Tuesday 17 January 2017

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 f(x), an old friend from Chaos Theory namely ax(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.

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