Hi Chris, Xin Wei and Pavan,
I'm home! Sorry I missed your meeting yesterday. We returned to Phoenix on Wednesday night and I was making some medical rounds yesterday. We were on a very tiny cruise ship from Venice to Rome and I re-injured my foot in Croatia. Rough seas for the ensuing days and I was unable to tender ashore. No worries -- I'm super happy and had a great time!
The good news --- I had a blissful day anchored off Sicily with a view of Mt. Etna and read the first couple of chapters of Chaos and Time-Series Analysis. Very rich and delicious book -- thanks, Pavan. Lyapunov exponents are introduced in Ch. 5 and the chapters leading up to it are dense with thought-provoking implications of dynamical systems.
My thought right now is to focus on a simulation for next week and create a little demo by next Thursday's Synthesis meeting. At the end of each chapter, there is a simulation exercise and these build on each other leading to Lyapunov and beyond. So, I could do the exercise in Chapter 1 for next week -- I think it would be a good way to get my feet wet and see where it leads.
For reference, here is the exercise:
1.8 Computer project: The logistic equationThis project gets you started using the computer to model chaotic processes and to explore some of the more obvious properties of the logistic equation,.... The logistic equation isi perhaps the simplest example of a chaotic system. It models a process that exhibits initial exponential growth with a nonlinearity that ultimately stops the growth. Most of the common features of chaos are manifest in this simple example. The variable X is advanced successively in discrete time steps denoted by Xn for n = 0,1,2,.... Start with an initial condition of X0 = 0.1 and iterate the logistic equation many times. {This goes on for several paragraphs}
There are several steps to the exercise and I'll go through as many as possible and devise a small scenario to play out on the iStage using Max, and report on the experience and any results.
I'm sure this kind of thing has been done before, but I think it will be a good introduction and will require that I can play with the simulation, create a Max sub-patch, and create something experiential with it. I hope it will be interesting.
Please let me know what you think. I'll also post this and future notes on the dynamical-systems Posthaven site and on the Slack channel.
Good to be home! Please feel free to share this with anyone who may be interested.
Regards,
Brenda
p.s., I think Monday is a holiday, so I'll be in Matthews on Tuesday morning at 10am.
