(This article was first published on

**Econometrics by Simulation**, and kindly contributed to R-bloggers)# 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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