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!

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**Tags:** bifurcation diagram, Feigenbaum, logistic map, R