The sl_3 spider is a diagrammatic category used to study the representation
theory of the quantum group U_q(sl_3). The morphisms in this category are
generated by a basis of non-elliptic webs. Khovanov- Kuperberg observed that
non-elliptic webs are indexed by semistandard Young tableaux. They establish
this bijection via a recursive growth algorithm. Recently, Tymoczko gave a
simple version of this bijection in the case that the tableaux are standard and
used it to study rotation and joins of webs. We build on Tymoczko's bijection
to give a simple and explicit algorithm for constructing all non-elliptic sl_3
webs
