# ·
par(mfrow=c(1,1)) 

BMsim <- function(npaths,nSamples){
	p <- npaths
	N <-  nSamples
	y <- matrix(rep(0,(N+1)*p),nrow=N+1)
	t<-(c(0:N))/N
	
	for(j in 1:p){
	z<-  rnorm(N,0,1) 
	y[1,j]  <-  0
		for (i in 1:N) {
		y[i+1,j]<- (1/sqrt(N))*sum(z[1:i])
		}
	}
	y
}

fig  <-  function(npath) {
	p  <-  npath 
	for(i  in 1:p) {
		N <-  10^i 
		y <-  BMsim(1,N) 
		t <-  (c(0:N))/N 
		if(i  ==  1)  { 
			matplot(t,  y,  type  =  "l",  xlab =  "t",  ylab =  "Brownian motion", 
			lty = 1,  col =  1,ylim=range(-2.5,2.5)) 
		}
		else if(i  >  1) {
			lines(t,y)
		}

	}
}