When I use the word "stream", I'm referring to the audio that virtual instruments produce as they receive data from my in-house VST plugin, the Aleator. The plugin reads XML documents on the local machine that describe sets of intervals (i.e. key agnostic progressions), modulations and melodic groupings. All of this information is used along with randomizing components to write musical compositions on the fly. Also included in this system are changes in instrumentation, tempo and other parameters. You can get an idea of what's involved by viewing the diagram immediately following this paragraph. At a high level, the audio generated by the synths loaded running in the DAW (e.g. Reaper) is sent to a streaming server real time and is accessible online immediately.
The XML documents that hold the composition data, along with the synth and preset selections, are what really give the individual streams their character. Those documents are blueprints that define what is allowed to occur when the computer creates a movement - the specifics beyond that are left to chance.
Streams are designed to run live 24 hours a day, 7 days a week. The Aleator will play through the compositions indefinitely, rendering the movements anew with each iteration. The result is that the listener will hear themes recited from one set to the next, but no composition is ever repeated exactly. Instead of songs, it's really a collection of moving targets that only come into focus after repeated listens. Whereas a recording artist commits music to disk or tape as songs or albums, the audio in my streams only exists at the particular time you hear it. Unless you were to record it, you'd never hear that movement again. That's a stream.
I have two streams live right now - Facets and Static Void. Visit the pages to catch up. For both, I used Omnisphere 2, with the Trapsphere and Moog Tribute Library expansions, along with Addictive Drums 1. It's for the culture.