Mercurial > hg > cip2012
changeset 17:e47aaea2ac28
Added images
| author | Henrik Ekeus <hekeus@eecs.qmul.ac.uk> |
|---|---|
| date | Wed, 07 Mar 2012 15:12:49 +0000 |
| parents | d5f63ea0f266 |
| children | ca694f7dc3f9 |
| files | MatrixDistribution.png TheTriangle.pdf draft.tex |
| diffstat | 3 files changed, 14 insertions(+), 3 deletions(-) [+] |
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--- 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.