# Strategic Zombie Simulation – Animation

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# Escape Zombie Land! # This is a simulation an escape from a hot zombie zone. It freezes and gives an error if you get get killed so you had best not. You attempt to navigate the zone by constructing waypoints. # This is not a very clean set up and I would like to clean it up. However, I have spent way more time on it than I intended. So I might come back to it another day. # Zombies are distributed on a 10 x 10 grid. gridxy = c(10,10) # The number of zombies on the map nzombies = 40 # How close a zombie needs to be to take out a human is defined here same.space = .05 # This is how close a human needs to be to consider that the human has reached the waypoint. waypoint.hit = .2 # I set up the zombie distribution randomly initially. set.seed(1) zombiexy = cbind(runif(nzombies)*gridxy[1], runif(nzombies)*gridxy[2]) plot(zombiexy, main="Zombies!", xlab="X", ylab="Y", col=grey(.2), xlim=c(0,gridxy[1]), ylim=c(0,gridxy[2])) # Humans startpoint = c(.5,.5) humans = data.frame(x=c(0,-.25, .25), y=c(0,.25, -.25), name=c("You","Pete", "Jimmy")) humansxy = humans[,1:2] # Count humans nhumans = nrow(humansxy) (humansxy = humansxy+rep(startpoint, each=nhumans)) # Plot humans points(humansxy, pch=8) # Safety safety = c(9.5,9.5) # Waypoints, specify the waypoints the humans are to take to get to the destination. waypoints = rbind(c(2.5,2), c(5,6), c(9.75, 7)) # Route route = rbind(startpoint, waypoints, safety, safety, safety) lines(route) # A vector that will be shortenned as the simulation progresses route.unreached = route points(safety[1], safety[2], pch=7) # Now let's imagine that each zombie has a sensory distance in which the zombie can detect humans. detection.dist = 3 # How fast the zombies can move. Zombies have no inertia. zombie.acceleration = .075 # How fast humans can move human.acceleration = .075 # Humans can outrun zombies by building up inertia human.inertia = .6 # Initially everybody is at rest. hmovement = zmovement = 0 # --------------------------------------------------- #### Set up a single loop to check programming. # First the zombies move # First let's check how close each zombie is to each human. # We will accomplish this by going through each zombie and checking how far away each zombie is from each human. distances = matrix(NA, nrow=nzombies, ncol=nhumans) for (i in 1:nzombies) for (ii in 1:nhumans) distances[i,ii] = (sum((zombiexy[i,]-humansxy[ii,])^2))^.5 target = matrix(1:nrow(humansxy), ncol=nzombies, nrow=nrow(humansxy))[apply(distances, 1, order)[1,]] # The apply command will apply the order command to each row while the [1,] selects only the critter that is closes. plot(zombiexy, xlab = "X", ylab = "Y", main="If zombies did not have perception limitations") for (i in 1:nzombies) arrows(x0=zombiexy[i,1], y0=zombiexy[i,2], x1=humansxy[target,][i,1], y1=humansxy[target,][i,2], length=.1, col="red")

points(humansxy, pch=8) # Safety points(9.5,9.5, pch=7) # However, if the target is outside of detection range then zombies cannot target that human. target[distances[cbind(1:nzombies,target)]>detection.dist]=NA # Plot the relationship between zombies and humans plot(zombiexy, xlab = "X", ylab = "Y", main="Escape Zombie Land") for (i in 1:nzombies) arrows(x0=zombiexy[i,1], y0=zombiexy[i,2], x1=humansxy[target,][i,1], y1=humansxy[target,][i,2], length=.1, col="red") # Plot humans points(humansxy, pch=8) # Safety points(9.5,9.5, pch=7) # This calculates the difference between the current position of each zombie and that of the closest human. ab = zombiexy-humansxy[target,] ab=ab[!is.na(target),] # Now calculate the difference in the horizontal and vertical axes that the zombies will move as a projection into the direction of the closest zombie outside of the perceptive zone. a.prime = zombie.acceleration/(1 + (ab[,2]^2)/(ab[,1]^2))^.5 b.prime = (zombie.acceleration^2-a.prime^2)^.5 # This corrects the movement to