n<-75
c<-heat.colors(n)
set.seed(9825054)
a<-rnorm(n,mean=0,sd=1/sqrt(n))
b<-rnorm(n,mean=0,sd=1/sqrt(n))
Bx<-0
By<-0
for (t in 1:n) {
  Bx[t+1]<-Bx[t]+a[t]
  By[t+1]<-By[t]+b[t]
}
png(filename = "BrownBew2dim.png", width=1300, height=900)
par(bg="grey")
plot(x=Bx,y=By,type="l",xlab="",ylab="",xaxt="n", axes = FALSE)
axis(4, pos=0,col="black")
axis(3, pos=0,col="black")
arrows(Bx[seq(1,n)],By[seq(1,n)],Bx[seq(2,n+1)],By[seq(2,n+1)],col=c,lwd=4, length=0.1)
symbols(x=0,y=0,circles=c(0.03),inches=FALSE,add=TRUE,fg="black",lwd=3)
symbols(x=Bx[n+1],y=By[n+1],circles=c(0.04),inches=FALSE,add=TRUE,fg="black",lwd=3)
title(main="Zweidimensionale Brownsche Bewegung",cex.main=3)
text(x=c(-0.055,Bx[n+1]),y=c(0.06,By[n+1]),labels=c("Start","Endposition"),col="blue")