|Update 30 December 2022: Fine-tuned some of the sonifications of the locality-preserving properties of several traversals in up to seven-dimensional Euclidean space and eight-dimensional permutation space, and restructured the web pages with respect to that topic.
|Update 17 November 2021: Added new sonifications of the locality-preserving properties of several traversals in up to seven-dimensional Euclidean space, and in eight-dimensional permutation space.
|Update 18 February 2018: New tracks through turning-function/direction mapping: hear the Peano curve's gentle rocking motion on multiple levels, and hear the interesting metre of the Meander curve.
|Update 20 December 2017: Added sound tracks of four-, five-, and six-dimensional Harmonious Hilbert curves.
I am exploring approaches to make sonifications (or music?) of space-filling curves. So far, I have tried three approaches that gave interesting results. All of them sonify some properties of the curve as one follows it from the beginning to the end. In order of increasing complexity, the three approaches are:
Actually there is a fourth approach: Axis mapping is another approach to sonify the direction of travel such that it illustrates a particular property of a particular class of higher-dimensional Hilbert curves—but it does not seem to applicable to other space-filling curves.
The example sound tracks on the four web pages linked above use various techniques, resulting in musical styles that vary from kind-of-classical to minimalist. People visiting this web page seem to have different opinions on which tracks are their favourites. Regardless of your musical taste, I recommend you first check out the page on location mapping, and listen to the beginning of some of the tracks, just to get accustomed to the main idea of what is going on here. If, however, you first want to get a sense of the end results, here is a sample:
| Technical issues with play-back:
* When using Internet Explorer, instead of audio files you might see error messages “Invalid source”. Workaround: right-click on the player and select “Copy audio URL”, then paste the url into the address bar. Or use another browser.
* I recommend using good speakers/headphones. On mediocre laptop speakers/headphones, you might miss the lower tones.