Hi all,
Thank you all again for this opportunity! It was a fun week.
My plan for this week was to work through the computer project at the end of Ch. 1 of Chaos and Time-Series Analysis (Sprott, 2003) as an introduction to dynamical systems and a slide into Lyapunov equations.
The project for this week was to simulate the logistic equation and port it into Max, and possible play with it on the iStage.
I started with MathCad and ran through some tutorials and observed that the scripting language looked very object-oriented, so I scanned around for some examples of code, moved over to JavaScript, went through some tutorials there. This led me to be curious about what Max/MSP could provide in terms of JavaScript training.
Well...some of you may know the answer. The very first JavaScript tutorial in Max/MSP is for the logistic equation. :-)
From reading ahead to Ch. 2 in Sprott, I was aware of the effect of changing the initial condition and also what I would call a fitting parameter (constant A in Sprott and r, the Malthusian parameter in other online documentation). I looked at the behavior of the logistic equation and noted that it performs in the Max patch as expected from the discussion in Ch. 2 of the book. I made a few modifications to the Max patch example so that I could interactively change the initial condition and the r value.
The output of the Max patch are tones. As the simulation moves from one region into another (and eventually into Chaos for r = 4), the tones clearly provide an example of the range in question.
Ch. 2 of Sprott goes into much more detail about the logistic equation. Here's my proposal for Week 2:
- Review and summarize the behavior of the logistic equation from the reading.
- The computer project at the end of Ch. 2 has to do with creating bifurcation diagrams of the logistic equation to illustrate that the period of the function doubles just prior to the onset of chaos -- I think it would be interesting to put this into an interactive iStage demonstration. The thought would be to make it very simple.
- Perhaps using XOSCs (left hand is initial condition, right hand is r?) so the user can experience and control the period doubling and onset of chaos by moving their hands.
- The response would be sound.
- The deliverable for the week would be the Max patch and a video demonstrating the operation.
Thoughts and suggestions?
Many thanks,
Brenda