A set of Chladni standing wave patterns generated in sand on the surface of a vibrating metal plate. The sand collects in the areas of the plate where the waves in the plate cancel each other completely. Each resonant wave pattern occurs at a specific frequency. This set was originally published by John Tyndall in 1869, it has been reorganized to show the periodic families that emerge as the frequency of the vibration increases.
The DNA of a Eukaryotic chromosome has the shape of a fractal helix with six levels of coiling. The fractal shape allows for all sizes of the chromosome to be unpacked and transcribed efficiently, from individual genes to long sections of DNA with thousands of co-dependent genes and regulatory sequences. It has been hypothesized that DNA can act as a fractal antenna which responds to electromagnetic waves in the environment by packing or unpacking its helicies.
The Fibonacci Sequence is a sequence of numbers where each number is the sum of the previous two—i.e., 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…and so on to infinity. The ratio of one number to the next is approximately 1.61803, which is called “phi”, or the Golden Ratio. It’s not a magical mathematical equation of the universe, but it definitely reflects natural, aesthetically beautiful patterns. The ratio been used as the ideal proportion standard by artists and architects throughout history, and it’s also found in nature because it’s one of the most efficient way to pack things together. The human body can mostly be divided up in terms of the golden ratio, with one nose, two eyes, three segments to each limb, five fingers on each hand, and our measurements and proportions also reflect the ratio, especially the proportions of the human face—the width of the nose, position of the eyes, length of the chin. Our attraction to another person increases if their body and features are symmetrical and proportional, since we perceive them to be healthier, and so the Golden Ratio appears to be connected with humans ideals of beauty. It’s worth noting, however, that although the ratio can create a beautiful face, it can’t create a beautiful mind.