A Novel Way to Generate Fractals

1. INTRODUCTION. For more than twenty years, fractals have intrigued mathematicians and nonmathematicians alike due to their inherent beauty and widespread appearance in nature and computer graphics. Intuitively, a fractal is a geometric object with intricate detail on an arbitrarily small scale and some measure of self-similarity. Formally, a fractal is a metric space with topological dimension strictly less than its Hausdorff dimension [4, p. ix]. For example, the Sierpi´nski triangle (Figure 1) is a fractal with topological dimension 1 and Hausdorff dimension ln 3/ ln 2. This means that the Sierpi´nski triangle is " thinner " than a solid triangle, but " thicker " than a line. Therefore, its Hausdorff dimension lies between the dimensions of a solid triangle and a line (two and one, respectively).