Video

I'm currently not working on it, but I might pick it up again later. I've looked at FMM before but haven't had the time to play with it yet. It looks interesting though

2d simulation

I draw everything using Allegro5

I render the frames during the simulation using Allegro 5. So no files (apart from the images ofc) are used. Afterwards I just convert the images into a video.

@@zarro110 but where is the source code?

The quadtree allows to make approximations for longer distances, reducing the amount of calculations that have to be made per particle. There are many resources on the Barnes-Hut algorithm that you can look up if you're interested.

You can if you have a decent GPU, meaning most gaming setups probably will be able to do this. This was rendered on my (albeit pretty powerful) laptop

No, I haven't found (and to be fair, I haven't looked for it in a while too) any good resources on building trees efficiently on the GPU. The tree here is build on the CPU and then shipped over to the GPU for the force calculations. Barned-Hut is still O(n log n) so with a million particles the bulk of the calculations is still done on the GPU that way.

spliting the calculation using quad tree and running it on CUDA, my guess is that this can in theory run in real time.

This sim ran at around 10 fps I think

@@zarro110 10 fps is not bad at all considering the particle numbers. I recently learned that FMM algorithm can drop the calculation down to O(N) instead of O(N log N). Might take a long while before I get how it works.

@@zarro110 I see, I see, ok, thanks for answering, sorry to bog you, but on what sort of machine? But from your answer I get that it is not (easily run at) real time, thanks again

​@@alvarobyrne I did this with my laptop with a GeForce RTX 2070 Max-Q and a i7-10750H

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Go and write one?

It sounds like you're assuming that gravity is static in GR. As each particle moves, its gravitational effect changes too. In both cases each particle interacts with every other particle and this interaction changes at each time step. The difference is that in GR you have to take a lot of other effects into account, like how gravity also affects time, not just space. And not only mass causes gravity, but also pressure, momentum, and radiation, for example. And you even have to take gravitational waves into account.

I love octrees / n-dimensional octrees. They make space all cut up and nice to work with.

I will act like I understand this comment( I don’t).

@@tyn_joueurswitch1505 Such a function would be optimal if all entities were equally spread out across all of space. With a gravity sim they may start that way but they will eventually all clump together into a single or small number of grid cells.

It's constant for all particles. Especially these older sims are not too sophisticated, most speed comes from the fact that it is able to run on the gpu

How accurate is friction for galaxy sized simulations though? I thought that on that scale point masses are good enough as the distance between stars is big enough anyways

@@zarro110 Real galaxies consist of 200-300 billions of stars. Even if we make simulation with 1million particles, these particles aren't separate stars, they are globular clusters which contain 200-300 thousands of stars. For example, if distance between two such particles less than radius of cluster, then force of attraction must decrease. Between particles space is'n empty. In this sense it is like simulation of gas or fluid.

@@zarro110 "How accurate is friction for galaxy sized simulations though" - it's difficult question. I use sticky-particle method.

We need add gaseous component with friction. In this simulation there is only stellar particles without collisions. I make simple simulation with 20K bodies for spiral galaxy: czcams.com/video/nZI3SOoqPtI/video.html And for barred galaxy: czcams.com/video/74f5qApTWfE/video.html

I'm currently building the quadtree on the CPU, and then sending it to the gpu for the force calculations. I'm also still looking for a nice reference on building quadtrees on the gpu lol

I'm fully rebuilding the tree each frame

@@zarro110 May I ask why did you choose to do that ? Do you think there would be no performance benefit of some updating logic or ? Also is this real-time and how many frames if so ?

@@rafmy-0788 I think real-time was 10 fps or so. The quadtree is constantly changing size and all of the particles are in constant motion. I'm doubtful that there is much that can be reused for an performance gain. I haven't tested that however

Glad you like the video! You're welcome to use the clip in your video as long as you give proper credit. I do have to warn you that the simulation is limited to 2D and does not account for effects such as those from relativity, so it may not be fully realistic.

@@zarro110 I thank you very much for the permission. A reference to the source is self-evident and of course always given with a link. Thank you for the warning, but I am very familiar with the matter, deal with me in this gebiet estimated 40 years. Currently I am working as a volunteer scientist for NASA and ESO on various projects. This simulation is already very close to a HL, a young star with protoplanetary disk.

also is there a particular textbook or lectures u watched when u started making these sims? cool vids!

It's a gravity simulation. I learned most of this stuff just by googling and watching random videos on the internet. Simple gravity simulations aren't that hard to do and there is a lot of tutorials out there for them. C++ and Cuda are a bit harder but still doable on your own

No the source code is a real mess haha. I struggle to read it myself sometimes

I don't exactly know how long it took to calculate this, I made it quite a while ago. I do know that it wasn't real time, as the brute force method can be quite slow for large numbers of objects. My new simulations would be able to do this real time, using the Barnes-Hut method.

This is a gravity simulation to a point or towards each other? Also I was woking on something simular today and I used C++ with CUDA to do this with about 2 million particles at a decent frame rate (real time). A trick is also to use samples for gravity rather than calculating the total force for ALL psrticles individually. You just take samples from about 0.1% of all particles and multiply the force by 1000. Some particles may act strangely at times, but overall it works quite well.

​@@the_untextured It is an Nbody simulation, meaning they all influence eachother. While not your method, my new simulations use the Barnes-Hut method which makes use of a quadtree to make approximations that have smaller error than simply random sampling.

@@zarro110 don't really know about that method but I will definitely look it up. I am not an ezpert in the field and this is the first time I properly take a look at many particles. The thing with my method is that it is not random sampling: it is systematic, so the particle set is subdivided into groups of n particles, on the first tick, the first group are used for thw calculations, on the next tick the second group is etc, which will end up removing random bias. However it still is not perfect, but for real time, it will be more accurate than not doing this because a low framerate will often cause huge inaccuracies. (in my case itr caused particles flying away because they would end up too close to each other and since g is proportional to 1/r^2, a small distance means a huge force, which caused them to fly off. (the repulsive force between them did not have the time to repel the particles)