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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 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.r <- seq(2.5, 4, by=0.005) system.time(Orbit <- sapply(my.r, logistic.map, x=0.001, N=1000, M=300)) ## user system elapsed (on a 2.4GHz Core2Duo) ## 1.834 0.011 1.840 Orbit <- as.vector(Orbit) r <- sort(rep(my.r, (M+1))) plot(Orbit ~ r, pch=".") Let's not forget when Mitchell Feigenbaum started this work in 1975 he did this on his little calculator!