I had been hesitant to harvest spherical harmonic functions for art. There are so many visualizations of them out there already!
Usually, they are displayed as solid surfaces. Their lobes are colored in two distinct colors, like blue and red – to indicate the sign of the function, + or -. “Spherical” means that every point on a unit sphere is assigned a distance. If the calculated distance would come out negative, this part of the function is not flipped over. Instead, the negative sign is added as an additional color tag.
When I draw these surfaces with code, I am showing a mesh of contour lines instead. The simplest spherical harmonic function looks like a sphere. Contour lines could be – for example – the meridians and the circles of latitude. The idea for more complex orbitals is the same: I am walking over the surface (with code, in a loop), and for a single contour line I keep the “longitude” or the “latitude” constant.
I wanted to make it look less like a scientific visualization and more enigmatic. So, I nested several of these meshes of contour lines, gradually varying the color of the contours. Colors have no significance in science.
This is the same function, using contours either along either “latitude” or “longitude”:
The simple basis functions were still a bit too symmetric for me.
Before I found a crazier way to color them, I played with combining two of them – a purplish and a yellowish one!
The combination is still symmetric. But due to the different colors and all the intersections of their lobes it is possible to find more interesting viewpoints.
The images below show the same structures from different viewpoints.
I feel like an explorer investigating an unknown object in deep space.
Of course, this is a spaceship – maybe in a retro video game of last century!
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