Organic Geometry

Fractals are generally considered highly mathematical, geometrically based structures, computer-generated and precisely constructed. But they are present everywhere, everywhere. These infinitely recurring patterns, in which structures are constructed of smaller versions of themselves, which are in turn constructed of yet smaller versions, are organic. They manifest themselves everywhere, be the scale microscopic or larger than perceivable to the eye.

How? The arrangement of veins on a leaf, for instance, is translatable to the arrangement of the branches’ spacing, which in turn might be translatable to the tree’s growth patterns or range distribution. There is a method in the shapes of waterways, their curvatures, erosion patterns. There is a pattern in the ridges of mountains, in the way lightning forks, in the formation of crystals, of the shapes and proportions of life-forms, for limbs and facial features and the famously cited nautilus shell spiral. The Fibonacci number and golden ratio are not purely isolated, theoretical concepts that exist only as abstracts. They just happen to be the most efficient way for organic forms to grow and propagate, for inorganic ones to form. It’s physics.

Slime molds are another oft-cited example; planted on a map of existing cities, for instance, it will develop optimal paths for nutrient transport—paths that very nearly exactly model actual major roads and highways. Patterns are not restricted to static structures, for in movements (eddies in a rivulet or air current) and behaviors (flocks, swarms) there is also something to be mapped.

Here, Catherine Ulitsky creates geometric networks out of flocks of starlings.

In another instance, photographer Thomas Jackson’s Emergent Behavior series is “inspired by self-organizing, ‘emergent’ systems in nature such as termite best wining today mounds, swarming locusts, schooling fish and flocking birds,” organic systems consisting of individuals but behaving as cohesive entities. This, posits a commentator, “[creates] an uneasy interplay between the natural and the manufactured and the real and the imaginary.”

The forms and shapes and patterns we observe everywhere are not as arbitrary as we are inclined to think. They organize themselves into strikingly orderly arrangements, creating forms that manmade designs might care to imitate.