Connectivity calculus of fractal polyhedrons

作者：

Highlights：

• This paper analyzes the connectivity information of fractal polyhedra.

• This paper recalls homology strong-deformation retracts as an appropriate tool for doing so.

• This paper illustrates the relevance of this tool for Menger sponge and Sierpinski pyramids.

• This paper provides examples and detailed proofs.

摘要

Highlights•This paper analyzes the connectivity information of fractal polyhedra.•This paper recalls homology strong-deformation retracts as an appropriate tool for doing so.•This paper illustrates the relevance of this tool for Menger sponge and Sierpinski pyramids.•This paper provides examples and detailed proofs.

论文关键词：Connectivity,Cycles,Topological analysis,Tunnels,Directed graphs,Betti number,Fractal set,Menger sponge,Sierpiński pyramid

论文评审过程：Received 27 December 2013, Revised 6 April 2014, Accepted 27 May 2014, Available online 6 June 2014.

论文官网地址：https://doi.org/10.1016/j.patcog.2014.05.016