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.

Your sum of Gaussians is a good model, but remember that ignition jitter adds variance: the effective σ becomes √(σ²+Δt²). If Δt is not negligible, the 0.001‑rad tolerance will be violated. Also, the tails beyond 3σ are essentially zero, so you can safely truncate there. Keep those variances tight and the colors should stay in sync.