From art to physics: spatial pattern formation in flowing paint

Pattern formation is a captivating gateway into non-equilibrium physics, yet its study usually requires complex laboratory equipment and abstract partial differential equations. In this paper we present an accessible low cost experiment using gravity-driven flow of low-cost common art-grade paint down an inclined plane. This leads to emergent spatial patterns comprising long fingers of paint with a characteristic spacing dependent on plane inclination. We present experimental results and relate these to concepts from hydrodynamic theory. While this is suitable for high-school students, we also suggest how it may be extended to both primary school settings and undergraduate classes. From a conceptual study of paint fingering we propose a generic model of spatial pattern formation using Turing’s reaction-diffusion equations.