Pattern Formation in Nonequilibrium Growth

"We are surrounded by a nature out of equilibrium, a nature which presents the scientist with a bewildering and mesmerizing universe of patterns." [Ben-Jacob, Garik]

Introduction

All of the pictures above have a few things in common: they are all out of equilibrium, they all involve some type of feedback mechanism and they are all reproducible. Of course, they are not reproducible in the sense that you can reproduce the exact design, but in the sense that you can reproduce the same type of design. Everyone can recognize a lightning bolt, or a snowflake, even though each one is different from the other. So what is it about these patterns that we recognize? How are these shapes formed?

Another peculiar thing about these pictures is that they all come from completely different systems operating on completely different scales. How is it that the branches of the tree seem so similar to the branches of the lightning bolt or the crevices of the river valley or the branches of the electrodeposition of copper? To what extent are they similar? Can we come up with some type of universal "Laws of Pattern Formation"?

In this project we are using an electro-deposition cell to study the aggregations of copper ions in driven growth. We also performed a modified simulation of diffuision limited aggregation (DLA). From these studies we hope to understand better how patterns form in systems far from equilibrium.

This type of knowledge is not only important for theoretical reasons, but also for understanding how fractures occur in materials, how river valleys and oil wells are formed, or even how microscopic DNA can be amplified into a full-fledged human being.