Galleri — Fractals

The first six levels of the Sierpinski triangle in LaTeX. For some beautiful variations (and more information), see http://www.oftenpaper.net/sierpinski.htm

In this we examine the concept of the dimension of fractals, extending the idea of integer dimension to fractals, which we define and investigate here in. Moving on we consider the Minkowski dimension, sometimes referred to as the "box dimension", of a fractal. We then continue to define and examine another type of dimension; the Hausdorff dimension. We then investigate under what conditions these are equal finally moving on to prove Hutchinsons Theorem,

Four dragon curves tessellating the plane using tikz. Order of recursion limited by TeX memory/compile timeout.