  We study the automorphisms \phi of a finitely generated free group F.
Building on the train-track technology of Bestvina, Feighn and Handel, we
provide a topological representative f:G\to G of a power of \phi that behaves
very much like the realization on the rose of a positive automorphism. This
resemblance is encapsulated in the Beaded Decomposition Theorem which describes
the structure of paths in G obtained by repeatedly passing to f-images of an
edge and taking subpaths. This decomposition is the key to adapting our proof
of the quadratic isoperimetric inequality for $F\rtimes_\phi\mathbb Z$, with
\phi positive, to the general case. To illustrate the wider utility of our
topological normal form, we provide a short proof that for every w in F, the
function $n\mapsto |\phi^n(w)|$ grows either polynomially or exponentially.
