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After I've found this post I'm curious what kind of algorithms they use to generate these shapes (second image).

I can't imagine that the basic shapes are basing on a perlin or simplex noise or a voronoi diagram. With voronoi I'm a bit uncertain to be honest.

Well, so what do you think. What algorithm could be used to generate biome borders like they do?

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you first create a set of parameters that you will generate, for example elevation, humidity, temperature

then you can define a function that will return a biome from any combination of these parameters

how you generate those parameters is usually with perlin or simplex noise but you can let it depends on other (previously generated) parameters like elevation and prevailing wind to create a rain shadow.

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