Exploring Tehran with excitable medium

Abstract

An excitable chemical medium --- Belousov-Zhabotinsky (BZ) reaction --- is proven to be a fruitful substrate for prototyping unconventional computing devices. These include image processors, logical circuits, and robot controllers. We study a BZ potential for characterising a geometry of street networks on a fragment of Tehran street map. The city was chosen because it is one of the most populated cities in the World with nearly uncontrollable urban growth. In numerical experiments with Oregonator model of BZ reaction, we demonstrate that excitability of the medium allows it to act as a selector between omnidirectional waves and soliton-like localised excitations. We uncover a phase-transition like dynamics, controlled by the excitability, of coverage of the street network by excitation wave-fronts. In the cluster analysis, we show how the network geometry, when it meets propagation of BZ wave-front, relates to the traffic flow of Tehran.