Visualizing the logistic map with a microcontroller

The logistic map is one of the simplest nonlinear dynamical systems that clearly exhibits the route to chaos. In this paper, we explore the evolution of the logistic map using an open-source microcontroller connected to an array of light-emitting diodes (LEDs). We divide the one-dimensional domain interval [0,1] into ten equal parts, an associate and LED to each segment. Every time an iteration takes place a corresponding LED turns on, indicating the value returned by the logistic map. By changing some initial conditions of the system, it is easy to observe the transition from order to chaos exhibited by this map.