What is the best metaphor for software growth?
There is none. In the immortal words of Forrest Gump, "Software is as software does." (Groom 94) Code construction has many correlations, yet no metaphor fully conveys its subtleties, just as you could never fully describe the beauty of a sunrise in words.
Analogies can be misleading; software is a very different substance from any physical item, and building it is accordingly different. There are fewer physical constraints, and you can manipulate it in many more ways.
There is a glimpse of truth in each metaphor. Learn what you can from them, but don't be tunneled into an incorrect view of software.
Looking at a program's development ...