“…There are several works devoted to the Lipschitz classification of non-totally disconnected fractal squares with contraction ratio 1/3, that is, a kind of Sierpinski carpets ( [10,13,17,23]), but the problem is unsolved in case of the fractal squares with 5 branches. Using neighbor automaton, Rao-Zhu [16] proved that F 1 F 2 in Figure 1, but it is not known whether F j , j = 2, 3, 4, 5 are Lipschitz equivalent or homeomorphic.…”