  Factor complexity $b_\phi(n)$ for a vertex coloring $\phi$ of a regular tree
is the number of colored $n$-balls up to color-preserving automorphisms.
Sturmian colorings are colorings of minimal unbounded factor complexity
$b_\phi(n) = n+2$. In this article, we prove an induction algorithm for
Sturmian colorings using colored balls in a way analogous to induction
algorithm of Sturmian words. Furthermore, we characterize Sturmian colorings in
terms of the data for the induction algorithm.
