Nature’s Aesthetic : Patterns

Patterns can be observed everywhere in nature. These visible regularities of form recur in many contexts, and can be modelled mathematically. Fractal geometry, a complex mathematical concept, serves as a means of explaining these patterns. Fractals are self-similar patterns, meaning that they are similar at every scale; zooming in and out on a fractal pattern will reveal that nothing changes and the pattern repeats itself. Mathematician Benoit Mandelbrot coined the term, summarizing it as “beautiful, damn hard, increasingly useful. That’s fractals.” (Fractal). Leonardo Fibonacci introduced his number sequence to describe mathematical relationships in growth patterns of plants, animal horns, and mollusc shells. These mathematics “govern what patterns can physically form.” (Patterns in Nature). The laws of physics apply mathematical abstractions to natural phenomenon, and approximate fractals can be found in nature everywhere, in finite scale ranges. Wikipedia provides the following examples of natural phenomena known “or anticipated” to have fractal features:

clouds, river networks, fault lines, mountain ranges, craters, lightning bolts, coastlines, goat horns, animal coloration patterns, broccoli and other vegetables, heart rates, heartbeat, earthquakes, snow flakes, crystals, blood and pulmonary vessels, ocean waves, DNA, soil pores, and Psychological subjective perception
 

Types of patterns found everywhere in nature include symmetry, branching, spirals, cracks, spots, stripes, chaos, flows, meanders, waves, dunes, bubbles, foam, arrays, crystals, and tilings. Many of these can be described using fractal geometry. When comparing two seemingly unrelated materializations in nature, such as blood vessels and river networks, the similarity in their geometric makeup reveal themselves.

Fractals in Art

When we start to notice patterns in nature, her true artistry begins to reveal itself all around us. Some describe this phenomenon as sacred geometry. Others think it is merely coincidence, the result of evolution. Regardless of the explanation of fractal geometry, nature’s patterns provide an aesthetic that many artists attempt to emulate or capture. Leonardo DaVinci’s detailed drawings explore applications of the golden ratio. Max Ernst used a technique called Decalcomania, the pressing of paint between two surfaces and pulling them apart, resulting in fractal-like patterns. Even Jackson Pollock’s seemingly chaotic splatter paintings have demonstrated fractal patterns.

Perhaps more intriguing than human pursuits of mimicry, however, is visuals that Mother Nature herself provide. Remote sensing imagery allows us to witness evidence of fractal patterns on a large scale:

 

 

 

Scientists at Tel-Aviv University are experimenting with colorized bacteria grown on petri dishes to gain understanding of the mechanisms behind the cell patterns. The images they captured are a stunning insight into nature’s geometric code:

 

 

Learn More!

 

About fractals in nature:

Check out NOVA’s program titled FRACTALS: Hunting the Hidden Dimension, available for purchase on their website.

Watch this TED Talk with Mandelbrot himself: