  Plants have developed different tropisms: in particular, they re-orient the
growth of their branches towards light (phototropism) or upwards
(gravitropism). How these tropisms affect the shape of a tree crown remains
unanswered. We address this question by developing a propagating front model of
tree growth. This model being length-free, it leads to self-similar solutions,
independent of the initial conditions, at long time. Varying the intensities of
each tropism, different self-similar shapes emerge, including singular ones.
Interestingly, these shapes bear similarities with existing tree species. It is
concluded that the core of specific crown shapes in trees relies on the balance
between tropisms.
