Geometric fractals using traversal strategies

Description

In the literature it is assumed that given a line segment and a generator there is only one way to replace the line segment by the generator to produce the fractal image, i.e., a fixed traversal direction is assumed for each segment. We introduce the concept of traversal strategies wherein each of the segments of the initiator and generator can be traversed in three ways. This results in 3M • 3Q fractal images for a Q-segment initiator and an M-segment generator; these are referred to as the traversed geometric fractals. In contrast, a single fractal image is obtained without the use of traversal strategies. A software tool, Rangoli, has been developed to generate traversed geometric fractals. Several examples are included. Keywords: Geometric fractals, traversal strategies, generators, initiators, fractal images.