ensure that the zombies are moving at the humans rather than away from them. zmovement = cbind(a.prime * sign(ab[,2]), b.prime * sign(ab[,1])) between = function(xy1,xy2,point) ((point>xy1&point<xy2)|(point>xy2&point<xy1)) zmovement = zmovement*(-1)^between(zombiexy[!is.na(target),],humansxy[target[!is.na(target)],], zombiexy[!is.na(target),]-zmovement) # Set the new xypos (zombiexy[!is.na(target),] = zombiexy[!is.na(target),]+zmovement) points(zombiexy, col="red") # Check if any of the zombies caught a human distances = matrix(NA, nrow=nzombies, ncol=nhumans) for (i in 1:nzombies) for (ii in 1:nhumans) distances[i,ii] = (sum((zombiexy[i,]-humansxy[ii,])^2))^.5 zombie.feast = distances[cbind(1:nzombies,target)]<same.space zombie.feast[is.na(zombie.feast)]=F humans.down=NULL (humans.down=unique(c(humans.down, unique(target[zombie.feast])))) # Remove victorious zombies from zombie pool (occupied) (zombiexynew = zombiexy[!zombie.feast,]) # Check if you are eaten if (1 %in% humans.down) stop("You died") # Display messages: if (length(humans.down)==1) warntxt = paste(humans[humans.down,3], "'s down!", sep="") if (length(humans.down)>1) warntxt = paste(humans[humans.down,3], "are down!") # Remove any "captured" humans if (length(humans.down)>0) { humansxy = humansxy[-humans.down,] nhumans = nrow(humansxy) } # Now the surving humans get to move. # However, we only calculate the movement for the leader (you) since all of the other humans move in parrellel to you. # Movement is also much simpler since humans just run from one waypoint to the next. # First we check if we have reached any waypoints (which we have since we start on one). way.distance = (sum((humansxy[1,]-route.unreached[1,])^2))^.5 if (length(route.unreached)==0) stop("Congraduations! Safety reached!") if (way.distance<waypoint.hit) (route.unreached = route.unreached[-1,]) # Now calculate the next place to move ab = humansxy[1,]-route.unreached[1,] # Now calculate the difference in the horizontal and vertical axes that the humans will move as a projection into the direction of the closest human outside of the perceptive zone. a.prime = human.acceleration/(1 + (ab[,2]^2)/(ab[,1]^2))^.5 b.prime = (human.acceleration^2-a.prime^2)^.5 # This corrects the movement to ensure that the zombies are moving at the humans rather than away from them. hmovement = cbind(a.prime * sign(ab[,2]), b.prime * sign(ab[,1])) between = function(xy1,xy2,point) ((point>xy1&point<xy2)|(point>xy2&point<xy1)) hmovement = hmovement*(-1)^between(humansxy[1,],route.unreached[1,], humansxy[1,]-hmovement) # Let's see what this looks like! points(humansxy, pch=8) lines(route) points(safety[1], safety[2], pch=7) points(route.unreached[-nrow(route.unreached),], pch=17) # Set the new xypos (humansxy = humansxy+ t(matrix(hmovement,nrow=2, ncol=nhumans))) # hmovement0 will save the movement to allow for inertia hmovement0 = t(matrix(hmovement,nrow=2, ncol=nhumans)) points(humansxy, pch=8, col="blue") # ------------------------------------------------------ # Let's turn this into an animation. ani.pause=F library(animation) flocking = function (ani.pause=F) { # This is text displayed on the map initially warntxt = "We need to make a run for the safe zone. Choose a route." while (nrow(route.unreached)>2) { # First let's check how close each zombie is to each human. # We will accomplish this by going through each zombie and checking how far away each zombie is from each human. distances = matrix(NA, nrow=nzombies, ncol=nhumans) for (i in 1:nzombies) for (ii in 1:nhumans) distances[i,ii] = (sum((zombiexy[i,]-humansxy[ii,])^2))^.5 if (nrow(humansxy)>1) target = matrix(1:nrow(humansxy), ncol=nzombies, nrow=nrow(humansxy))[apply(distances, 1, order)[1,]] if (nrow(humansxy)==1) matrix(1, ncol=nzombies, nrow=1) # The apply command will apply the order command to each row while the [1,] selects only the critter that is closes. target[distances[cbind(1:nzombies,target)]>detection.dist]=NA # Plot the relationship