## How to Dance with a Tree: Visualizing Fractals With Dance

Here’s a fun project that my friend Upasana and I put together some weekends ago. It’s a visual exploration of fractals through dance, a piece of generative art that’s part performance and part mathematical exploration.

The two ingredients that went into creating this were the Microsoft Kinect sensor, which lets your computer track how your body moves, and Processing, a programming language that lets you create interactive visuals with code. Put the two together, and you can use your body to control virtual shapes and objects.

The idea for this project came about while I was walking home from work late October, idly watching the recently bare tree branches swaying in the wind. And for some reason that made me wonder, what would it be like to be a tree for an evening? Imagine lifting your arms, and a tree waves its branches.

And then I remembered reading about fractals in Daniel Shiffman’s book Nature of Code. Fractals are those wonderfully intricate structures that look the same as you keep zooming in to them. Benoit B. Mandelbrot was one of the earliest explorers of the fractal world. He coined the word fractal to mean a kind of geometric shape whose parts resemble “a reduced-size copy of the whole.”  (Some fractal humor: What does the B in Benoit B. Mandelbrot stand for? Benoit B. Mandelbrot.)

At the heart of being a fractal is self-similarity, the idea that each piece appears similar to the whole. Think of how a coastline on a map appears similarly wrinkly across different levels of zoom. The same could be said of the jagged terrain of a mountain.

Or picture the ever branching paths that lightning follows as it travels down to the Earth.

Or the nested arrangement of leaves within a fern.

Or the buds in a head of Romanesco broccoli. Each bud contains smaller buds upon it, arranged in the same spiraling pattern.

From coastlines to broccoli, and lightning to trees, many of nature’s patterns are better described by fractals than by the usual cast of shapes like lines, circles, and triangles. (In the real world, objects can only be roughly fractal, at some level of zoom the repetition will end. But in mathematics, the self-similarity of fractals continues forever.) Continue reading How to Dance with a Tree: Visualizing Fractals With Dance