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\title[Classical Fractals]{Classical Fractals}
\author[R Marangell]{Robby Marangell}
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\maketitle
\section{The Cantor Set}
The Cantor set is awesome. You can read how awesome it is yourself in \cite{peitgen2004chaos}. It is made by an iterative procedure. \Cref{fig:cantor1} shows how to construct the Cantor set from the set $[0,1]$. 
\begin{figure}[h]
\includegraphics[scale=1]{cantor1}\caption{The Iterative procedure that makes the Cantor set}\label{fig:cantor1}
\end{figure}

\subsection{Properties of the Cantor Set.} \Cref{fig:cobwebbing} shows how the Cantor set can be realised as the prisoner set of a `feedback' loop for the piecewise function:
\begin{equation}
f(x) =  \left\{
\begin{array}{l c r}
3 x       &   & x \leq \frac{1}{2} \\
& & \\
-3x + 3 &  & x > \frac{1}{2} 
\end{array}
\right.
\end{equation}

\begin{figure}[h]
\includegraphics[scale=1]{cobwebbing}\caption{It is way easier to make a better picture using the computer.}\label{fig:cobwebbing}
\end{figure}

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