Q: What do proteins, snowflakes, and these figures have in common?
A minimum inventory/maximum diversity system is a kit of modular parts and rules of assembly that gives you maximal design bang for your design-component buck. It’s a system that achieves a wide variety of effects from a small variety of parts. Nature excels at this game: every one of the many millions of natural proteins is assembled from an inventory of just 20 amino acids. Snowflakes are all just arrangements of the humble water molecule, H2O.
The same idea applies to the forms in the figure above, which are all constructed from semicircles joined at connection points evenly distributed along a vertical line. I stumbled onto this minimum inventory/maximum diversity system while playing with logo designs for a previous blog post, Exploring Logo Designs with Mathematica.
In my previous post, I was exploring parametric variations of logo designs in Mathematica. Although this concert-hall logo is trivially easy to parameterize and get into Mathematica, I nearly didn’t try doing so because I didn’t think that the exploration would lead anywhere interesting. So much for my intuition. Relative to its simplicity, the idea of joining semicircles at fixed points along a line is one of the richest and most expressive component systems that I’ve run across.