between zombies and humans plot(0,0, type="n", xlab = "X", ylab = "Y", main="Escape Zombie Land", xlim=c(0,gridxy[1]), ylim=c(0,gridxy[2])) # Safety points(9.5,9.5, pch=7) text(5,.25,warntxt) # This calculates the difference between the current position of each zombie and that of the closest human. ab = zombiexy-humansxy[target,] ab=ab[!is.na(target),] # Now calculate the difference in the horizontal and vertical axes that the zombies will move as a projection into the direction of the closest zombie outside of the perceptive zone. a.prime = zombie.acceleration/(1 + (ab[,2]^2)/(ab[,1]^2))^.5 b.prime = (zombie.acceleration^2-a.prime^2)^.5 # This corrects the movement to ensure that the zombies are moving at the humans rather than away from them. zmovement = cbind(a.prime * sign(ab[,2]), b.prime * sign(ab[,1])) between = function(xy1,xy2,point) ((point>xy1&point<xy2)|(point>xy2&point<xy1)) zmovement = zmovement*(-1)^between(zombiexy[!is.na(target),],humansxy[target[!is.na(target)],], zombiexy[!is.na(target),]-zmovement) # Set the new xypos zombiexy[!is.na(target),] = zombiexy[!is.na(target),]+zmovement points(zombiexy) # Check if any of the zombies caught a human distances = matrix(NA, nrow=nzombies, ncol=nhumans) for (i in 1:nzombies) for (ii in 1:nhumans) distances[i,ii] = (sum((zombiexy[i,]-humansxy[ii,])^2))^.5 zombie.feast = distances[cbind(1:nzombies,target)]<same.space zombie.feast[is.na(zombie.feast)]=F humans.down=NULL humans.down=unique(c(humans.down, unique(target[zombie.feast]))) # Remove victorious zombies from zombie pool (occupied) zombiexynew = zombiexy[!zombie.feast,] # Check if you are eaten if (1 %in% humans.down) warntxt = "You died" # Display messages: if (length(humans.down)==1) warntxt = paste(humans[humans.down,3], "'s down!", sep="") if (length(humans.down)>1) warntxt = paste(humans[humans.down,3], "are down!") # Remove any "captured" humans if (length(humans.down)>0) { humansxy = humansxy[-humans.down,] nhumans = nrow(humansxy) } # Now the surving humans get to move. # However, we only calculate the movement for the leader (you) since all of the other humans move in parrellel to you. # Movement is also much simpler since humans just run from one waypoint to the next. # First we check if we have reached any waypoints (which we have since we start on one). way.distance = (sum((humansxy[1,]-route.unreached[1,])^2))^.5 if (length(route.unreached)==0) stop("Congraduations! Safety reached!") if (way.distance<waypoint.hit) (route.unreached = route.unreached[-1,]) # Now calculate the next place to move ab = humansxy[1,]-route.unreached[1,] # Now calculate the difference in the horizontal and vertical axes that the humans will move as a projection into the direction of the closest human outside of the perceptive zone. a.prime = human.acceleration/(1 + (ab[,2]^2)/(ab[,1]^2))^.5 b.prime = (human.acceleration^2-a.prime^2)^.5 # This corrects the movement to ensure that the zombies are moving at the humans rather than away from them. hmovement = cbind(a.prime * sign(ab[,2]), b.prime * sign(ab[,1])) between = function(xy1,xy2,point) ((point>xy1&point<xy2)|(point>xy2&point<xy1)) hmovement = hmovement*(-1)^between(humansxy[1,],route.unreached[1,], humansxy[1,]-hmovement) # Let's see what this looks like! points(safety[1], safety[2], pch=7) points(route.unreached[-nrow(route.unreached),], pch=17) # Set the new xypos humansxy = humansxy+ t(matrix(hmovement,nrow=2, ncol=nhumans))+hmovement0*human.inertia # hmovement0 will save the movement to allow for inertia hmovement0 = t(matrix(hmovement,nrow=2, ncol=nhumans)) points(humansxy, pch=8, col="blue") # This is only used in the event that the animate package is in use. if (ani.pause) ani.pause() } } ani.options(interval = .15) flocking()

# Let's see how we do at escaping zombie land ani.options(ani.width=600, ani.height=600, interval=.25) saveGIF(flocking( ani.pause=T), movie.name = "Zombies.gif", replace=T)

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