[R] Why does the graph converge?

[mousy0815]

I have a set of functions:

Probability <- function(N, f, w, b, l, n, q) {
	#N is the number of lymph nodes
	#f is the fraction of Dendritic cells (in the correct node) that have the
antigen
	#w is time in terms of hours
	#b is the starting position (somewhere in the node or somewhere in the gap
between nodes. It is a number between 1 and (x+t))
	#q is the length of the time step
	#l is the LN transit time in hours
	#n is the gap transit time in hours
	
		y <- n/q #y is the number of time steps it takes to traverse the gap 
		t <- l/q #t is the number of time steps it takes to traverse a node. 
	
		m <-(w%/%q)
		A <- 1/N
		B <- 1-A
		C <- 1-f
		D <- (((m+b-1)%%(y+t))+1)
	
		if (b<=t) {########starts inside node
			if (m<=(t-b)){return(B + A*(C^m))} # start & end in first node
			if (D<=t) { # we finish in a node		
				a <- (B + A*(C^(t-b))) #first node
				b <- ((B + A*(C^t))^(floor((m+b)/(y+t))-1))  # intermediate nodes (if
any)
				c <- (B + A*(C^D))  # last node  
				return(a*b*c)
			} else {return(Probability(N, f, ((m*q)-q), b, l, n, q))} ## finish in a
gap	
		} else {###### starts outside node
			if (m<=(y+t-b)) {return(1)} #also end in the gap
			if (D<=t) { #end in a node
				b <- ((B + A*(C^t))^(floor((m/(y+t)))))
				c <- (B + (A*(C^D)))
				return(b*c)
				} else {return(Probability(N, f, ((m*q)-q), b, l, n, q))} #outside node
		}
	}		

step.2 <- function(N, f, w, l, n, q) {##the sum of all the possible position
(times the probability)
	y <- n/q
	t <- l/q
	
	A <- sapply(1:(y+t), function(x) Probability(N=N, f=f, w=w, b=x, l=l, n=n,
q=q))
	B <- sum(A)
	C <- 1/(y+t)
	return(B*C)
}


step.3 <- function(N, f, w, l, n, q, X) { #X is the number of cells 
	return((1-((step.2(N, f, w, l, n, q))^X)))}



when I graph the Probability as a function of the transit time I get the
following graph:

tmax = 30
tlist <- seq(from=0, to=tmax, by=1)
cells = 1000
plot(tlist, sapply(tlist, function(x) step.3(N=500, f=0.001, w=24, l=x,
n=10, q=0.1, X=cells)), type='l', xlab="LN Transit Time (hours)",
ylab="Probability after 24 hours", main ="The Effect of DC frequency on the
Dip - 1000 cells", ylim = c(0,1))
lines(tlist, sapply(tlist, function(x) step.3(N=500, f=0.005, w=24, l=x,
n=10, q=0.1, X=cells)), col="coral") 
lines(tlist, sapply(tlist, function(x) step.3(N=500, f=0.01, w=24, l=x,
n=10, q=0.1, X=cells)), col="turquoise") 
lines(tlist, sapply(tlist, function(x) step.3(N=500, f=0.05, w=24, l=x,
n=10, q=0.1, X=cells)), col="blue") 
lines(tlist, sapply(tlist, function(x) step.3(N=500, f=0.1, w=24, l=x, n=10,
q=0.1, X=cells)), col="red")
lines(tlist, sapply(tlist, function(x) step.3(N=500, f=0.5, w=24, l=x, n=10,
q=0.1, X=cells)), col="green", type = 'l')  
legend((tmax*0.75), 0.5, c("f=0.001", "f=0.005", "f=0.01", "f=0.05",
"f=0.1", "f=0.5"), fill = c("black", "coral", "turquoise", "blue", "red",
"green"))

http://r.789695.n4.nabble.com/file/n3748957/Picture_2.png 


Why do the top three lines converge? Is it some bug in my function?

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