# Gary Greenfield

Professor of Mathematics and Computer Science

University of Richmond

Richmond, Virginia, USA

Many of my computer generated algorithmic art works are based on simulations that are inspired by mathematcal models of physical and biological processes. In exploring the space of parameters that govern the simulation, I try to focus the viewer's attention on the complexity underlying such processes.

Right Angle Triangles in Flatland A

18" x 12"

Digital Print

2010

Four Flatlanders are sweeping through Flatland celebrating their discovery of how to draw right triangles. Their method is as follows: (1) pseudorandomly generate a turning angle alpha and an adjacent side length x; (2) calculate the complementary angle beta and use trigonometry to calculate the opposite side length y and hypotenuse length h; (3) then swivel right, forward x, turn alpha, forward h, turn beta, forward y, swivel left. These Flatlanders belong to the caste required to "wag" from side to side when they walk. Thus they defy convention by drawing perfectly straight thick lines when presenting their right triangle discovery. Here, Flatlanders are implemented as simulated drawing robots obeying obstacle and collision avoidance, and their wag is implemented by making one of their pens swing side to side in such a way that a sinusoidal track is drawn as they make their through Flatland.