Fractal shapes and the natural world

By Kenneth Falconer

Fractal shapes, as visualizations of mathematical equations, are astounding to look at. But fractals look even more amazing in their natural element—and that happens to be in more places than you might think.




Snowflake
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They’re also present in snowflakes, a gentler product of the sky.

Romanesco broccoli
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Sometimes fractals are edible—such as this common example, Romanesco broccoli.

Pine cone
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The fractal doesn’t fall far from the tree. Pinecone seeds display fractal formations as well.

Peacock
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Fractals appear in walking creatures as well. They are at their most vivid in the tail of the male peacock.

Lightning
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Fractals are in the sky as well, from the clouds to the lightning that strikes out from them.

Trees
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Fractal precipitation then gives way to fractal foliage, such as these trees.

Neurons
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And of course, fractals exist within us—specifically, in our neurons (pictured) and genes.

Fractals in mountains
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Mountain ranges and rivers exhibit branching fractal shapes. The Andes are a perfect example.

Kenneth Falconer is a mathematician who specializes in Fractal Geometry and related topics. He is Professor of Pure Mathematics at the University of St. Andrews and a member of the Analysis Research Group of the School of Mathematics and Statistics. Kenneth’s main research interests are in fractal and multifractal geometry, geometric measure theory and related areas. He has published over 100 papers in mathematical journals. He is author of Fractals: A Very Short Introduction.

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Image credits:


Snowflake: Creative commons via Gui Seiz Flickr


Romanesco broccoli: Feliciano Guimaraes. Creative commons via Feliciano Guimaraes Flickr


Pine cone: Photo by Don Miller. Creative commons via Don Miller Flickr


Peacock: Photo by Bill Dolak. Creative commons via Bill Dolak Flickr


Lightning: Photo by John Fowler. Creative Commons License via snowpeak Flickr


Trees: Photo by Petteri Sulonen. Creative commons via PrimeJunta Flickr


Neurons: Photo by Jason Snyder. Creative commons via Functional Neurogenesis Flickr


Fractals in mountains: Creative commons via NASA Goddard Space Flight Center

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