Modeling Chaos with Iterative Simulation
Perhaps the first tenet of chaos theory is that complex behavior need not arise from a complex source. More specifically, systems of relatively simple differential equations, impossible to solve classically, can be iterated in software or hardware to bring to life their nuanced behavior.
In my previous work, I used an analog circuit to solve Chua's equations, using the output as audio to act as a synthesizer for music and sound design work. I am currently investigating new interfaces for this system to make it more playable. My first vision is to track both of the users hands in three dimensions and to use each hand-dimension as a control input, allowing six parameters to be controlled simultaneously. In order to simplify the design, I intend to first realize the actual chaotic synthesis system in software, using iterative solutions, because achieving the finely-grained control of circuit parameters under microcontroller control necessary in the analog circuit will be a quite difficult problem in and of itself.
I am currently experimenting in Java and Processing with software realizations of Chua's equations and also intend to investigate the usability of other similar systems of equations. The screenshot below is from a first generation Processing applet, available here (requires the JSyn browser plugin). Move the mouse around to change parameters and control the system. If it runs out of bounds or stops, click the mouse button to reset it.