Posts Tagged: escape velocity

Jun 10

Reaching escape velocity

Sample once from the Uniform(0,1) distribution. Call the resulting value [latex]x[/latex]. Multiply this result by some constant [latex]c[/latex]. Repeat the process, this time sampling from Uniform(0, [latex]x*c[/latex]). What happens when the multiplier is 2? How big does the multiplier have to be to force divergence. Try it and see:

iters = 200
locations = rep(0,iters)
top = 1
multiplier = 2
for(i in 1:iters) {
	locations[i] = runif(1,0,top)
	top = locations[i] * multiplier


# Optional save as movie, not a good idea for more than a few hundred iterations. I warned you!
# library("animation")
# saveMovie(for (i in 1:iters) plot(locations[1:i],1:i,pch=20,col="blue",xlim=c(0,max(locations)),ylim=c(0,iters),xlab="Location",ylab="Iteration"),loop=1,interval=.1)