Ad Infinitum

Yesterday’s virtual tour of The Zymoglyphic Museum introduced me to an animal I’d never met before, but which illustrates the concept of Fractal Earth perfectly.

It’s Xenophora pallidula, the pallid carrier snail. Xenophora means “stranger carrier,” but it might aptly be called a “snail-carrying snail.” Like the decorator crab that glues living animals to its carapace, the carrier snail glues non-living things to its shell – usually other snail shells – probably for camouflage; it looks indistinguishable from a pile of snail shells on the seafloor. It may also be a means of preventing itself from sinking in the muck; by adding surface area to itself, its shell becomes a sort of snowshoe. Whatever the reason, note the form: a snail shell radiating into smaller snail shells. Now, if that carrier snail glued other carrier snail shells to it, and those carrier snails had glued other carrier snail shells to them…

It’s been a while since I explained Fractal Earth, so here’s a more detailed definition. Fractals are “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole.” In other words, they replicate themselves, inward and outward. They are too irregular to be described by classic Euclidean geometry. They are simple and self-repeating, potentially infinitely so. They are beautiful. And they happen everywhere in nature.

Here is your classic fractal, the Mandelbrot Set:

Look closer, and you can see how it repeats itself in infinite detail:

In nature, the classic geometric fractal is the nautilus shell. But fractals are found everywhere, in peacocks, ferns and their fiddleheads, aloe vera, coral and sea urchins and starfish, coastlines and rivers, snowflakes and crystals, mountain ranges, lightning bolts, clouds and hurricanes, trees and leaves and pine cones and pineapples, the human cardiovascular system, and motherfucking cauliflower.

I could go on.

The theory of Fractal Earth is that, because living things live to replicate themselves, and because a fractal is the simplest design for that, Earth is itself a fractal so large it is difficult to see… or is trying to become one. It takes place in 4 dimensions, as water wears down the mountains and clams bore into the rock. It repeats its pattern from the largest tectonic plates down to the smallest microbes, creating smaller and smaller niches. Peak biodiversity is an illusion; the planet has room for an indeterminate and limitless number of species, if given enough time. If the atmosphere of Earth were the red plastic frame of an Etch-A-Sketch, the aggressive force of life would be drawing a fantastically complex Mandelbrot set within the screen… if only catastrophes (like asteroids) weren’t always coming in from outside the frame and shaking things up. But perhaps even the asteroids are part of the mathematical function… the fractal continuing outward, beyond its atmospheric borders, into the vast universe.

So many natural things large and small are born as fractals. The simple seashell exemplifies them. But a seashell that isn’t just born a fractal, but that actively tries to become a fractal? That gives me hope for a world without borders.