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.
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.
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.
I visualize surfaces via delicate contour lines: I draw lines on all these lobes, keeping either the longitude or the latitude constant. This is a mesh of lines in three-dimensional space, a virtual sculpture.
I am creating JavaScript code based on the framework three.js to bring this to life (No AI). I am scaling the whole sculpture and I am nesting several 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.
Elke Stangl (elkement) (she/her) is an Austrian physics PhD working as an engineer. Her mathematical art is borne out of her life-long passion for the theoretical underpinnings of her craft. She is creating virtual three-dimensional structures from mathematical functions – digitally with code or with ruler and compass, using.. Read more…