3 ms·

Navier-Stokes Visualized as 1kB i386 demos

22 points by chaostaco 13d ago

chaostaco 13d ago
I was making a web project about some of my 1996 era 386 graphics code when I saw the visualizations related to the recent solution to the smoothness problem of Navier-Stokes and thought "that would look cool as a 90s-era demo". So here you go, a palette cycler and a particle animation, both using the real equations and both as sub-1kB binaries, rendered online via js-dos/DOSBox as well as JavaScript ports with knobs to go far beyond 386 quality. All source and pre-compiled 386 binaries included and free in every way. And since I know this is divisive on HN, I should be up front that this effort was AI-assisted, but hey, so was OpenAI's solution of the Millennium problem that inspired my effort.
westurner 13d ago
Neat! Geisswerks has Navier-Stokes visualizations that run on Win98/2k IIRC. Milkdrop3/projectM can vary visualization parameters according to audio attributes samples in real time. Could be in an open source bowling alley: https://news.ycombinator.com/item?id=48971134 https://news.ycombinator.com/item?id=48971134 I've my own particle visualizations, after editing the ThreeJS particle attractor example I've started building a collection of these with R3F ReactThreeFiber and Drei in westurner/particlewavefluid: https://github.com/westurner/particlewavefluid https://github.com/westurner/particlewavefluid ThreeJS can use WebGPU if available or fallback to WebGL. I haven't yet implemented NS; I should prioritize building Fedi's SQG and DDF Dilatant Dark Fluid models of black holes with only just one vortex moisture with GOE Gross-Pitaevskii equation. I did do (ai) review and try to find extensions from the new NS for Incompressible fluids solution. There are connections from Navier-Stokes to Lagrangian mechanics through the Madelung transformation; https://news.ycombinator.com/item?id=49637058 https://news.ycombinator.com/item?id=49637058 But SQS and DDF say that the Superfluid of space-time is a dilatant fluid that is both compressible and incompressible, and there's a 4th term. So far, I've used 4x4 normed tensor Gaussian splatters to quantize the fluid simulations and it seems advantageous because FWIU the normed tensors already naturally do conservation of energy in the sim. Also working with sim optimizations on limited architectures; Re: the first version of MU-AV (in C++) on an ESP32-S3 with a 1Hz ePaper price tag screen; https://news.ycombinator.com/item?id=49060309 https://news.ycombinator.com/item?id=49060309 A few weeks ago in the CircuitPython implementation of MU-AV (Mu Animation Video) codec and gaussian splatter scene rep, I implemented loop unrolling for a 14X return (actually 100% to 5% utilization on 1 (one) core)) over nested lists in the CPython on x86-64 emulated version for the 156Mhz TI-84 ARM processor dedicated to running Python. But will it work on a really slow processor with no SIMD or GPU shaders? Did i386 have SIMD? Re: "SIMD-accelerated computer vision on a $2 microcontroller": https://news.ycombinator.com/item?id=40784199 https://news.ycombinator.com/item?id=40784199 "Show HN: WebGPU Particles Simulation" https://news.ycombinator.com/item?id=38678703 https://news.ycombinator.com/item?id=38678703
- chaostaco 8d ago
  I spent ages staring at Milkdrop in the Winamp days. Thanks for the links.
Kotlopou 9d ago
This is pretty, but none of those visualisations look very... singular to me? Can anyone tell me where to look in those simulations to see the blowup? Does speed go infinite in some region (which one? the blue or orange part?), or just non-smooth?
- eig 9d ago
  “ This is not the smoothness problem solution, but rather the Burgers vortex, an exact solution of the Navier–Stokes equations published by J. M. Burgers in 1948, chosen because it has the same anatomy: fluid drawn inward in a plane, stretched along the axis and thrown out of both ends, spinning fastest in a core.”
- pfortuny 9d ago
  It might be that the velocity at the spiraling axis is not infinity (i.e. there is no blow-up in finite time). Viscosity is a bitch.
  - chaostaco 8d ago
    I believe a core element of the smoothness problem solution is that it does blow up in finite time, even with viscosity. Perhaps an expert could provide a more accurate response, but here is how ChatGPT tried to explain it to me: "In this construction, the viscous term becomes large along with the acceleration, pressure-gradient, and nonlinear momentum-transfer terms, but they balance/cancel in a very precise way. That allows the velocity in the concentrating vortex core to grow without bound even though ν is nonzero."
- chaostaco 8d ago
  I'm no expert in this field, but my understanding is that it would occur in the concentrating vortex core. The orange part would become narrower and narrower (the OpenAI article says "like spaghetti"), and the velocity in that concentrating region would grow without bound as the finite blowup time is approached. The rendered flow never literally shows "infinity" because every snapshot before the blowup time is still finite.

