It’s [pretty well established](https://www.youtube.com/watch?v=heLTiUjWzII) what colors come from [burning different elements and metals.](https://www.youtube.com/watch?v=TMz_XR3o5mg)
Copper burns green blue, strontium red, iron sparky red orange etc.
This technique can even be used to tell the composition of far away stars since different elements will produce different burning stars.
Fireworks and explosives involve a lot of chemistry and knowledge despite being rather fun looking.
As for designs and shapes, those are relatively easy. Arranging them in certain ways around the main central explosive means they will shoot out in certain directions. Want a star? Arrange the pellets made of different metals and chemicals into a star shape, then put the explosive in the middle.
People can get pretty good at directing how things explode in certain ways, in warfare it’s an entire field of how different explosives do what, and how to use them properly.
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