Fractals: Neverending Geometric Shapes

Fractals: Neverending Geometric Shapes

Mandelbulb fractal close-up. Illustration of a 3D shape derived from a Mandelbrot Set using spherical coordinates.

Ice crystals, tie-dye swirls, and lightning bolts all play by the same rules in fractal geometry. 

Ubiquitous in nature, the fractal is a pattern or shape that repeats itself progressively at smaller and larger scales.

First observed by Leibniz in the 17th century, the concept of self-similarity evolved for generations, until Benoit Mandelbrot coined the term ‘fractal’ in 1975. His invention of the Mandelbrot set, one of the most recognizable fractals, drew significant parallels between mathematics and the natural world.  He discovered that fractals could be found throughout the known universe, in everything from tree canopies to heartbeats.

Fractals became a popular theme in psychedelic art, often presented as infinite spirals in the famous Mandelbrot set. Their use long predates this, however, appearing first in African design and a variety of architectural schools.

View Fractal Images & Video

Fun facts: Over 50 works by the painter Jackson Pollock are considered fractal in nature; the novel Infinite Jest by David Foster Wallace is also said to have a fractal structure.

Fractal Themed Custom Gifts

  • Challoner, Jack. How Mandelbrot’s fractals changed the world.
  • Fractal.

About the Author: