I searched "Tower of HanoiTower of Hanoi" on arXiv (with 18 results at time of last edit):
- The Group of Symmetries of the Tower of Hanoi GraphThe Group of Symmetries of the Tower of Hanoi Graph
- The Tower of Hanoi and Finite AutomataThe Tower of Hanoi and Finite Automata
- Shortest paths in the Tower of Hanoi graph and finite automataShortest paths in the Tower of Hanoi graph and finite automata
- Asymptotic aspects of Schreier graphs and Hanoi Towers groupsAsymptotic aspects of Schreier graphs and Hanoi Towers groups
A search on Wikipedia returned the Tower of Hanoi and Magnetic Tower of Hanoi. Also the Flag Tower of Hanoi.
People are interested in the graph of Tower of Hanoi positions, which seems to be related to the Sierpinski Gasket, the longest solution and Hamiltonian paths. (sources: wikimedia.org)
][10] (source: [wikimedia.org](https://upload.wikimedia.org/wikipedia/commons/thumb/d/da/Tower_of_Hanoi-3_Longest_Path.svg/440px-Tower_of_Hanoi-3_Longest_Path.svg.png)) There seems to be a language (in the sense of automata theory) related to the Tower of Hanoi, and a fractal structure.