Morphology-Induced Collective Behaviors: Dynamic Pattern Formation in Water-Floating Elements

Kohei Nakajima,Aubery Marchel Tientcheu Ngouabeu,Rolf Pfeifer,Shuhei Miyashita,Maurice Göldi,Rudolf Marcel Füchslin

doi:10.1371/journal.pone.0037805

Abstract

Complex systems involving many interacting elements often organize into patterns. Two types of pattern formation can be distinguished, static and dynamic. Static pattern formation means that the resulting structure constitutes a thermodynamic equilibrium whose pattern formation can be understood in terms of the minimization of free energy, while dynamic pattern formation indicates that the system is permanently dissipating energy and not in equilibrium. In this paper, we report experimental results showing that the morphology of elements plays a significant role in dynamic pattern formation. We prepared three different shapes of elements (circles, squares, and triangles) floating in a water-filled container, in which each of the shapes has two types: active elements that were capable of self-agitation with vibration motors, and passive elements that were mere floating tiles. The system was purely decentralized: that is, elements interacted locally, and subsequently elicited global patterns in a process called self-organized segregation. We showed that, according to the morphology of the selected elements, a different type of segregation occurs. Also, we quantitatively characterized both the local interaction regime and the resulting global behavior for each type of segregation by means of information theoretic quantities, and showed the difference for each case in detail, while offering speculation on the mechanism causing this phenomenon.

Highlights

Self-organization is one of the ways nature builds artifacts on various scales
We investigate floating elements on a container filled with water, half of which were actuated by a vibrating buzzer mounted on their tops, and the other half were merely floating on the water
Experimental System Overview In order to investigate the effect of morphology on a collection of distributed agents, we employ an experimental platform developed in our group [27,28,29,30,31,32]

Summary

Introduction

Self-organization is one of the ways nature builds artifacts on various scales. Nature offers diverse examples. Pattern formation or self-assembling processes can be split into two classes, static and dynamic [9,10]. Crystal formation and the assembly of polypeptide chains, for example, can be understood in terms of the minimization of free energy. In the case of biological tissues or swarms of agents, one is confronted with systems operating far from equilibrium, which can be classified as dynamic pattern formation. We focus on dynamic pattern formation and place special emphasis on the role of the morphology of the elements acting on it. We focus on dynamic pattern formation and place special emphasis on the role of the morphology of the elements acting on it. ‘‘Morphology,’’ in this context, refers to the shape of the elements, and mechanical properties such as friction coefficients, weight or elasticity

Objectives

Methods

Results

Conclusion