When you think of fractals, you might think of Grateful Dead posters and T-shirts, all pulsating with rainbow colors and swirling similarity. Fractals, first named by mathematician Benoit Mandelbrot in 1975, are special mathematical sets of numbers that display similarity through the full range of scale — i.e., they look the same no matter how big or how small they are. Another characteristic of fractals is that they exhibit great complexity driven by simplicity — some of the most complicated and beautiful fractals can be created with an equation populated with just a handful of terms. (More on that later.)
One of the things that attracted me to fractals is their ubiquity in nature. The laws that govern the creation of fractals seem to be found throughout the natural world. Pineapples grow according to fractal laws and ice crystals form in fractal shapes, the same ones that show up in river deltas and the veins of your body. It's often been said that Mother Nature is a hell of a good designer, and fractals can be thought of as the design principles she follows when putting things together. Fractals are hyper-efficient and allow plants to maximize their exposure to sunlight and cardiovascular systems to most efficiently transport oxygen to all parts of the body. Fractals are beautiful wherever they pop up, so there's plenty of examples to share.
This block of plexiglass was exposed to a strong current of electricity that burned a fractal branching pattern within. This can be best thought of as bottled-lightning.