Although the definition of a cactus graph lobe in terms of its intrinsic structural components is logically sufficient it is also useful to characterize the structure of a lobe in extrinsic relational terms, that is, to view the structure that typifies a lobe in relation to the structures of other PARCs and to mark the inclusion of the special type within the general run of PARCs.

That approach to the question of types results in a form of description that appears to be a bit more analytic, at least in mnemonic or prima facie terms, if not ultimately more revealing.  Working in that vein, a lobe can be characterized as a special type of PARC called an unpainted root plant (UR‑plant).

An UR‑plant is a PARC of a simpler sort, at least, with respect to the recursive ordering of graph‑theoretic cacti being followed here.  As a type, it is defined by the presence of two properties, that of being planted and that of having an unpainted root, defined as follows.

• A PARC is planted if its list of attachments has just one PARC.
• A PARC is UR if its list of attachments has no blanks or paints.

In short, an UR‑planted PARC has a single PARC as its only attachment, and since that attachment is prevented from being a blank or a paint, the single attachment at its root has to be another sort of structure, that which we call a lobe.

Resources

• Cactus Language • Mechanics
• Survey of Animated Logical Graphs
• Survey of Theme One Program

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science