Scaled pier fractals do not strictly self-assemble
| Autor: | David Furcy, Scott M. Summers |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Computational Geometry (cs.CG)
FOS: Computer and information sciences Pier Self assemble Block (permutation group theory) Geometry 0102 computer and information sciences 02 engineering and technology 01 natural sciences Computer Science Applications Tree (descriptive set theory) Fractal 010201 computation theory & mathematics Theory of computation 0202 electrical engineering electronic engineering information engineering Computer Science - Computational Geometry 020201 artificial intelligence & image processing Point (geometry) Mathematics Generator (mathematics) |
| Zdroj: | Natural Computing. 16:317-338 |
| ISSN: | 1572-9796 1567-7818 |
| DOI: | 10.1007/s11047-015-9528-z |
| Popis: | 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 $$c \times c$$ block of points, for some $$c \in \mathbb {Z}^+$$ . We prove that no scaled discrete self-similar pier fractal strictly self-assembles, at any temperature, in Winfree’s abstract Tile Assembly Model. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink