Although I think this also has applications as a mechanical control mechanism, replacing expensive potentiometers with relatively cheaper 3D-printed parts. I've dreamed-up an optical/laser variant in my head a hundred times, fun to look at it in the audio domain.

2. Define a goal function describing the desired outcome (like the "rainbow" shape of the linked article)

3. Permute the shape you started with iteratively with algorithms like simulated annealing, using the goal function from 2 as a means of defining the quality of the current solution.

The actual scientific paper (https://www.science.org/doi/10.1126/sciadv.ads7497) is worth reading. The goal function is the "Figure Of Merit" (FOM), described in equation 1. They also make a two-prong version they call the "lambda emitter" that takes in a mix of sound frequencies and directs low and high-frequency sound waves in different directions.

Genetic algorithm would be one approach. You map the printable shape space onto a bit vector and define a fitness function (optimization objective function) to guide the search. Hardest part is coming up with a fitness function that gives you what you want, this gets tricky when you are trying to balance multiple constraints.

Perhaps if they added some more constraints (e.g. on smoothness) they would end up with a shape like that.