Bifurcation diagram of the logistic map [online version]

One of the reasons why mathematics is so amazing is that even a simple at first glance concepts have interesting behaviors and features. I think that the bifurcation diagram of the logistic map is a great example.

The logistic map is given by the equitation:

x_n+1 = rx_n(1 - x_n), x₀ < 1, r ∈ (0,4]

Below you may generate its bifurcation diagrams for different ranges and for different values of the x₀. It's amazing that those diagrams have fractal nature - self-similarity is even visible at first glance.

X-axis represents values for different r values, Y-axis represents x_0...n element value, n < 90 because in real world we can't show elements ad infinimum.

r_start>0: r_stop≤4: x₀<1:

The script was originally created a couple of years ago, so it may not be aligned with the modern JavaScript way of doing things. If you are interested how it works, please take a look on the source code of this page.