When the user selects the "Static black hole" mode, this texture is computed on the GPU and cached. The "Kerr black hole" textures, however, have been precomputed in Mathematica, due to the need for double precision floating point math, which is not natively available in Apple's Metal shading language.
The source code, including the Mathematica notebook, can be found here https://github.com/graveltr/BlackHoleVision.