Fort Point Arches

If you look carefully at the picture of the arches above, you can see that we are standing in an arch, looking through an arch.

Arches within arches.

To the right and ahead other arches lead deeper into the depths of Fort Point, San Francisco. To the left, arches open out into the sunlight.

The photographer, Cheri Lucas Rowlands, posted it as an example of emptiness, and maybe it is. But to me, it’s an example of recursiveness, patterns within patterns.

My first experience of this was in elementary school. Someone, not one of my regular teachers that I can remember, was talking about the golden ratio.

A golden ratio is when two quantities have the same ratio as the ratio of their sum to the larger of the two quantities.

Most readers, at this point are totally lost. It’s ok. Take a deep breath. It’s not so bad. All it means is that, if you have two numbers, and you add them together, their total compared to the larger of the two numbers you just added gives you the same fraction as if you arranged the two original numbers as a fraction.

Wait a minute. That probably didn’t help either. Let me give you an example. Take this diagram, for instance:

golden ratio rectangles

If you start with the blue square on the left, and push the pink rectangle up against it on the right, you can see that the whole thing together (the rectangle that goes all the way around both the pink and blue areas) is exactly the same as the pink rectangle, only bigger. The only difference is the red rectangle is standing up, the whole big rectangle is lying on its side.

You can add another square alongside the larger rectangle to make another exactly-the-same rectangle. Keep adding squares, and connect the edges as you go, and you get a spiral.

Fake Real Log Spiral

Spirals occur everywhere, from shells to tornados.

Beyond spirals, though, recursion happens whenever patterns repeat themselves, whether it’s a pattern of triangles:

Sierpinski Triangle

Or a computer screen showing us a picture of itself.

Recursive Screenshot

Or the multiple images you see of yourself in a funhouse room of mirrors.

Recursion also happens when you repeat the same process over and over again. Like when DNA replicates, life procreates. It’s the same pattern within a pattern. A human in utero is a living organism within a living organism with the capacity to replicate within itself yet another living organism. You’re more like every other human on the planet than different – at least on a cellular level.

Recursion explains how wildly chaotic stuff very often results in stunningly predictable regularity. Like random movement of air that results in consistent weather patterns.

At every level, recursion is built into the universe. And it’s beautiful.

Take the Mandelbrot Set.

Mandelbrot Set

It’s a beautiful fractal pattern just to look at, but along its edges as you zoom in, you find an amazing universe of patterns. And, what’s even more amazing, as you zoom in you come again and again to points where the whole universe of the pattern is repeated within itself.

Mandelbrot Zoom

It’s no wonder that humans, recursive creatures that we are, can’t help but imitate the recursive elements from which we are made.

From the ancient Greeks using the golden ratio in their temples


To the recursive drawings of M.C. Escher

Eschers Relativity

To the arches within arches of Fort Point.

Fort Point Arches

Patterns within patterns, worlds within worlds.

A universe of swirling clusters of swirling galaxies of swirling solar systems of swirling planets of swirling oceans of swirling molecules of swirling atoms.

These arches are not empty. They are a snapshot of all that is.

(Arches of Fort Point by Cheri Lucas Rowlands. All others via Wikipedia.)