Feigenbaum Constants

The Feigenbaum constants are right up there with the big ones but it was only after watching a Numberphile video that I understood the significance of the delta 𝛅 constant. Here is the video that I watched:

The Feigenbaum constant 𝛿 is defined by Wikipedia as follows:

It's easier to see with a specific example of \( \text{f}(x) \), an old friend from Chaos Theory namely \(a  x(1-x) \) and a table of values for \(a\):

I created a spreadsheet in Google Sheets to illustrate the bifurcation process. Below is an example of the first bifurcation when a=3.3:

Below is an example of the second bifurcation, taken when a=3.5:

And so on it goes.