Forma, Vol. 10 (No. 1), pp. 17-21, 1995
Original Paper

Differential Fractals of Pinnation Pattern on Fern Leaf-Blade

Satoshi Kano and Toshiyuki Sato

The Institute of Low Temperature Science, Hokkaido University, Sapporo 060, Japan

(Received May 2, 1994; Accepted June 9, 1994)

Keywords: Fern, Fractal dimension (D), Differential Fractals (DFD), Leaf-blade, Pinna, Pinnule, Trajectory

Abstract. Fractal dimension (D) of leaf-blade of Dryopteris erythrosora from southern Honshu was calculated by applying with different resolution levels from 0.212 to 52.92 mm side lengths of square. The fractal dimension was about 1.779 on intact leaf-blade. Two manupulations for pinnules and pinnae elimination were conducted on the leaf-blade; and fractal dimensions (Ds) were compared among those of three samples. The Ds increased into 1.825 and 1.893 on the manupulated silhouettes. The "Differential Fractals (DFD)" represented by D/dr was calculated to detect fine difference during measurements with different resolution levels. The fluctuating and separating trajectories were obtained for pinnules elimination at 4 mm and pinnae at 25 mm side lengths of grids' resolution levels. The pinnation pattern will be quantified by the DFD measurements on plant leaf-blades.