Scaling Behavior of a Self-Affine Fractal Interface in a Tree Line

Abstract

Scaling behavior of a self-affine fractal interface observed in a tree line is examined. A series of relatively horizontal tree lines are photographed, and each 9 cm × 13 cm color print is scanned and digitized to obtain the interface height h(x) as a function of position x. From these, the interface with w(L) is determined as a function of system size L. It is found that the interface width scales with system size L as w(L)~Lα with α=0.66±0.03. The result is assessed in comparison with other relevant experimental and theoretical results.