https://github.com/pbrehmer/asasine
Audio-visuals from the Kuramoto-Sivashinsky equation
https://github.com/pbrehmer/asasine
audio creative-coding partial-differential-equations sonification
Last synced: 2 months ago
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Audio-visuals from the Kuramoto-Sivashinsky equation
- Host: GitHub
- URL: https://github.com/pbrehmer/asasine
- Owner: pbrehmer
- Created: 2022-04-09T22:58:20.000Z (about 3 years ago)
- Default Branch: master
- Last Pushed: 2023-07-22T21:10:24.000Z (almost 2 years ago)
- Last Synced: 2025-01-23T03:27:54.723Z (4 months ago)
- Topics: audio, creative-coding, partial-differential-equations, sonification
- Language: Julia
- Homepage:
- Size: 13.7 MB
- Stars: 1
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Asasine
Generates audio and visual data from the solution of the Kuramoto-Sivashinsky (KS) partial differential equation
$$\frac{\partial u}{\partial t} + \frac{\partial^2 u}{\partial x^2} + \frac{\partial^4 u}{\partial x^4} + \frac{1}{2} \Big(\frac{\partial u}{\partial x}\Big)^2 = 0 .$$
The visual component is a heatmap plot of the solution function $u(t, x)$, while the audio component is the solution mapped onto a frequency spectrum that is written to an audio buffer at each time $t$. This audio-visual feed can be streamed in real time or rendered to a file.
The sonification process is implemented as follows: At each time step, from the KS solution vector `u` a collection of values is picked via an index vector `freqidx` with corresponding frequencies `freqs`. The solution values determine the sine wave amplitudes at the respective frequencies. Here, much of the sound characteristics and creative freedom resides in the choice of `freqs`. Additionally, we apply a mapping `ampmap` that further modifies the amplitudes of the produced sine waves; we often times use monomials of odd order, e.g., `ampmap = a -> a^5` to sharpen the features of the produced frequency spectrum and still retain negative values ($u(t, x)$ takes on both negative and positive real values). In simplified (code) terms, we generate the audio buffer at each time step via:
```julia
buf = zeros(buflen)
for (i, ν) in zip(freqidx, freqs)
buf .+= ampmap(u[freqidx[i]]) .* sin.(2pi * buflen * ν)
end
```
In order to create an interesting stereo image, the KS solution is translated to a stereo buffer by mapping all negative and positive values of `u` to the left and right channel, respectively.
For more details, check the notes in the [introductory notebook](/examples/introduction.ipynb) as well as the provided [examples](/examples/).
## Sample outputs
https://github.com/pbrehmer/Asasine/assets/62562093/12be5335-50ec-4fb0-9d9c-f89316e291ab
https://github.com/pbrehmer/Asasine/assets/62562093/708c931b-094a-43c5-b908-2e7d0a1b55d6
https://github.com/pbrehmer/Asasine/assets/62562093/fccf0a0d-4552-45a1-af34-3017ef682f7c
https://github.com/pbrehmer/Asasine/assets/62562093/8ab0b70b-41a6-4a5b-971f-e21d810e4236
https://github.com/pbrehmer/Asasine/assets/62562093/fbcf4d37-eda0-443f-93db-93f712121480
## References
The idea for this project was sparked by a blog post series by John Carlos Baez [1] on the Kuramoto-Sivashinsky equation. The CNAB2 Julia implementation was largely inspired by Mathab Lak's code [2], which is also used in Ref. [1].
[1] John Carlos Baez, [The Kuramoto–Sivashinsky Equation](https://johncarlosbaez.wordpress.com/2021/10/17/conjectures-on-the-kuramoto-sevashinsky-equation/)\
[2] Mathab Lak, [Test case for PDEs: Kuramoto-Sivashinsky](https://online.kitp.ucsb.edu/online/transturb17/gibson/html/5-kuramoto-sivashinksy.html)
## Todo
- add interactive elements
- fix button: fixes `U[x,t]` slice and halts evolution
- restart button
- generate audio buffer via IFFT for improved performance
- investigate divergence of CNAB2 stepping for certain wave number orderings