Fractals-The beautiful repeating patterns of nature

You can keep your old boring circles, squares and triangles. Sure, they are useful-but they aren’t as beautiful and fascinating as fractals, the beautiful repeating patterns of nature some call “the thumbprint of God.”


I never got excited about math until I watched Fractals: The Colors of Infinity (available free online.) “That’s it!” I thought, “The answer to life, the universe and everything.” However, I could not explain how it was the answer; it was just an intuitive response. And don’t knock intuition. Einstein said, “The intuitive mind is a sacred gift and the rational mind is a faithful servant. We have created a society that honors the servant and has forgotten the gift.”

Certain mathematical geniuses discovered that certain mathematical procedures produce iterating patterns that repeat like history repeats-that is, they repeat in discernible patterns with slight variations on a theme. Only when they illustrated these equations did they discover something else: they are beautiful. They figured out that these equations can depict the patterns in a tree root, in the tree’s branches and down to the veins in the tree’s leaves. The same patterns occur in our neural network, our circulatory system and river beds as seen from satellite photos. Everything is connected.

I study fractals as I paint. There it is again! The veins in the butterfly’s wings match the veins in the leaf on which it chonked when it was a caterpillar. There is order in the universe, with slight variations that repeat from infinitesimally small to (we presume,) infinitesimally huge.

Yesterday I was working on painting from memory of heat lightening dancing over Sarasota Bay at night. It was quite a show, let me tell you. When I tried to paint the waves I ran into trouble. “All right, there is some fractal issue going on,” I thought. So I drew a wave pattern and discovered it was also the pattern of a school of fish joined in a chain. Of course I had to blend it a bit to “read” correctly– but fish and waves, butterflies and leaves, our neural networks and river beds from space. Everything is connected.

Each of us is part of something really beautiful.

Watch a fractal zoom  

Fish swimming head to tail is same pattern waves make. Below fishwave (unblended and blended)
Fish swimming head to tail is same pattern waves make. Below fishwave (unblended and blended)


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