Hanoi Attractor is a mixture of Sierpinski Gasket and intervals. To construct a graph approximation, start with a triangle and six inner functions, where $F_1, F_2, F_3$ are contraction maps to 3 small copies of Hanoi Attractor and $F_4, F_5, F_6$ are projections to the intervals.
Haotian Gu, Yuming Chen, Robert Strichartz and Zirui Zhou
Families of Symmetric, Self-similar Laplacians on Sierpinski Gasket
Analysis on Projective Octagasket
Code: Hanoi Attractor, SG3 and Quantum Graphs