# Feigenbaum

## Fun with the Raspberry Pi

Since Christmas I have been playing around with a Raspberry Pi. It is certainly not the fastest computer, but what a great little toy! Here are a few experiences and online resources that I found helpful. Setup Initially I connected the Raspberry Pi via HDMI to a TV; together with keyboard, mouse and an old USB Wifi adapter. Everything worked out of the box and I could install Raspbian and set up the network.

## Logistic map: Feigenbaum diagram in R

The other day I found some old basic code I had written about 15 years ago on a Mac Classic II to plot the Feigenbaum diagram for the logistic map. I remember, it took the little computer the whole night to produce the bifurcation chart. With today’s computers even a for-loop in a scripting language like R takes only a few seconds. logistic.map <- function(r, x, N, M){ ## r: bifurcation parameter ## x: initial value ## N: number of iteration ## M: number of iteration points to be returned z <- 1:N z[1] <- x for(i in c(1:(N-1))){ z[i+1] <- r *z[i] * (1 - z[i]) } ## Return the last M iterations z[c((N-M):N)] } ## Set scanning range for bifurcation parameter r my.