TLDR: the number of particles used, and the memory required was far too big to fit on one machine. more over, machines needed to pass data to each other, they chose to use files for that.
Long story:
Forgive me if you already know this, I'm going to start with a toy example and then ramp up the scale.
Imagine that you are doing a "normal" simulation of something like a ball rolling down a ramp into a pot. That's fairly simple, but you need to know the position of the ball, the force vector and the location of any object near by that might collide with it.
It gets a bit harder when there are two balls, as they might also interact, so you need to store the state of two balls.
At a thousand balls, you start to need to think about scaling/threading/parralising (I mean you probably don't, you'd just use physX from nvidia and make it the library's problem, but bear with me) One way is to divide up the simulation area into a bunch of voxels and treat them as individual processing areas. When an object enters/exits an simulation area, you pass the object over with its force vector, and mass, and let that simulator deal with it.
Now, I'm not a physics engine person. The above may or may not happen as I describe, but the key thing is, there are sub simulation to allow you to run in parallel. You need to make sure that each processing voxel has completed it's processing for that time step before you can move on.
Once you have calcuated the position of each object, you can save that to disk and begin to calculate the next frame. Note, this isn't rendering, this is just working out the "pose" (position and rotation) of each active object.
The simulation of the black hole was effectively a massive particle simulation. I don't recall how many particles, but something like 14 billion sticks in my mind. It might have only been a billion. So they need to calculate and store the id, position, rotation, velocity and probably other details for every single particle. Even if everything is in a single float for a billion particles, its 28 gigabytes for position and rotation alone (xyz for position, quaternion for rotation) That's without any other state info like heat, force vectors, the weird quantum stuff or weight.
Once you have the position of all the particles, you then need to fire photons through them to work out what colour the pixel should be. That involves loading in the position of the particles, firing rays through them all and recording what it hits and why.
But why so much file IO? didn't the machines talk directly?
DNEG at the time was as close to being a "perfect" unix/linux shop as you could get. everything was ephemeral, even the file servers. All the nodes in the render farm could configure themselves from scratch (pretty much) from power on. You'd plug it in, switch it on and it would work out what it's hostname is, image themselves and join the rendering system autonomously. Most binaries that you used were stored on an NFS share somewhere. this meant that you had more or less complete control over the data flow. For example `rm` wasn't actually rm, it was a wrapper that moved files into a 'deleted' area, rather than binning them.
There were many layers of backup, all the way to tape.
Your home directory followed you everywhere, which meant so did your environment. This meant that if you wanted a specific version of a program, we had a wrapper that set that for you. So typing "maya" would spin up the right version of maya, use the correct plugins, and safe your files to the correct fileserver.
Everything was divided into shows. so you'd cd /shows/$showname/$department/$shotnumber/$version and you'd magically be on the right fileserver. This was done via the magic of symlinks.
So everything was files, and if you wanted to exchange large amounts of data, you'd use files.
If anyone is interested I'll talk about the system they used to coordinate all the rendering (no it wasn't k8s)