The paper is devoted to an object well known in combinatorcs of words, namely to so-called morphic sequences. The main goal of the paper is to solve (at least partially) the following question raised by J.-J. Pansiot in 1985: what can the factor complexity function of an arbitrary morphic sequence be?

We study structure of pure morphic and morphic sequences and prove the following result: the factor complexity of an arbitrary morphic sequence is either Θ(n^1+1/k) for some k∈N, or is O(n log n).