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I already tried the Time.timescale approach but unfortunately it messes up the physics system causing the creatures to behave and move differently when everything is sped up, which ruins the whole simulation.

If anybody knows a different way I could implement a speedup that doesn't break the physics in Unity I would definitely give it a shot.

You might be able to loop all of the code multiple times in the main loop to speed it up. This is usually how I speed up physics simulations without screwing up the actual physics.