  We present those properties of planar doodles, especially when regarded as
4-valent graphs, that enable us to classify them into {\it prime} and {\it
super prime} doodles by analogy to a knot sum. We describe a method for
partially characterising a doodle diagram by a {\it doodle code} that describes
the complementary regions of the diagram and use that code to enumerate all
possible prime and super prime doodle diagrams via their dual graph. In
addition we explore the relationship between planar doodles and twin groups,
and note that a theorem of Tutte means that super prime doodles have a
Hamiltonian circuit. We hope to expand upon this last point in a follow-up
paper.
