The Recursive Burger

We’ve had the burger with donuts for buns and the burger with grilled-cheese sandwiches for buns and now the sandwich with fried chicken for buns.

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But they must all bow before my invention: the recursive burger, the burger that has recursive burgers for buns. That’s right, each bun is replaced by a burger, each of whose buns is replaced by a burger, each of whose buns is replaced…

Luckily the recursive burger is available in two sizes: finite and infinite. In the finite burger, each bun is replaced with a recursive burger that’s been compressed to 1/3 the height. The final burger is therefore three units high (patty and bun are each one unit high). In the infinite burger, each bun is replaced with a full-sized recursive burger (or, really, a recursive burger of any size > 1/3 size) and the thing is unboundedly large. It’d be hard to make a business of selling infinite recursive burgers.

If you think the (finite) recursive burger sounds like an interesting and tasty concoction, consider this: it converges to a big pile of meat. If you’re having trouble visualizing it, consider this diagram:

Make it happen, Carl’s Jr.