22 points by chaostaco 13d ago

I was making a web project about some of my 1996 era 386 graphics code when I saw the visualizations related to the recent solution to the smoothness problem of Navier-Stokes and thought "that would look cool as a 90s-era demo". So here you go, a palette cycler and a particle animation, both using the real equations and both as sub-1kB binaries, rendered online via js-dos/DOSBox as well as JavaScript ports with knobs to go far beyond 386 quality. All source and pre-compiled 386 binaries included and free in every way. And since I know this is divisive on HN, I should be up front that this effort was AI-assisted, but hey, so was OpenAI's solution of the Millennium problem that inspired my effort.

westurner 13d ago

Neat! Geisswerks has Navier-Stokes visualizations that run on Win98/2k IIRC. Milkdrop3/projectM can vary visualization parameters according to audio attributes samples in real time. Could be in an open source bowling alley: https://news.ycombinator.com/item?id=48971134 https://news.ycombinator.com/item?id=48971134 I've my own particle visualizations, after editing the ThreeJS particle attractor example I've started building a collection of these with R3F ReactThreeFiber and Drei in westurner/particlewavefluid: https://github.com/westurner/particlewavefluid https://github.com/westurner/particlewavefluid ThreeJS can use WebGPU if available or fallback to WebGL. I haven't yet implemented NS; I should prioritize building Fedi's SQG and DDF Dilatant Dark Fluid models of black holes with only just one vortex moisture with GOE Gross-Pitaevskii equation. I did do (ai) review and try to find extensions from the new NS for Incompressible fluids solution. There are connections from Navier-Stokes to Lagrangian mechanics through the Madelung transformation; https://news.ycombinator.com/item?id=49637058 https://news.ycombinator.com/item?id=49637058 But SQS and DDF say that the Superfluid of space-time is a dilatant fluid that is both compressible and incompressible, and there's a 4th term. So far, I've used 4x4 normed tensor Gaussian splatters to quantize the fluid simulations and it seems advantageous because FWIU the normed tensors already naturally do conservation of energy in the sim. Also working with sim optimizations on limited architectures; Re: the first version of MU-AV (in C++) on an ESP32-S3 with a 1Hz ePaper price tag screen; https://news.ycombinator.com/item?id=49060309 https://news.ycombinator.com/item?id=49060309 A few weeks ago in the CircuitPython implementation of MU-AV (Mu Animation Video) codec and gaussian splatter scene rep, I implemented loop unrolling for a 14X return (actually 100% to 5% utilization on 1 (one) core)) over nested lists in the CPython on x86-64 emulated version for the 156Mhz TI-84 ARM processor dedicated to running Python. But will it work on a really slow processor with no SIMD or GPU shaders? Did i386 have SIMD? Re: "SIMD-accelerated computer vision on a $2 microcontroller": https://news.ycombinator.com/item?id=40784199 https://news.ycombinator.com/item?id=40784199 "Show HN: WebGPU Particles Simulation" https://news.ycombinator.com/item?id=38678703 https://news.ycombinator.com/item?id=38678703

chaostaco 8d ago
I spent ages staring at Milkdrop in the Winamp days. Thanks for the links.

Kotlopou 9d ago

This is pretty, but none of those visualisations look very... singular to me? Can anyone tell me where to look in those simulations to see the blowup? Does speed go infinite in some region (which one? the blue or orange part?), or just non-smooth?

eig 9d ago
“ This is not the smoothness problem solution, but rather the Burgers vortex, an exact solution of the Navier–Stokes equations published by J. M. Burgers in 1948, chosen because it has the same anatomy: fluid drawn inward in a plane, stretched along the axis and thrown out of both ends, spinning fastest in a core.”
pfortuny 9d ago
It might be that the velocity at the spiraling axis is not infinity (i.e. there is no blow-up in finite time). Viscosity is a bitch.
- chaostaco 8d ago
  I believe a core element of the smoothness problem solution is that it does blow up in finite time, even with viscosity. Perhaps an expert could provide a more accurate response, but here is how ChatGPT tried to explain it to me: "In this construction, the viscous term becomes large along with the acceleration, pressure-gradient, and nonlinear momentum-transfer terms, but they balance/cancel in a very precise way. That allows the velocity in the concentrating vortex core to grow without bound even though ν is nonzero."
chaostaco 8d ago
I'm no expert in this field, but my understanding is that it would occur in the concentrating vortex core. The orange part would become narrower and narrower (the OpenAI article says "like spaghetti"), and the velocity in that concentrating region would grow without bound as the finite blowup time is approached. The rendered flow never literally shows "infinity" because every snapshot before the blowup time is still finite.