diff --git a/.gitignore b/.gitignore index fd63870..6f08d6c 100644 --- a/.gitignore +++ b/.gitignore @@ -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 diff --git a/wk11/week11.tex b/wk11/week11.tex index d7852e2..eb69514 100644 --- a/wk11/week11.tex +++ b/wk11/week11.tex @@ -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}