By Varun Gudi and Peicong Dong
Fractals are fragmented shapes that can be split into parts, which are reduced-sized copies of the whole. Each reduced-sized copy is called an iteration, and this can be seen in many phenomena. In Mathematica, fractals are represented in the form of If statements. Fractals are all capable of holding vector spaces within, the dimension of which is called the Hausdorff dimension. A fractal's Hausdorff dimension is always between the dimension that the fractal began from and the one lower, and is calculated by the size of the object removed from each iteration. For example, the Hausdorff dimension of a Sierpinski triangle is approximately 1.585.
Try the different types of fractals in the Mathematica notebook! Note: Clicking the "iterate" button excessively can lag your computer; as a rule, only iterate 6 times.
Copyright © Spring 2011