"...closing the air intake during a burn..." = with an Intake valve ?

I suspect I've read what you didn't intend.

To be honest, I believe opening and closing it at the right timing points, would allow the opening to be completely closed, since it would generate a tornado, and a tornado is equivalent to a vacuum, so it would have to be timed so that dying fuel when initially closed, and open before completely dying out, would start a simple harmonic motion to the air, or a tornado in the air vapors, so it would keep the fuel in a tornado that selectively draws from it in a completely closed engine neither intaking or exiting exhaust/air. In that scenario, the exhaust would be always closed, because the tornado would suck air, not the vacuum from a completely burned piston cycle. It seems to me that the piston would have to be disconnected periodically from the spinnnig driveshaft, because momentum would interfere with creating the initial beat. There's a difference between creating churning air, and having it build up to a tornado, so it might be extremely complicated to figure out how to close the opening at the right timing points.

Swirl Flaps are already a thing. For example, the Mercedes M272 engine has swirl flaps that change the rotation of the charge depending on conditions.

I think you could have two openings side-by-side. You can only open or close the right opening for instance. It's like a feedback loop, in that you're sending air into a feedback, but it only travels the short distance, to make the short snake curl. That means that inside the engine, in the swirling air, there will be other ones that will make a snake curl. But you have to limit air coming into the engine, to "compress the video image of the picture of swirling things", and that means a type of feedback loop that regularly chops off unnecessary swirls, or the train of varying height impulse points, you would remove some, so that you can create a tornado. It would seem like a neural net that deals with feedback loops could decide when to close or open the right opening. The exhaust would be closed off.

By the way two opening side-by-side is the double slit experiment, so by closing the right opening regularly, you're creating a delay in the choice, but the neural net closes the gap, so that creates cavitation or a tornado forming. I could be wrong, but it may just need one opening that's closed at different times, because the air inside would come out but then hop right back in on another open cycle, so what this is, is a type of double slit experiment that only involves one opening, it's interfering with a past particle. I noticed on the hpp gas automata, it has one large dark opening that mixes it. I also noticed that if you shift the edge wrapping on the left-right edges by one square, there is an instantaneous action across the automata, and I assume you would have to get a neural net to time when to regularly shift by one square the left-right edge wrapping (like pac-man). By doing that you can model mixing and it would learn so that it would time on a specific points in time, so you wouldn't have to model it on an engine. I think the neural net would come across a sudden change in the video appearance if it is getting close to the interference.

When it opens or closes the one opening, there could be a great delay, because you're looking for a particle that left, and the same particle to return. That leads me to believe that the entire neural net franchise can be re-made with a simple thing of counting particles. (And the good thing about the hpp gas automata, is that the number of particles is constant), so it may be a bit complicated but it's either you're recording the video with a lossy form of video compression and counting particles and seeing when one "leaves", and then it should "re-appear". That's probably at the precise time you open the hole to the engine, or something similar, you may be linking the automata with the neural net and that is where the feedback occurs, that when the particle "re-appears", that triggers something in the neural net that is watching the screen for it to appear. So it's probably the video compression (nothing to do with shifting the edges), that particles will appear to leave (the count goes down), particle enter (count goes up of particles), and that would simply be linked to the compression of the engine with it's exhaust closed, you are opening the engine to lower the compression of the engine at the time a particle re-appears.

Well actually, you want there to be a constant random entering and exiting of air, that means the compression goes down and you're in the tornado regime, no reliance on compression. The idea is that you can compress a file, down to nothing, if you can create a percolation like this of particles leaving and entering constantly.

I'm not sure, but it sounds like you're working with shock waves, so you might find Michigan State University's Wave Disk Engine interesting. It was good enough to attract $3 million in funding from the Department of Energy (DOE) Advanced Research Project Agency - Energy (ARPA-E), but I don't know what's come of it since. Engines such as what you're proposing face a number of challenges. The first is understanding and controlling the air flow (which will require a lot of CFD work). The second is understanding how much energy (fuel) can be burnt, what the peak temperature is, and how much energy is lost to turbulent flow across a large surface area (all of which require a lot of thermodynamics work). Who knows? You may be onto something, but you won't know for sure until you get through the mathematical analysis, prototyping, and testing.