I've recently implemented a differential equation based vegetation simulation on planetary scale. Each terrestrial tile of my roughly 1 million triangle planet performs an individual simulation. Precipitation, light and temperature determines the amount and kind of vegetation that thrives.
Along the equator a band of tropical rainforest emerges. At +- 30 degrees latitude deserts tend to form. The vegetation distribution is heavely influenced by precipitation. In order to get even better results i will have to write a more realistic precipitation model. But for now this works fine.