I accidentally stumbled upon a rather neat graph while playing with the state space of the Tower of Hanoi game. Viewed as a computer network model, it exhibits quite interesting properties, such as naturally supporting greedy, memory-less routing with a unique shortest path - no routing tables, no global state. Node addresses are assigned locally and are meaningful, reflecting either network proximity or content semantics, instead of being mere random or consecutive numbers assigned globally. The network mixes strong points of both hierarchical and P2P topologies and is resilient to dynamic changes such as nodes or links joining, requiring zero reconfiguration. I got interested and decided to share: if you like math riddles, help me identify what this thing is, mathematically. I'll call it the Hanoi network for now. Shape Examples of the first two levels of base-4 (left) and base-3 (right) nets A base-N Hanoi net has a recursive, fractal structure.…