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In physics this is called harmonic analysis. Basically needs these things:

Geometric surface
Vibration
Liquid or particles, both work
Gravity

In engineering (FEA = Finete Element Analysis) you can simulate this on 3D CAD models. The results of the simulation are some vibration modes, which can be displayed like a static map (indicating amplitude with color scale). In reality the map is made visible by adding liquid or particles.

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In practice the geometry works as a kind of seed, on which the vibration modes "grow". But this all goes fast as sound, so we won't see it with our eyes. Some people have been connecting this to things like ancient knowledgde, sacred geometry, everything is a vibration and other out-of-world stuff like that:

<a href="https://www.youtube.com/v/HJhXr9pmh5Y&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/HJhXr9pmh5Y&rel=1&fs=1&hd=1</a>

<a href="https://www.youtube.com/v/VjpCKZ7cEoY&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/VjpCKZ7cEoY&rel=1&fs=1&hd=1</a>

<a href="https://www.youtube.com/v/QUQj5Fh_550&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/QUQj5Fh_550&rel=1&fs=1&hd=1</a>

<a href="https://www.youtube.com/v/o0gBoV0ygJc&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/o0gBoV0ygJc&rel=1&fs=1&hd=1</a>

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This one is kinda cool:
<a href="https://www.youtube.com/v/1yaqUI4b974&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/1yaqUI4b974&rel=1&fs=1&hd=1</a>

This is is with fire, way coolor!
<a href="https://www.youtube.com/v/2awbKQ2DLRE&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/2awbKQ2DLRE&rel=1&fs=1&hd=1</a>

(just look for Pyro Board : https://www.youtube.com/results?search_query=pyro+board )

If you want fractal programs to simulate vibration mode effects, perhaps look at this one :

http://www.fractalforums.com/gallery-b238/pyrotechnics/

And ask the artist.

thanx  youhn