Minimalist art from cellular automata

Abstract

My interest in algorithmic, generative and evolutionary art stems from my exposure to artists featured in the SIGGRAPH art exhibitions of the early 1980s such as Roman Verostko, Hans Dehlinger, Yoichiro Kawaguchi, Mark Wilson, Jean-Pierre Hébert, Karl Sims, andWilliam Latham to name just a few. My own computer generated artworks arise from visualizations of mathematical, physical or biological processes. My objective is to draw the viewer’s attention to the complexity and intricacy underlying such processes. Previously, in this journal, I have written about minimalist art derived from maximal planar graphs (Greenfield, 2008). Elsewhere, I have written about various generative art projects using cellular automata (Greenfield, 2016, 2018, 2019). Here, I will provide details about an artwork from a recent project onminimalist art derived from the so-called ‘rotor router’ model used for simulating deterministic random walks in the plane (Doerr & Friedrich, 2009; Holroyd & Propp, 2010). I first became aware of this model thanks to an archiv preprint of Neumann, Neumann, and Friedrich (2019). Consider a 200 × 300 toroidal grid such that each cell has four rotors that advance independently. Assume the rotors have 8, 5, 4 and 4 segments numbered 1–8, 1–5, 1–4 and 1–4, respectively. For each cell, randomly initialize its rotor settings and colour the cell grey. Next, select four cells to receive ‘painting objects’. The painting objects have finite tapes over the alphabet (R)ight, (D)own, (L)eft, (U)p. There are purple, blue, green and orange objects with tapes of length 8, 5, 4 and 4 respectively. At each time step, those cells with objects assume the colour of the object, use the value of the appropriate rotor as an index for decidingwhere to send the object, and then advance the appropriate rotor. For example, using the randomly chosen cell positions (52,68), (32,222), (65, 71) and (32,246) plus the randomly generated tapes DLULL, DUURLDDR, RUDL and DULU for the purple, blue, green and orange objects, respectively, after 15,000 time steps the random walk painting on the left of Figure 1 is obtained. At first glance, it may not be clear that I have specified a two-dimensional cellular automaton. Space prohibits providing the formal details, but if one thinks about what is happening from the point of view of the cells this claim should seem plausible. The random painting on the left in Figure 1 was selected from an initial randomly generated population