Scaled pier fractals do not strictly self-assemble

2014/06/17 by David Furcy, Furcy, David, Scott M. Summers +1
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #cs.CG

paper · pdf · doi:10.48550/arxiv.1406.4197

arxiv created 2014/06/17 · arxiv updated 2014/06/18

Abstract

A pier fractal is a discrete self-similar fractal whose generator contains at least one pier, that is, a member of the generator with exactly one adjacent point. Tree fractals and pinch-point fractals are special cases of pier fractals. In this paper, we study scaled pier fractals, where a scaled fractal is the shape obtained by replacing each point in the original fractal by a c × c block of points, for some c ∈ ℤ⁺. We prove that no scaled discrete self-similar pier fractal strictly self-assembles, at any temperature, in Winfree's abstract Tile Assembly Model.

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