  We give a new description of computads for weak globular $\omega$-categories
by giving an explicit inductive definition of the free words. This yields a new
understanding of computads, and allows a new definition of $\omega$-category
that avoids the technology of globular operads. Our framework permits direct
proofs of important results via structural induction, and we use this to give
new proofs that every $\omega$-category is equivalent to a free one, and that
the category of computads with generator-preserving maps is a presheaf topos,
giving a direct description of the index category. We prove that our resulting
definition of $\omega$-category agrees with that of Batanin and Leinster and
that the induced notion of cofibrant replacement for $\omega$-categories
coincides with that of Garner.
