Frozen Harmonics Floating in Deep Space

First, I saw only boring structures. Now I am overwhelmed with choices!

It took me a while to find a strategy for harvesting the so-called spherical harmonic functions for art. Spherical harmonics pop up in different sub-fields of physics – whenever you need to describe something that changes along the surface of a sphere, using two angles as co-ordinates. Think longitude and latitude.

You encounter spherical harmonics when calculating the quantum mechanical wave function for the hydrogen atom. These functions are the building blocks of the lobe-shaped orbitals known from chemistry – the clouds that indicate the probability to find an electron at a certain point in space.

Just as any periodic function – as spiky as it may be – can be built up from sine and cosine waves of different frequencies, any function on a sphere can be built from a basis of spherical harmonic functions. These are the highly symmetrical shapes with several lobes, depicted in science books.

Here, I’ve tried to use just one these basic functions. Each set of longitude and latitude is assigned a value – like the distance from the origin at that combination of angles. The function can be viewed as a surface in three dimensions, built up from all these points.

I visualize surfaces via delicate contour lines: I draw lines on all these lobes, keeping either the longitude or the latitude constant – whatever I like better. This is a mesh of lines in three-dimensional space, a virtual structure. I call it a virtual sculpture.

I am creating JavaScript code based on the framework three.js to bring this to life. I am showing not only a single surface, but I am scaling the whole sculpture and I am nesting all of them, coloring the contour lines on each of the meshes differently. Then I rotate it and pan my virtual camera to find an interesting viewpoint.

Having played with the basis functions for a while, I found them a bit regular, symmetric, predictable.

Then I had an epiphany: These are basic building blocks! I am allowed to combine several of them! They form a basis that lets you build up any function on a sphere. But then, I can actually pick a more interesting function on the sphere!

Does that feel like amending my rules on-the-fly when I get stuck with Found Poetry? Yes! Do I feel bad about it! Not at all!

This is a crazier function, made up from different sine and cosine functions of the two angles, using different frequencies and different powers of sine and cosine:

The tell-tale lobes of the orbitals are still there. But tweaking the trigonometric functions of both angles makes the structure appear chaotic.

A butterfly-shaped spaceship appeared. Maybe something an ancient civilization has built? Now it is forever floating in space, frozen.