Scale Invariance of Spatial Distributions of Tree Branches, Leaves, and Petals

Takashi Matsuo¹, Masato Nakakubo² and Keijiro Yamamoto³

¹Medical Research Institute, Tokyo Medical and Dental University, 1-5-45 Yushima, Bunkyo-ku, Tokyo 113, Japan
²Tsukuba Institute of Technology, Kamitakatsu, Tsuchiura, Ibaraki 300, Japan
³Department of Mechanical Engineering, Kanagawa Institute of Technology, Shimo-ogino, Atsugi, Kanagawa 243-02, Japan

(Received October 3, 1996; Accepted January 9, 1997)

Keywords: Fractal, Tree, Branch Structure, Leaves, Petals

Abstract. The box-counting method was applied to measure the fractal dimensions for ramification patterns of trees and the spatial distributions of leaves and blossoms. The relationships between box size and the number of boxes necessary to cover the pattern for tree branches were found to obey the power law in a scale length of one decade. On the other hand, the distribution of leaves and petals showed scale invariance over a wider scale length of 2 orders when observation conditions were properly selected.