Wow, that first one is so cool.

Yeah, I misremembered the Interstellar paper that said it was the first simulation for a movie and thought it was the first image simulation ever. It’s even referencing the old one there.

The second one. The image is simulated as how an external observer would see it. It was firstly done for the Interstellar movie.

Also the 2D gaussian integral is used to give an insight on why the 1D gaussian integral is sqrt of pi. Here is a video with cool visualization for anyone interested.

That should be an approximation. To get exactly pi the range of both integrals should be from minus infinity to infinity like this. It’s the integral of the 2D Gaussian, which is fairly known.

https://en.m.wikipedia.org/wiki/One-electron_universe

Enlightened centrist

Speak for yourself