plot(0, type="n",xlim=c(0,0.5),ylim=c(0,50))
abline(v=1/6,lty=2,col=2)
grid()

n_data=1e3
for (p in c(1:5,10,15,20,25,50,100,250,500)){
    x=matrix(runif(n_data*p),ncol=p)
    all_dist=as.vector(dist(x))^2/p
    lines(density(all_dist))
}