Fwd: Week of June 6, 2016: Dynamical Systems


---------- Forwarded message ----------
From: Brenda McCaffrey <brendamc@asu.edu>
Date: Thu, Jun 9, 2016 at 3:43 PM
Subject: Week of June 6, 2016: Dynamical Systems
To: Xin Wei Sha <xinwei.sha@asu.edu>, Christopher Roberts <christopher.m.roberts@asu.edu>, Pavan Turaga <pavan.turaga@asu.edu>
Cc: Todd Ingalls <Todd.Ingalls@asu.edu>


Hi all,

Incredibly active week working hand-in-hand with the team on the iStage to reorganize and clean.  This was a great way to get hands dirty and become engaged.  Here are a few highlights from the week:

  • Helped organize and clean the iStage area, learning about
    • how the iStage is controlled (video hub, etc.)
    • how to clean the dance floor
    • how to coil and manage cables
  • Tried incorporating the basic Logic Equation with XOSC so I can use hand motion to trip the model into chaos, etc.
    • broke the patch (yay!?)
    • still working on it!
  • Started viewing archived online course:
Goals for next week:

  • Get the LogicEquation/XOSC patch working and demo it informally among the Synthesis folks on site.  
    • Create a little video showing functionality.
  • Continue taking Santa Fe course.
  • Read Ch. 3 of Sprott.  The chapter is entitled "Nonchaotic multi-dimensional flows."
Thoughts, suggestions, questions?

Thanks,
Brenda

Fwd: Great first week and unexpected progress on The Logistic Equation



Begin forwarded message:

From: Brenda McCaffrey <brendamc@asu.edu>
Subject: Great first week and unexpected progress on The Logistic Equation
Date: June 2, 2016 at 3:39:05 PM MST
To: Xin Wei Sha <xinwei.sha@asu.edu>, Pavan Turaga <pavan.turaga@asu.edu>, Christopher Roberts <christopher.m.roberts@asu.edu>, Brenda McCaffrey <brenda@bmccaffrey.com>
Cc: Todd Ingalls <Todd.Ingalls@asu.edu>

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