Dendrites, Viscous Fingers, and the Theory of Pattern Formation

Science  03 Mar 1989:
Vol. 243, Issue 4895, pp. 1150-1156
DOI: 10.1126/science.243.4895.1150


There has emerged recently a new theoretical picture of the way in which patterns are formed in dendritic crystal growth and in the closely analogous phenomenon of viscous fingering in fluids. Some interesting questions that arise in connection with this theory include: How broad is its range of validity? How do we understand dynamic stability in systems of this kind? What is the origin of sidebranches? Can weak noise, or even microscopic thermal fluctuations, play a role in determining the macroscopic features of these systems?