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].


In this elective, I have learned to work with mathematical formulas to create patterns on processing. Throughout the explorations with algebra and calculus within this course, I found out that mathematics could play an important role in Design.  I am especially impressed by the possibilities of how mathematics could enhance the aesthetics of a design. It is also an interesting method to implement mathematics in my daily lives. Through using different mathematical formulas, different patterns could be generated. This elective has improved my skills in working with Processing and has enhanced my skills in Math Data & Computing.
+ Math Data & Computing
+ Creativity & Aesthetics


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.
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