Exploratory design with mathematics in Processing

Golden Ratio and Generative Arts | Math and Processing

Tesselations with Turtle Graphics


For this lecture, two small projects are created by using the program Processing. The first project is an exploration of using Processing to analyze perspectives and symmetries in a Renaissance painting. "The School of Athens" is taken as an example. Through using scale transformation the right proportion could be measured in this painting and through using the Catmull-Rom spines [1] in processing, a composition could be found in the painting.

Final design

The final design of this elective is focused on making a tesselation art piece in Processing using Turtle Graphics. In the designed artwork, Heesch-Kienzle style C3C3C3C3 is used. This tessellation shape consists of four lines: AB, AC, DB, and DC, in which AB is the same line as AC and DB is the same line as DC. Turning the line AB in around point A over 120 degrees clockwise falls into the position AC. Point D is a reflection-point of point A with respect to the line BC. Whereby turning DB around point D counter-clockwise over 120 degrees will fall into the line DC. An example of a Processing code from Feijs is used for visualizing this tessellation[2].


1. Twigg, C. (2003). Catmull-rom splines. Computer41(6), 4-6.
2. Feijs, L. M., & Hu, J. (2013). Turtles for tessellations. Proceedings of Bridges, 241-248.