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

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Kelvin Davis 2018-05-18 16:17:48 +10:00
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@ -27,6 +27,7 @@ wk7/week7.pdf
wk8/week8.pdf
wk9/week9.pdf
wk10/week10.pdf
wk11/week11.pdf
mini_proj/report/waldo.pdf
## Waldo data for the mini_proj

37
wk11/week11.tex
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@ -1,3 +1,31 @@
\documentclass[a4paper]{article}
% To compile PDF run: latexmk -pdf {filename}.tex
\usepackage{graphicx} % Used to insert images into the paper
\graphicspath{ {} }
\usepackage{float}
\usepackage[justification=centering]{caption} % Used for captions
\captionsetup[figure]{font=small} % Makes captions small
\newcommand\tab[1][0.5cm]{\hspace*{#1}} % Defines a new command to use 'tab' in text
% Math package
\usepackage{amsmath}
%enable \cref{...} and \Cref{...} instead of \ref: Type of reference included in the link
\usepackage[capitalise,nameinlink]{cleveref}
% Enable that parameters of \cref{}, \ref{}, \cite{}, ... are linked so that a reader can click on the number an jump to the target in the document
\usepackage{hyperref}
% UTF-8 encoding
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc} %support umlauts in the input
% Easier compilation
\usepackage{bookmark}
\usepackage{natbib}
% \usepackage{graphicx}
\begin{document}
\title{Week 11 - Virtual experiments}
\author{Kelvin Davis \and Jip J. Dekker\and Anthony Silvestere}
\maketitle
\section{Simulating Time}\label{simulating-time}
In this section we use Cellular Automata to show how different updating
@ -19,14 +47,13 @@ f(1,0,0) & = & 1\\
\text{otherwise }f(\_,\_,\_) & = & 0
\end{eqnarray*}
\subsection{Why do different patterns appear with different update
\subsection*{Why do different patterns appear with different update
rules?}\label{why-do-different-patterns-appear-with-different-update-rules}
There are 6 updating schemes:
\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\tightlist
\item
Synchronous - updates cells all at once for each time step
\item
@ -48,7 +75,7 @@ The synchronous method updates all the cells at once for each time-step.
As shown this results in a plot that is consistent. The Random
Independent method allows any cell to be updated at any time
\subsection{A common mistake in writing programs to run simulation
\subsection*{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
@ -65,7 +92,7 @@ which then results in sparse plots due to only two out of the eight
possible rules being active i.e.
\[\dfrac{\sum_{x\in\{0,1\}^3}{f(x)}}{|\{0,1\}^3|} = \dfrac{2}{8}\]
\subsection{Suggest cases where the clock scheme or random asynchronous
\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}
@ -91,3 +118,5 @@ 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.
\\
\end{document}