>of course this is a simplified visualization

Its titled a "physically accurate black hole"! Please don't do this, if its intentionally not physically accurate and heavily simplified! The general public on here don't know better, and it takes someone else with years of experience simulating black holes to dig through your code to show what you've simplified. There's like a few hundred people who have the right experience worldwide to know that you've got some of your equations incorrect

The issue is when you're communicating doppler, if you want to correctly show the change in doppler, you can't make the intensity or colour mapping arbitrary

There's two ways to communicate accurately an example linear change in emissive power:

1. Use a perceptual brightness system, so that a linear change in power represents a linear perceptual change in perceived brightness. This accurately communicates to a viewer the underlying shift in power emission, if you want to show off how a radio telescope perceives a black hole for example

2. Use an emitted power <-> sRGB mapping (with tonemapping), so that a linear change in power is perceived as if it were a physical light getting brighter. This is more "what would this look like to a person?"

At the moment the change in your image brightness doesn't correspond to anything, which means that its not really communicating any science, and it doesn't correspond to doppler. Which is fine if its just illustrative and that's clear, but again vanishingly few people will know this is a visualisation not a physically accurate render