CS 170: Computing for the Sciences and MathematicsAdministriviaExample: Cellular AutomataFire: Initializing the SystemUpdating RulesSlide 6Slide 7BoundariesHOMEWORK!Spread of FireDiffusion using Cellular AutomataCS 170:Computing for the Sciences and MathematicsAdministriviaLast time (in P265)Runge-Kutta 2/4Cellular Automata/Game of LifeTodaySimulation / AutomataHW #8 Due!HW #9 assignedNext time in P115Example: Cellular AutomataStructureGrid of positionsInitial valuesRules to update at each timestepoften very simpleNew = Old + “Change”This “Change” could entail a diff. EQ, a constant value, or some set of logical rulesFire: Initializing the SystemGrid-site values:0 - emptyprobTree = probability of grid site occupied by tree; i.e., tree densityprobBurnin g = If tree, probability that tree is burning; i.e., fraction of burning treesHow do we represent and initialize an n-by -n grid (forest) in Maple? 1 - non-burning tree2 - burning treeUpdating Rulesvon Neumann neighborhood Function spread(site, N, E, S, W) returns next value of site, based on values in locations site, N, E, S, and WUpdating RulesAt next time step, empty site remains emptyBurning tree burns down; site becomes emptyprobLightning = probability of lightningEach step, there is this probability of each tree catching fire based on lightning strikeUpdating RulesTree has chance of catching fire only if a nearest neighbor (N, E, S, W) is a burning treeprobImmune = probability of immunity from catching fireProbability of catching fire if exposed to fire = ?BoundariesHOMEWORK!Homework 9Due THURSDAY 11/11/2010Monday’s Class in