Emergent Themes in Aperiodic Non-deterministic Musical Compositions

The directed graph in the video has information flowing through it as time passes. A vertex represents a change to the incoming signal - it either increases or decreases the pitch of the signal as it continues to the next vertex.

A vertex with more than one edge leading to other vertices can have one of three modes to pass the signal forward:

1. Parallel - the signal will continue to all connected vertices at the same time.

2. Sequential - the signal will only continue to one vertex. This mode allows a configuration of how many time would the signal pass through one edge before it will pass to a different edge.

3. Random - the signal will move through a random edge (weighted random choice)

A signal in this system might terminate in two ways:

1. The placement of “dead-end” vertices in the system that do not have outgoing edges.
2. As any vertex can modulate the signal, and signals might enter the vertex with any random pitch value from previous vertices, the outgoing value might be beyond what the instrument (in this case, a piano) can play.

This composition “terminates” under the second option - while there are still signals moving in the system they are in non-renderable ranges.

In this composition, the author put a strong emphasis on random vertices to turn the otherwise deterministic periodic composition into an aperiodic non-deterministic one. The result is an emergence of novel themes not originally composed by the author. Very much as in aperiodic deterministic systems, The composition might continue the original theme for a while, before descending into chaos, only to emerge with a new theme for a short while before returning to the original theme.