Visiting the Getty Villa, I was intrigued by the hypnotic floor of the Temple of Herakles and tilework on the ground inside the circular benches of the Outer Peristyle. These floors use 2nd century Roman designs and appear to have circles and sweeping curves. However, upon closer inspection, they are made up completely of triangles with straight edges. The parallel to computer graphics did not escape me, so I went home and worked out the arrangement of the triangles to produce the effect.
The simulation is built with Processing and rendered here with Processing.js. The triangle bases are layed out as chords along concentric circles creating a regular polygon. The points on each polygon/circle are offset by half the chord arc from the circle inside it. The each point is connected to the two points on the circle outside it, forming a series of triangles and holes. For the flooring, "triangles" were given one color and "holes" were given another color, creating the optical illusion.
It is interesting to note that there are always the same number of triangles in each concentric circle. Also, I was hoping that the implied curves radiating from the center would be segments of logarithmic spirals, but an initial check of the math indicates that they are not. This could be addressed by spacing the concentric ngons at progressively doubling radii instead of equidistant, but that was not the pattern used by the Romans. (Although, they did vary the distance.)
Click in the window and use the arrow keys to increase or decrease the number of sides. I find that prime number ngons generate the more pleasing effect.
dfrerichs
