15 Natural Instances of Self-Similarity That Will Blow Your Mind

Ancient scholars had a name for the weird phenomenon of self-similar repeating patterns of growth in the natural world. They called it "sacred geometry." What is self-similarity? A self-similar object is an object in which a part of the whole replicates the whole itself. In some cases, this replication is only approximate, like how parts of the universe (such as hurricanes or the insides of our brains) appear similar to the universe itself. In other cases, though, the replication is precise, and a part of the whole replicates the whole exactly. It just does so on a smaller scale.

This results in naturally occurring fractals all around us, and they create some weird self-similarities. Crystals, broccoli, feathers - there are numerous examples of objects that, upon close inspection, comprise dizzyingly magnificent parts that replicate their whole at unbelievable scales. This list explores some of the craziest and most beautiful cases of self-similarity. Keep reading below. 

Photo: Jsome1 / flickr / CC-BY 2.0

  • Romanesco Broccoli

    Romanesco broccoli is a variant of cauliflower. That's a boring fact. Here's a cooler one: Romanesco broccoli is also perhaps the most insanely fractal vegetable in the world. Its pattern perfectly illustrates the Fibonacci sequence, the pattern of numbers in which every number in the sequence is the sum of the two numbers that precede it. Romanesco broccoli exemplifies the sequence in its appearance, with spirals upon spirals of the vegetable pattern repeating themselves at different levels of scale.

  • Leaves

    Photo: Unknown / Wikimedia Commons / CC BY 2.0

    If you look closely at many leaves – especially those from deciduous trees – you'll notice that the branching veins, from the smallest to the largest, mimic the shape of the leaf as a whole. This is described as a "recursive formula" in generating the leaf pattern. At the smallest, almost microscopic level, leaf vein patterns are truly an exquisite work of the natural world.

  • Peacock Feathers

    Peacock feathers also show a certain amount of fractal patterning. In fact, all feathers do. Feathers are composed of a main vein that runs through the center off of which many smaller barbs extend. Even smaller barbs, called “barbules,” extend off of the barbs. So, a feather is really comprised of lots of tiny barbules hooked together and attached to barbs, which are attached to the main vein. Peacocks provide a dramatically beautiful example of this phenomenon. 

  • Salt Flats

    Pictured above are the famous Salar de Uyuni salt flats in southern Bolivia. Salt flats – which are formed by the crystallization of salt on ancient lake and sea beds – demonstrate random, yet consistent, fractal patterns. Here, the pentagonal pattern of the evaporated salt would be visible from numerous levels of focus.

  • The Internet

    The Internet
    Photo: Wikimedia Commons / CC-BY

    When graphically mapped, internet traffic provides a striking example of self-similarity in the technological world. In this fractal model, internet hubs (like Google and Facebook) are represented as the largest nodes on the graphic. Smaller nodes branch off of the major ones, and these represent popular, but slightly less traveled, sites (like say, AirBnb or Pinterest). And this pattern repeats. At the furthest reaches of the graphic are local networks that receive very little daily traffic. So, basically, based just on graphic representations, our brains, the universe, and the internet are all the same thing.

  • Snowflakes

    Is being told you’re a super special snowflake somehow less special when you know that snowflakes are another example of self-similarity in nature? When water crystallizes, it does so in repeating patterns. Water crystallization is the process that forms things like frost and snowflakes. Snowflakes each demonstrate unique fractal patters as a result of this process. So, the next time you wake up to frost on your windshield, consider taking a moment to marvel at nature’s fractals before you crank the defrosters.