Peano-Gosper curves and the local isomorphism property
Francis Oger
Abstract:We consider unbounded curves without endpoints. Isomorphism is equivalence up to translation. Self-avoiding plane-filling curves cannot be periodic, but they can satisfy the local isomorphism property: We obtain a set Ω of coverings of the plane by sets of disjoint self-avoiding nonoriented curves, generalizing the Peano-Gosper curves, such that: 1) each C ∈ Ω satisfies the local isomorphism property; any set of curves locally isomorphic to C belongs to Ω; 2) Ω is the union of 2 ω equivalence classes for the r… Show more
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