Solve the 2D Poisson's equation
$$
\frac{\partial^2}{\partial x^2} f(x, y) + \frac{\partial^2}{\partial y^2} f(x, y) = g(x, y)
$$
in parallel using OpenMPI: github.com/Roninkoi/ParPS
The problem is parallelized using domain decomposition and each piece solved using successive over-relaxation.This can be run on a single PC or a multi-node compute cluster

@dosnostalgic Thought this looked like Wings, but it actually predates it by 8 years!

RIES (mrob.com/pub/ries/index.html) is such a fascinating tool. Sometimes it can even find closed-form solutions from the numerical values of integrals that Mathematica can't do!

Two VGA mode X triangle filling strategies I've been considering. 1. fill one plane at a time 2. fill edges one plane at a time and fill center using all planes at once. The second approach should be faster for large fills, while requiring only one extra plane change

Building a small Ryzen 9 5950X system for light compute workloads

Raymarching gives mirror effects for free, so I've been playing around with reflection. Here's a that draws the main mirror the James Webb Space Telescope shadertoy.com/view/sstcW7

Heard someone was wreaking havoc on our department's compute cluster. Super relieved it wasn't my fault 😅

Roninkoi boosted

Seen some cool Rubik's Cube cakes last night and I had to make one out of voxels. Have a piece guys!

#art #MastoArt #voxelart #voxel #artist #cake

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Okay, I can't keep the urge of making my own spreadsheet program at bay any longer.

Let's get started.

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Some hexagonal #turingdrawings from my #cellularautomata simulator-thingy I'm working on.

Up next: anything that doesn't involve clicking restart 500 times to discover those that aren't a straight line.

@henryseg Interesting idea! It would probably help to some extent, but eventually it would get noisy again. The noise seems to get worse with large \(K\)

If you're into chaos, you might enjoy this visualization of the standard map
\begin{align}
p_{n+1} = p_n + K \sin \theta_n, \\
\theta_{n+1} = \theta_n + p_{n+1},
\end{align}
with varying \(K\). It's pretty hypnotic shadertoy.com/view/WdjcW3

@tpfto Thanks! Your posts have helped me many times over the years

Roninkoi boosted

No matter what distro you use, I think most of us appreciate the work done on the Arch Wiki :nyarch:

As it turns out, there is a better approach using Clenshaw's algorithm! A review of different methods is given in arXiv:1410.1748 [physics.chem-ph]. Now I could get up to high values of \(\ell\) and \(m\) without everything blowing up! From the ALPs we can then simply obtain the SHs as
\[
Y_\ell^m(\theta, \phi) = \sqrt{\frac{(2 \ell + 1) (\ell - m)!}{4\pi (\ell + m)!}} P_\ell^m (\cos \theta) e^{i m \phi}.
\]
The final code can be viewed at shadertoy.com/view/3dKGWG, which borrows from iq's shader

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In 2019, I wanted have spherical harmonics \(Y_\ell^m\) in shader, solved in real time instead of from precomputed functions. After looking at some papers, one approach was to solve them using the hypergeometric function, which gives \(P_\ell^m\) as
\[
P_\ell^m(x) = \frac{1}{\Gamma(1-m)} \frac{(1+z)^{m/2}}{(1-z)^{m/2}} {_2F_1}\left( -n, n + 1, 1-m, \frac{1-x}{2} \right).
\]
This requires computing a series consisting of many factorials, which is slow and results in precision problems

Roninkoi boosted

Here’s my

I’m a mechanical engineer by trade, and designed many components for various Macs over the last decade. I recently quit my job in order to return to school and obtain a PhD in math.

I find geometry fascinating and make Rubik’s-cube-like puzzles as a hobby. Last year when trying to answer some open questions regarding these puzzles, I was introduced to concepts I had never been exposed to. During that exploration, I simply fell in love and decided to dive in head first.

Roninkoi boosted

Here we see Hickson Compact Group 88, a quartet of galaxies that are surprisingly chilled out given how crowded their environment has become!

Usually these galaxy interactions are stressful events, and here we see some evidence of galaxy evolution: the two northern galaxies are flinging away some of their older (redder) stars. But the two southern galaxies seem to be quite undisturbed!

#astronomy #space #science #physics

Roninkoi boosted

Oh man oh man oh man oh man -- the Ingenuity Helicopter on #Mars swung over and took a view of the backshell and parachute used to land Perseverance on Mars! It is so cool what we can get up to when we have a little drone accompanying our rovers. #JPL #Mars #Astronomy #Perseverance #Space #Science
Raw image: mars.nasa.gov/mars2020/multime

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