DNA self-assembly is a powerful technology for controlling matter at the nanometre to micron scale, with potential applications in high-precision organisation and positioning of molecular components. How-ever, the ability to program DNA-only self-organisation beyond the mi-croscopic scale is currently lacking. In this paper we propose a computa-tional method for programming spatial organisation of DNA at the cen-timetre scale, by means of DNA strand displacement reaction diffusion systems. We use this method to analyse the spatiotemporal dynamics of an autocatalytic system, a predator-prey oscillator and a two-species con-sensus network. We find that both autocatalytic and oscillating systems can support travelling waves across centimetre distances, and that con-sensus in a spatial context results in the spontaneous formation of distinct spatial domains, in which one species is completely eliminated. Together, our results suggest that programmed spatial self-organisation of DNA, through a reaction diffusion mechanism, is achievable with current DNA strand displacement technology.