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Frazzoli and some grad students devised a differential equation expressing all the possible positions of a bird at a given location at a given speed. Then they developed a model of a forest, using statistical distribution models used by ecologists. Then the team calculated the probability that a bird would hit a tree while flying at a certain speed. They figured out that for any given density of trees (or other obstacles of choice), there exists a speed above which there is no “infinite collision-free trajectory,” as MIT News explains. The bird will surely crash, because there’s no way for it to avoid the obstacles. But below that threshold, things should be fine.
