Animated apollonius diagrams

An Apollonius diagram shows Voronoi edges between discs of varying sizes. Here is an animation where the sites move and reduce in size from frame to frame. By increasing the angle of direction the sites form a spiral.

This animation is the same but the sites oscillating perpendicular to the direction of travel.

In these two simple animations we have seen size (weighting), direction of travel and oscillation as properties of a Voronoi site that change over time. We may think of several other properties, such as speed of travel and origin. We may then map from properties of things from other domains, such as music.

Here is a simple example where musical note value is mapped to direction of travel. That is, as each note is triggered, a Voronoi site is created and animated according to the musical pitch of the note.

Apollonius diagrams and the Representation of Sounds and Music

The abstract from our paper submitted to ISVD07:


We introduce the use of weighted medial graph structures to represent sounds and musical events. Such structures permit the building of hierarchical neighborhood relationships (symmetries) while mapping time to a weight (of a note, or event). This is useful to relate perceptual organisations (groupings in the sense of Gestalt theory) both visually and aurally. We treat time in a cinematographic way, effectively using a space-time representation. The use of colour, modulation (of waveforms), orientation, speed, etc., allows us to integrate multiple musical features in our dynamic diagrams. We provide illustrations, including animations, of our ideas.

You may read the paper (Apollonius_diagrams-2007), and download sourcecode for the software mentioned in the paper here.


Welcome to another blog, in which we plan to document our findings in the area of music visualisation. Your comments on any part of the site or its contents would be most welcome.

The ‘logo’ at the top of the page depicts a Voronoi diagram of discrete points along a sine wave and its cosine. More on Voronoi diagrams of music to follow…