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Related Experiment Video

Updated: May 13, 2026

Mapping the Emergent Spatial Organization of Mammalian Cells using Micropatterns and Quantitative Imaging

Mapping the Emergent Spatial Organization of Mammalian Cells using Micropatterns and Quantitative Imaging

Published on: April 30, 2019

Competitively coupled maps and spatial pattern formation.

Timothy Killingback¹, Gregory Loftus, Bala Sundaram

¹Department of Mathematics, University of Massachusetts, Boston, Massachusetts 02125, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 19, 2013

Summary

This study introduces a simpler, robust model for spatial pattern formation using competitive coupling in coupled map lattices. This approach achieves spontaneous symmetry breaking and stable patterns, offering an alternative to complex reaction-diffusion systems.

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Area of Science:

Physics
Chemistry
Biology
Complex Systems

Background:

Spatial pattern formation is crucial in natural systems.
Understanding spontaneous symmetry breaking from homogeneous states is a key theoretical challenge.
Turing's reaction-diffusion systems are the standard model.

Purpose of the Study:

To present a simpler and more robust model for spatial pattern formation.
To investigate an alternative mechanism to diffusion for pattern generation.
To demonstrate spontaneous symmetry breaking and stable pattern formation.

Main Methods:

Formulation of a novel coupled map lattice model.
Coupling local site dynamics through competitive interaction, not diffusion.
Analysis of pattern formation based on interaction strength.

Main Results:

Competitive coupling induces spontaneous symmetry breaking.
Stable spatial patterns emerge from homogeneous initial states.
The mechanism is robust across various spatial geometries.

Conclusions:

The proposed coupled map lattice model offers a simpler, robust alternative for studying spatial pattern formation.
Competitive interaction is sufficient for generating complex patterns.
This model provides new insights into symmetry breaking in natural systems.