Below, you find the R code for computing the Game of life
n=20 # Size of matrix
mat=matrix(0,ncol=n,nrow=n) # Create a n x n matrix with zeros
mat[5:14,10]=1 # Add 10 live cells
temp_mat=mat # Create a temporary matrix
image(t(apply(mat, 2, rev)),col=c("grey50","seagreen1"),yaxt="n",xaxt="n") # Plot image
grid(nx=n,ny=n,col="grey70",lty=1)
mat1=mat[c(2:n,1),];mat2=mat[c(n,1:n-1),]; mat3=mat[,c(2:n,1)]; mat4=mat[,c(n,1:n-1)]; mat5=mat[c(2:n,1),c(2:n,1)]; mat6=mat[c(2:n,1),c(n,1:n-1)]
mat7=mat[c(n,1:n-1),c(n,1:n-1)];mat8=mat[c(n,1:n-1),c(2:n,1)];
for (k in 1:200){ # Repeat 200 times
numb_alive=mat1+mat2+mat3+mat4+mat5+mat6+mat7+mat8
temp_mat[mat==1 & numb_alive<2]=0
temp_mat[mat==1 & numb_alive>3]=0
temp_mat[mat==1 & (numb_alive==2 | numb_alive==3)]=1
temp_mat[mat==0 & numb_alive==3]=1
mat=temp_mat # Update matrix
mat1=mat[c(2:n,1),];mat2=mat[c(n,1:n-1),];mat3=mat[,c(2:n,1)];mat4=mat[,c(n,1:n-1)]
mat5=mat[c(2:n,1),c(2:n,1)];mat6=mat[c(2:n,1),c(n,1:n-1)];mat7=mat[c(n,1:n-1),c(2:n,1)]
mat8=mat[c(n,1:n-1),c(n,1:n-1)]
image(t(apply(mat, 2, rev)),col=c("grey50","seagreen1"),add=TRUE) # Plot image
grid(nx=n,ny=n,col="grey70",lty=1)
Sys.sleep(0.5) # To see changes on the screen we need to pause the loop
}
Below, you find the R code for the SIR model
rm(list=ls())
q=0.5 # Probability for recovery
n=50 # Size of matrix 50 x 50
mat=matrix(ncol=n,nrow=n,0) # Create matrix with zeros (Healthy individuals)
mat[25,15]=1 # Place an infected individual at pos (25,15)
image(mat,col=c("grey50","deeppink","seagreen1"),yaxt="n",xaxt="n",zlim=c(0,2)) # Plot image
grid(nx=n,ny=n,col="grey70",lty=1)
temp=mat
t=80 # Number of time steps
n_helalthy=rep(0,t) # Vector to count healthy at each time step
n_infected=rep(0,t) # Vector to count infected at each time step
n_resistant=rep(0,t) # Vector to count resistant at each time step
for (k in 1:t){ # Repeat t times
kH=0 # Initialize counter for healthy
kI=0 # Initialize counter for infected
kR=0 # Initialize counter for resistant
# Step through each element in the matrix
for (i in 1:n){
for (j in 1:n){
if (mat[i,j]==0) { kH=kH+1} # Count healthy
if (mat[i,j]==1) { kI=kI+1} # Count infected
if (mat[i,j]==2) { kR=kR+1} # Count resistant
R=0 # Initialize counter for number of infected neighbors
if (mat[i,j]==0){ # If healthy individual
E=i+1
W=i-1
N=j-1
S=j+1
# Check if outside the matrix
if (E==n+1) { E=1}
if (W==0) { W=n}
if (N==0) { N=n}
if (S==n+1) { S=1}
# Count number of infected neighbors
if(mat[E,j]==1){R=R+1} # East
if(mat[W,j]==1){R=R+1} # West
if(mat[i,N]==1){R=R+1} # North
if(mat[i,S]==1){R=R+1} # South
if(mat[E,N]==1){R=R+1} # North East
if(mat[E,S]==1){R=R+1} # South East
if(mat[W,N]==1){R=R+1} # North West
if(mat[W,S]==1){R=R+1} # South West
}
a=-1.5
b=0.6
Pinfect=(1/(1+exp(-(a+b*R)))) # Calc probability for healthy to become infected
g=runif(1) # Draw a random number between 0 and 1
if (g<Pinfect & mat[i,j]==0 & R>0){
temp[i,j]=1 # Healthy becomes infected
}
if (mat[i,j]==1){ # If infected individual
g=runif(1) # Draw a random number between 0 and 1
if (g<q){
temp[i,j]=2 # Infected becomes Resistant
}
}
}
}
image(mat,col=c("grey50","deeppink","seagreen1"),add=TRUE,,zlim=c(0,2)) # Plot image
grid(nx=n,ny=n,col="grey70",lty=1)
Sys.sleep(0.1) # To see movement on screen we need to pause the loop
mat=temp # Overwrite matrix
# Save number of healthy, infected and resistant at each time step
n_helalthy[k]=kH
n_infected[k]=kI
n_resistant[k]=kR
}
graphics.off()
plot(1:k,n_helalthy,type="l",ylab="Number",xlab="Time steps (weeks)",col=1,ylim=c(0,2600))
lines(1:k,n_infected,col=2)
lines(1:k,n_resistant,col=3)
legend(x=52,y=1599,c("Susceptible","Infected","Recovered"),lty=1,col=1:3)
