Python: Lorenz

If you follow my blog or have devoted at least a minute to run through the headings, you should know that I am a fanatic of Chaos Theory. Or rather, I am crazy about messing with very simple systems, which are related to the ideas of sensitive dependence on initial conditions, unexpectedly complex behavior and other stuff that the words ‘mathematical chaos’ bring to one’s mind. The key word here is ‘simple’, since, because of very modest math skills, during my exploration I kept avoiding things involving any non-trivial mathematics. The most notable here is the fact that I didn’t even try to approach the Lorenz system, whose phase portrait, along with the plots of Mandelbrot set, may be considered the symbol of the Chaos Theory. However, beside playing with the Barnsley fern the last month I also made up enough guts to try and code the most well-known chaotic system.

Exploring Chaos through Python and Tkinter

Overview

This relatively long entry describes some of my attempts to explore interesting stuff related to the origins of Chaos Theory. The experiments I describe here were carried out several decades ago, so I haven't invented something new, although I suppose that the stuff I show may encourage the reader to study the field on his own. 

While the first and the third parts focus on things related to Chaos Theory, some simple although nice math and, mainly, on the impression that this stuff made on me, the second part exposes code that I've written trying to achieve two goals. First, I actually wanted to do the metnioned experiments on my own, second, I tried to gain some experience with Tkinter python package for creating GUIs. Due to simplicity of the experiment I suppose that Part Two may be interesting only for those, who want to take a look on the simple interactions with Tkinter.

(In case you want just to see how complex can be the behavior of the simplest possible discrete chaotic systems, you may visit my site - there are some playable graphs)

Have a nice reading!