Fig. 2

(Top) Vicsek fractal GV 33 with N = 64 nodes. The starting node x₀ is in the center (red circle), the absorbing node x_a is one of the dead-ends (black circle), the trap x_h is located in one of two positions indicated by empty circles. (Bottom) FPT densities on this Vicsek fractal with \( {\tilde{\psi}}_{x{x}^{\prime }}(s)=1/\left( s\tau +1\right) \); τ = 1 in all nodes x except x_h, at which \( {\tilde{\psi}}_{x_h{x}^{\prime }}(s)=1/\left({s}^a{\tau}^a+1\right) \); a = 0.5. The trap x_h is placed either on the shortest path between x₀ and x_a (first location), or outside of this path (second location). We also consider the case with an additional link avoiding the trap x_h, which corresponds to the transition matrix with a local perturbation