\graphicspath{{misc/}}
\section{Fractal Poster}
On a wall in the main stairwell of the WPI mathematics bulding hung a poster depicting, in vivid color, an image of a spiral from a fractal.  Along the left side and top was the title, ``The Mathematics Art Bridge''.  This image is brightly colored, but it was created some time ago, and its effectiveness is somewhat diminished by the low printing quality.  The image was 22 inches wide by 28 inches tall, at a resolution of approximately 20 pixels per inch -- large enough that individual squares were easily visible.

As part of this IQP, we set out to replace the poster with an updated version using modern printing technology.  We selected a portion of the Julia set (described in section \ref{sec:julia} on page \pageref{sec:julia}) that resembled the original image, focusing on one of the main spirals of the Julia set with $c = 0.375 + 0.375\imath$.  We rendered the image using \emph{mandelbrot.cpp} described in appendix \ref{source:mandelbrot}, with the following command line:

\begin{verbatim}
  mandelbrot 500 2 -0.16677 0.433232 0.205014 0.805014 
    10000 10000 2 julia 0.375 0.375
\end{verbatim}

We used the rainbow palette, but rotated it slightly to accentuate the center of the image.  This produced a 10000x10000 pixel PNG file in approximately 15 minutes on one of WPI's servers.  We then opened the image in Paint Shop Pro 7, and cropped the image to the dimensions available in the poster.  We reduced the image to 9000x6600 pixels, so that it would be a bit larger than 22x28 inches when printed at 300 dots per inch.  Next, we added the fading effects and the title text.  Paint Shop Pro is unable to lighten a specific area of an image that uses only 256 colors, so we had to increase the image to true color.  This means that every pixel is defined by 3 values ranging from 0 to 256.  This means that every pixel requires one byte of storage, so the entire image filled approximately 170 megabytes of memory during editing.  We had the poster printed by the Academic Technology Center on glossy white paper, and it now hangs in a frame on the wall in Stratton Hall.  Figure \ref{fig:poster} contains a low detail version of the image.

\begin{figure}
\begin{center}
\includegraphics{poster}
\end{center}
\caption{A low detail version of the poster we created for the WPI Mathematics Department}
\label{fig:poster}
\end{figure}

