Swallowtail Catastrophe with a nod to Rene Thom
Dilemma: In the schoolyard perimeter the paper plane is made up of three surfaces of folds, which meet in two lines, which in turn meet at a single swallowtail bifurcation point. Then it crashes.
Formula: V = x5 + ax3 + bx2 + cx
Elucidation: It’s one thing to see a stuffed polar bear, moth eaten and dusty, its neck wrapped in beads and a silly hat on its head. Another to meet a real bear in the woods while oblivious to territorial claw marks but open to surreal wilderness experiences. Yet another to have your photo taken on Dali’s lip couch in the courtyard of his villa under the scorching Costa Brava sun with the Michelin man standing guard. And later, alone in the swimming pool back at the modest hotel observing wave patterns, angles of index and refraction, minimum-maximum pairs, and wondering about lost chances when a swallow dives just above your head, fanning its tail as if to say Follow me! What have you got to lose if you go with the dark Basque stranger to his parakeet sanctuary in the dusty hills? Your heart, your life, your plane ticket home?
Notation: Where V is the tip of the Swallow’s tail, x the object of attraction, a the direct route home, b the branching behaviour, and c the traveller.