Fractals: they’re famously found in nature and artists have created some incredible renderings as well. Fractals are purely a wonder – too irregular for Euclidean geometry; iterative and recursive and seemingly infinite. They turn up in food and germs, plants and animals, mountains and water and sky. Here are seventeen stunning examples:
1. Sea shells
Images via Sustainable San Mateo and Designer
The nautilus is one of the most famous examples of a fractal in nature. The perfect pattern is called a Fibonacci spiral.
2. Snow flake
Images via Popular Science and Daily Dose of Imagery
Images via howstuffworks, moonraker and Yale
Lightning’s terrifying power is both awesome and beautiful. The fractals created by lightning are fascinatingly arbitrary and irregular.
Image via docman
A special type of broccoli, this cruciferous and tasty cousin of the cabbage is a particularly symmetrical fractal. Cook it for your favorite mathematician.
Images via red dirt road and travelblog
The fern is one of many flora that are fractal; it’s an especially good example.
6. Queen Anne’s Lace
Image via Chrisjfry
The delicate Queen Anne’s Lace, which is really just wild carrot, is a beautiful example of a floral fractal. Each blossom produces smaller iterative blooms. This particular image was shot from underneath to demonstrate the fractal nature of the plant.
Image via American Feast
Though not as famously geometric as its relative the Romanescu, broccoli is also a fractal.
Images via National Geographic and Neatorama
Males of both the white peacock and standard peacock variety are resplendent examples of fractals in the animal kingdom. Trivia: the white peacock is not an albino.
The pineapple is an unusual fruit that is, in fact, a fractal. Though often associated with Hawaii the fruit is a native of southern Brazil.
Image via daily dose of imagery and Allan Ferguson
Look outside your window – you may see a fractal cloud at any moment.
Images via gdargaud, Indigo Society, ESRF and Designer
Both chemically-formed crystals and ice and frost crystals are breathtaking examples of fractals in nature.
12. Mountain ranges
Both shorelines and mountain ranges are considered loosely fractal. These particular examples are beautiful.
13. Trees and Leaves
Images via timalbertson, Yale, enchanter
From the macro view of a leaf to the span of a tree’s branches, fractals turn up frequently.
Image via Today is a good day
This stunningly complex fractal shoreline is none other than the pan handle of Florida.
15. Rivers and fjords
Images via Today is a good day
From the midwest of the United States to the icy fjords of Norway, fractals are often viewed by airline passengers – these particular travelers were savvy enough to snap photographs.
16. Sea urchins and sea stars
Images via jurvetson and curious animals
Sea urchins are compact, almost artistic little creatures; sea stars are more commonly referred to as starfish.
17. Stalagmites and stalactites
Images via wikimedia, Yale and Good Earth Graphics
By now you know that stalagmites shoot up from the ground while stalactites form overhead.
Amazing fractal configurations all. The links at the beginning of this post are highly recommended as they are a great start to exploring even more wondrous natural and artificial fractals.