The Universal Nature of Fibonacci Patterns

Patterns with regular structures are ubiquitous. One sees them on the tips of one's fingers, on long sandy beaches, as granular patches on the sun's surface, on fishskins, and even in megalithic art. In laboratories, one sees them in experiments on convection, as thin shell buckling, on fat laser beams. 2D planar geometry patterns have universal features in that the pattern textures, planforms (stripes, hexagons) and defects (point and line), are macroscopic objects which depend more on overall symmetries and less on microscopic details. Patterns in plants have many features similar to those in 2D planar geometries but there are also significant differences. prominent among these is the way the pattern is formed and the outcome which in many cases shows that the plants' phyllas lie on families of spirals, families ennumerated by Fibonacci sequences. The talk will address the question of how universal such features are.