As a mathematical modeller I always try to capture the essence of a living or technical system. To help others to understand the properties of a complex system, it is not sufficient to do the math alone - the simulation results also need to be visualised appealingly and an interactive user interface can help the user (who may possibly not be mathematically trained) to develop an intuitive understanding of the underlying mathematical concepts and relationships. This work is very similar to what I want to accomplish as a mathematical artist. To help myself and others to grasp the beauty and mystery of the world we live in, mathematical concepts, good visualisations and an interactive environment - exploratory systems - need to be created.
This is a still image from a performance staged in Summer 2014 at the Wilhelm Hack Museum in Ludwigshafen, Germany. The pattern was generated continuously during the performance using a Turing-McCabe process and projected onto a large screen. The figure was captured by a Kinect and merged live into the pattern, thereby interacting with the pattern generation process.
Three Turing-McCabe pattern generation processes running in parallel with loose coupling. The three pattern processes are represented by the three colour channels red, green and blue respectively. The processes are coupled in a circular way such that the red process controls the green process, the green process controls the blue process and blue process controls the red process.