**Fun with Fractals!**

By Varun Gudi and Peicong Dong

Updated 05/31/2011

By Varun Gudi and Peicong Dong

Updated 05/31/2011

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.

**Key Topics**

Geometry

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