In 1975, Benoit Mandelbrot proposed the term fractal to describe an iterative curve or geometric shape in the fractional dimension. Taking its etymology from the Latin fractus, meaning broken, his research sought to concretize a theory of roughness and fragmentation. Fractals’ recursive properties, often referred to as self-similarity, mean that their patterns repeat with near equal detail at infinitely and arbitrarily small scales. Because fractals scale by a power that is not necessarily an integer—compared to objects in the second and third dimensions, which scale at the second and third power, respectively—traditional Euclidean geometric language fails to offer an adequate description of these objects.
Fractals abound in nature. The rough edges of coastlines, the shapes of rivers and tributaries, the distribution of galaxies, and even the patterns of blood vessels in the human body are examples of naturally occurring fractals. The curled leaves of a fern or the spiral of a nautilus shell demonstrate fractals’ recursive properties. Both the tiny leaves and the crescent shape repeat endlessly, even when you zoom in closer and closer to the centre.
