######### a call to dlogistic will
######### generate a cobweb plot of discrete logistic growth,
######### x[t+1] = r*x[t]*(1-x[t])
######### for n steps starting from x[0] = x0
# By R. Gomulkiewicz (23 Sep 2013)
# modified from cobweb plot on http://bayesianbiologist.com/

dlogistic<- function(r = 1, x0 = runif(1,0,1), n = 100,...) 
#default values: r = 1, x0 = random uniform between 0 & 1, 100 steps
{
dlog<- function(r, x){r*x*(1-x)} #the discrete logistic map

x<-seq(from=0,to=1,length.out=100)
plot(x,dlog(r,x),type='l',xlab=expression(x[t]),ylab=expression(x[t+1]), ylim=c(0,1),main= substitute(paste(italic(r)," = ",x,sep=""),list(x=r)))
abline(a=0,b=1)


start = x0
end = dlog(r, start)

points(start,start, pch = 19)  #show the initial point
lines(x=c(start,start),y=c(start,end) )  #first draw line from (x0, x0) to (x0, f(x0)

vert=FALSE  #2nd line will be horizonatal from (x0,f(x0) to (f(x0),f(x0))
for(i in 1:(2*n))
{
if(vert) #draw vertical line from (x,x) to (x,f(x))
{
lines(x=c(start,start),y=c(start,end) )
vert=FALSE
}
else  #draw horizontal line from (x,f(x)) to (f(x),f(x))
{
lines(x=c(start,end),y=c(end,end) )
vert=TRUE
start=dlog(r,start)
end <- dlog(r, start)
}
}
}

###Call the cobweb plot function with values r = 2.5, 3.5, and 4
dlogistic(r = 2, x0 = 0.1)

quartz()
dlogistic(r = 3, x0 = 0.1)

quartz()
dlogistic(r = 4, x0 = 0.1)