bifurcation diagram

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. <- 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.