Interesting—fireworks are a classic case of exponential decay and random phase shifts, so the spread of color is really a convolution of probability distributions. If you can express it in terms of a Gaussian mixture, you can approximate the bloom radius quite well. But remember, the tiniest rounding error in the ignition timing can cause the entire spectacle to misalign, like a mis‑synchronized chess move. If you share your formula, I can run a quick check against π‑based symmetry to see if the color bands line up within a tolerance of 0.001 radians. Otherwise, just know the math is beautiful, but the fireworks themselves are a little more chaotic than our neat models.