Visualizing the logistic map with a microcontroller

TL;DR

This paper demonstrates how to visualize the behavior of the logistic map, a simple nonlinear system, using a microcontroller and LEDs to illustrate the transition from order to chaos.

Contribution

It introduces a practical method for visualizing the logistic map's dynamics with accessible hardware, making complex nonlinear phenomena more tangible.

Findings

LEDs visually represent the logistic map's evolution.

Transition from order to chaos observed through LED patterns.

Microcontroller setup effectively demonstrates nonlinear dynamics.

Abstract

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