Forma, Vol. 6 (No. 3), pp. 241-246, 1991
Original Paper

Combination Fractals from Different Shape-Unit on Fern Leaves

Toshiyuki Sato1, Shinichi Matsumoto1, and Fusayuki Kanda2

1The Institute of Low Temperature Science, Hokkaido University, Sapporo 060, Japan
2Hokkaido University of Education, Kushiro 085, Japan

(Received October 9, 1991; Accepted November 13, 1991)

Keywords: Combination Fractals, Dryopteris, Ferns, Sakhalin, Shape-Unit

Abstract. Fractal dimensions of leaves of three Dryopteris ferns from southern Sakhalin were calculated by applying different shapes of boxes, equilateral triangle (Dt), square (Ds) and hexagon (Dh). A combination of these dimensions was illustrated as a function of the side length (r-N) and area (S-N) of the shape-unit. Both r-N and S-N produced similar estimates of the three fractal dimensions. The largest r-N values (1.678-1.693) were measured on D.coreano-montana and the lowest values (1.459-1.594) were measured on D.amurensis. The presentation of the three fractal dimensions in combination characterizes the individuality of the sampleshape, i.e., a relative shifting to triangle-unit for D.amurensis and to hexagon-unit for D.austriaca. Such a combinatorial model of fractals derived from variable shapeunits will serve to expand a new science of the quantification of natural diversity and individual shape-character as well as shape-complexity in the wild.