A New Method of Constructing Fractals and Other Graphics

Abstract

The simplest type of Lindenmeyer or L-system can be used to construct graphics as follows. Two polygonal arcs A1 and A2 are chosen, such that the length of each line segment is an integral multiple of a fixed positive number, l, and if a line segment has length n l, then it is treated as a polygonal arc consisting of n line segments of equal length. Also, the angle between each pair of adjacent line segments is an integral multiple of a fixed angle, d. A1 is usually chosen as a single line segment or as the boundary of a regular polygon. Each line segment of A1 is replaced by a copy of A2, and then each line segment of the resulting polygonal arc is replaced by a copy of A2, and so on. The constructions are achieved by interpreting certain replacement rules for sequences as replacement rules for line segments [1].