A generalization of the Fibonacci word fractal and the Fibonacci snowflake

被引：13

作者：

Ramirez, Jose L. ^{[1
]}

Rubiano, Gustavo N. ^{[2
]}

De Castro, Rodrigo ^{[2
]}

机构：

[1] Univ Sergio Arboleda, Inst Matemat & Sus Aplicac, Bogota, Colombia

[2] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia

来源：

THEORETICAL COMPUTER SCIENCE | 2014年 / 528卷

关键词：

Fibonacci word; Fibonacci word fractal; Fibonacci snowflake; Polyomino; Tessellation;

D O I：

10.1016/j.tcs.2014.02.003

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. We associate with this family of words a family of curves that are like the Fibonacci word fractal and reveal some fractal features. Finally, we describe an infinite family of polyominoes stems from the generalized Fibonacci words and we study some of their geometric properties, such as perimeter and area. These last polyominoes generalize the Fibonacci snowflake and they are double squares polyominoes, i.e., tile the plane by translation in exactly two distinct ways. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：40 / 56

页数：17

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