Drawing with Recursion

Recursion is fundamentally based on the notion of self-similarity and repetition. Fractal art is probably the most well popularized example of mathematical recursion, first made famous by the striking images produced in the 1970s by Benoit Mandelbrot with early computer-aided visualizations. However visual art showing recursive themes appeared much earlier, in particular, M. C. Escher and Rene Magritte’s work comes to mind. Although fundamentally a mathematical construct and immensely applicable in general-purpose programming, recursion exhibits stunning symmetry and aesthetics when used in conjunction with geometric forms and topological patterns. In this chapter we will introduce basic recursion and recursive functions, as well as a data visualization example based on recursive treemaps.