Pattern Formation
Natural patterns with almost periodic structures are seen all over the place in
nature. One sees them as sandwaves on gently sloped beaches and in desert
dunes, on the tips of one's fingers and on the palms of ones hands, on cacti and
other plants, as stripes on tigers and angelfish. In the laboratory, one sees them
in convecting fluids, on wide aperature (fat)laser beams, in chemical experiments
and on flame fronts.
The striking similarity of these textures, both in the nature of their planforms (stripes,hexagons) and in the line and point defects, arising in many different microscopic situations, suggests that patterns are macroscopic objects which should be describeable by universal and canonical mathematical equations. They are! Such descriptions and their uses in explaining observed pattern behavior is a research interest of several faculty members and students.
Questions currently being addressed are: What is the mechanism which produces the epidermal ridges on which our unique fingerprints were encoded when we were each less than three inches long? What are the mechanisms involved in creating all the wonderful patterns we see on plants? How do sunflowers know to order their spirals according to Fibonacci sequences? Why do bacteria swimming in a pond create convection patterns?
Group Members
Former Graduate Students
- Michael Kuecken, now at the University of Bayreuth.
- Patrick Shipman, now at the Max Planck Institute for Mathematics in the Sciences.