuring sticks required to measure, for example, a coastline, changes with the scale applied to the stick.