The scaling and the scaling-relevant spectral properties of Penrose tiling are investigated.The fractal dimension df of this tiling is analytically obtained,which is two,equal to its Euclidean dimension.Similar to usual self-similar structure,the vibrational density of states for Penrose lattice is also found to follow a power law p(ω)~ωds^(-1) with spectral dimension ds=2,which accounts for a special vibrational excitation in quasicrystals:the fracton-like excitation,whose state is critical.The simulation of random walk on this Penrose lattice indicates that the diffusive dimension d_(w)=2,thus the relation ds=2df/d_(w) holds.
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