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Author Topic:  Waves hitting a Sierpinski carpet  (Read 226 times)

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Offline youhn

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Waves hitting a Sierpinski carpet
« on: June 22, 2021, 09:55:40 PM »
Physics simulation with fractals:

(not mine, just found on the web)

Nils Berglund:
Quote
After having done a number of simulations solving the heat equation in fractal domains, we are ready to do the same for the wave equation. This animation shows solutions of the wave equation outside 4 different approximations of a Sierpinski carpet. It illustrates why fractal materials can have an insulating effect, by trapping and reflecting sound waves.

Music: "The Emperor's Army", by Jeremy Blake

See also https://images.math.cnrs.fr/Des-ondes... for more explanations (in French) on  a few previous simulations of wave equations.

The simulation solves the wave equation by discretization. The algorithm is adapted from the paper https://hplgit.github.io/fdm-book/doc...

Reflections on the boundaries of the rectangle are minimized by adding Neumann-type boundary conditions on the time-derivative of the wave.
C code: https://github.com/nilsberglund-orlea...
https://www.idpoisson.fr/berglund/sof...
Many thanks to my colleague Marco Mancini for helping me to accelerate my code!


Linkback: https://fractalforums.org/index.php?topic=4288.0


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