2016-11-23 Walkin the Synth Space with Supercollider and Hilbert curves. https://github.com/abramhindle/hilbercurve-synth-controller
Space filling curves are curves that given a space will go through every point in that space. You have probably drawn many space filling curves before. The Hilbert curve is a pretty fun recursive u-shaped curve. One neat aspect of the Hilbert curve is that it can exist in multiple dimensions and it is easy to calculate how far along you are. So I take a 2D Hilbert curve and map it to a single value then I remap that value onto an N-dimensional hilbert curve. That value is communicated to supercollider who feeds it into a synthesizer effectively letting me explore synth space through a simple 2D input. Here’s a video of mucking around on a Hilbert curve https://www.youtube.com/watch?v=FM_Ne4YWx04&feature=youtu.be
Here’s an example of a Hilbert curve for mapping datapoints https://xkcd.com/195/
Here’s a wikipedia article on Hilbert curves https://en.wikipedia.org/wiki/Hilbert_curve
And here’s the algorithm for mapping to n-dimensional Hilbert curves http://citeseerx.ist.psu.edu/viewdoc/summary%E2%80%A6 .
Here’s an interactive 2D hilbert curve generator http://jsxgraph.uni-bayreuth.de/wiki/index.php/Hilbert_curve