Caterpillar with Green Stripe

For over twenty years a little caterpillar has captivated me not just because of its beauty, but also because it has steadfastly remained a puzzle I could not solve. Mystery itself can be a source of sustenance. For those of you who like puzzles . . . how does it work? It may not be how you think!

If you want to see if you’re right, or if you want a clue, follow this Hint.