# HG changeset patch
# User Henrik Ekeus <hekeus@eecs.qmul.ac.uk>
# Date 1331133169 0
# Node ID e47aaea2ac2886504ec9a014fa47e17808d92873
# Parent  d5f63ea0f266d0c0a48e4fa12917fa203e2564e9
Added images

diff -r d5f63ea0f266 -r e47aaea2ac28 MatrixDistribution.png
Binary file MatrixDistribution.png has changed
diff -r d5f63ea0f266 -r e47aaea2ac28 TheTriangle.pdf
Binary file TheTriangle.pdf has changed
diff -r d5f63ea0f266 -r e47aaea2ac28 draft.tex
--- a/draft.tex	Tue Mar 06 15:21:35 2012 +0000
+++ b/draft.tex	Wed Mar 07 15:12:49 2012 +0000
@@ -240,7 +240,14 @@
  	
 Before the Melody Triangle can used, it has to be ÔpopulatedÕ with possible parameter values for the melody generators.
 These are then plotted in a 3d statistical space of redundancy, entropy rate and predictive information rate. 
-In our case we generated thousands of transition matrixes, representing first-order Markov chains, by a random sampling method. In figure x we see a representation of how these matrixes are distributed in the 3d statistical space; each one of these points corresponds to a transition matrix.\emph{self-plagiarised}
+In our case we generated thousands of transition matrixes, representing first-order Markov chains, by a random sampling method. In figure \ref{InfoDynEngine} we see a representation of how these matrixes are distributed in the 3d statistical space; each one of these points corresponds to a transition matrix.\emph{self-plagiarised}
+
+\begin{figure}
+\centering
+\includegraphics[width=0.5\textwidth]{MatrixDistribution.png}
+\caption{The population of transition matrixes distributed along three axes of redundancy, entropy rate and predictive information rate.  Note how the distribution makes a curved triangle-like plane floating in 3d space.  \label{InfoDynEngine}}
+\end{figure}
+ 
 	
 When we look at the distribution of transition matrixes plotted in this space, we see that it forms an arch shape that is fairly thin. 
 It thus becomes a reasonable approximation to pretend that it is just a sheet in two dimensions; and so we stretch out this curved arc into a flat triangle. 
@@ -248,8 +255,12 @@
 	
 When the Melody Triangle is used, regardless of whether it is as a screen based system, or as an interactive installation, it involves a mapping to this statistical space. 
 When the user, through the interface, selects a position within the triangle, the corresponding transition matrix is returned. 
-Figure x shows how the triangle maps to different measures of redundancy, entropy rate and predictive information rate.\emph{self-plagiarised}
-	
+Figure \ref{TheTriangle} shows how the triangle maps to different measures of redundancy, entropy rate and predictive information rate.\emph{self-plagiarised}
+ \begin{figure}
+\centering
+\includegraphics[width=0.5\textwidth]{TheTriangle.pdf}
+\caption{The Melody Triangle\label{TheTriangle}}
+\end{figure}	
 Each corner corresponds to three different extremes of predictability and unpredictability, which could be loosely characterised as ÔperiodicityÕ, ÔnoiseÕ and ÔrepetitionÕ. 
 Melodies from the ÔnoiseÕ corner have no discernible pattern; they have high entropy rate, low predictive information rate and low redundancy. 
 These melodies are essentially totally random.