Merge branch 'master' of https://github.com/Dekker1/ResearchMethods

wk11/week11.tex

@@ -47,6 +47,17 @@ f(1,0,0) & = & 1\\
 \text{otherwise }f(\_,\_,\_) & = & 0
 \end{eqnarray*}
 
+\begin{figure}[H]
+	\includegraphics[scale=0.55]{plots}
+	\centering
+	\captionsetup{width=0.80\textwidth}
+	\caption{Plots of the execution of the cellular automata with the different
+    updating methods. From top-left to top-right: Synchronous, Random
+    Independent, Random Order. From bottom-left to bottom-right: Clocked,
+    Cyclic, Self-Synchronous}
+	\label{fig:plot}
+\end{figure}
+
 \subsection*{Why do different patterns appear with different update
 rules?}\label{why-do-different-patterns-appear-with-different-update-rules}
 
@@ -83,7 +94,7 @@ Independent method allows any cell to be updated at any time
 models is to scan through an array updating each cell in turn, based on
 the current values of its neighbours. Which of the update schemes
 demonstrated corresponds to
-this?}\label{a-common-mistake-in-writing-programs-to-run-simulation-models-is-to-scan-through-an-array-updating-each-cell-in-turn-based-on-the-current-values-of-its-neighbours.-which-of-the-update-schemes-demonstrated-corresponds-to-this}
+this?}
 
 The cycle option corresponds to updating each cell based on the current
 state of its neighbours. This can be verified by looking at the pattern
@@ -98,11 +109,16 @@ possible rules being active i.e.
 
 \subsection*{Suggest cases where the clock scheme or random asynchronous
 updating might bean appropriate way to model a system in the real
-world?}\label{suggest-cases-where-the-clock-scheme-or-random-asynchronous-updating-might-bean-appropriate-way-to-model-a-system-in-the-real-world}
+world?}
 
 In cases where we are modelling systems over continuous time, then the
 clock scheme or random asynchronous updating would be appropriate to
-use. These might be systems like
+use. An advantage of these schemes compared to the other schemes is
+that they allow for more complex agents as not all agents are updated
+at every step. This means that many multi-agent systems would probably
+use such a scheme. A well known example of this would be ``Boids'', a
+simulation of flocking birds where every bird is evaluated as a separate
+agent.
 
 \section{Sensitivity analysis - critical mass in a
 nuclear}\label{sensitivity-analysis---critical-mass-in-a-nuclear}
@@ -115,12 +131,20 @@ simulate the system at varying densities between 0\% and 20\% and use
 the graphs showing the energy released from the system over time to
 gauge how where the runaway reaction occurs.
 
+\begin{figure}[H]
+	\includegraphics[scale=0.70]{plots2}
+	\centering
+	\captionsetup{width=0.80\textwidth}
+	\caption{Plots of energy released over time. Each plot corresponds a
+    different density: 0\%, 5\%, 8\%, 10\%, 11\%, 12\%, 13\%, 15\%, 17\% and 20\%}
+	\label{fig:plot2}
+\end{figure}
+
 We take measurements of the energy released at densities of 0\%, 5\%,
 8\%, 10\%, 11\%, 12\%, 13\%, 15\%, 17\% and 20\%, sampling at shorter
 intervals of density closer to the density at which the maximum reading
-of the energy released exceeds 10 .
+of the energy released exceeds 10.
 
-This breakout first happens at 12, and so we deem this to be the
-critical density of the system.
-\\
+We found that the hightest desity for which no breakouts occur  is at
+10\%. We thus deem this to be the critical density of the system.
 \end{document}