### Abstract

The spectral dimension d of a network governs the massless singularity of a free field and the asymptotic behaviour of the diffusion on the network. Approximate values of d for two types of three-dimensional generalisations of the dual Sierpinski carpet are obtained using the POP approximation method. For one of them which is generated by a cube of side length three, with one block at the centre taken away, the value obtained is d(POP)=2 log 26/log(884/93) approximately=2.89. For the other one with seven cubes taken away, d(POP)=2 log 20/log (40/3) approximately=2.31. The algorithm of the POP method is explained. The results for 2D symmetric dual Sierpinski-type carpets are also reported.

Original language | English |
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Article number | 013 |

Pages (from-to) | 3117-3129 |

Number of pages | 13 |

Journal | Journal of Physics A: General Physics |

Volume | 21 |

Issue number | 14 |

DOIs | |

Publication status | Published - 1988 Dec 1 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Journal of Physics A: General Physics*,

*21*(14), 3117-3129. [013]. https://doi.org/10.1088/0305-4470/21/14/013