Recent studies of gene expression in the developing fruitfly leg suppo
rt a model - Meinhardt's Boundary Model - which seems to contradict th
e prevailing paradigm for pattern formation in the imaginal discs of D
rosophila - the Polar Coordinate Model. Reasoning from geometric first
principles, this article examines the strengths and weaknesses of the
se hypotheses, plus some baffling phenomena that neither model can com
fortably explain. The deeper question at issue is: how does the fly's
genome encode the three-dimensional anatomy of the adult? Does it dema
rcate territories and boundaries (as in a geopolitical map) and then u
se those boundaries and their points of intersection as a scaffolding
on which to erect the anatomy (the Boundary Model)? Or does it assign
cellular fates within a relatively seamless coordinate system (the Pol
ar Coordinate Model)? The existence of hybrid Cartesian-polar models s
hows that the alternatives may not be so clear-cut: a single organ mig
ht utilize different systems that are spatially superimposed or tempor
ally sequential.