Author
Gustavo N. Rubiano
Bio: Gustavo N. Rubiano is an academic researcher from National University of Colombia. The author has contributed to research in topics: Fibonacci word & Fibonacci number. The author has an hindex of 4, co-authored 11 publications receiving 41 citations.
Papers
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TL;DR: In this article, the authors introduce a family of infinite words that generalize the Fibonacci word and study their combinatorial properties, such as perimeter and area, and describe an infinite family of polyominoes.
18 citations
28 Feb 2015
TL;DR: In this paper, a word-combinatorial interpretation of the biperiodic Fibonacci sequence is presented, where the authors introduce a new family of infinite words and associate to these words a family of curves with interesting patterns.
Abstract: In this paper, we introduce a word-combinatorial interpretation of the biperiodic Fibonacci sequence We study some properties of this new family of infinite words Moreover, we associate to this family of words a family of curves with interesting patterns
9 citations
TL;DR: In this article, the k-Fibonacci words were defined in analogy with the definition of the K-Figer numbers, and the properties of these words were studied.
Abstract: Abstract In this paper we define the k-Fibonacci words in analogy with the definition of the k-Fibonacci numbers. We study their properties and we associate to this family of words a family of curves with interesting patterns.
9 citations
TL;DR: The p-circle inversion as discussed by the authors generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (P = 1). But it does not generalize the method called circle inversion fractal.
Abstract: In this paper, we introduce the p-circle inversion which generalizes the classical inversion with respect to a circle (p = 2) and the taxicab inversion (p = 1). We study some basic properties and we also show the inversive images of some basic curves. We apply this new transformation to well-known fractals such as Sierpinski triangle, Koch curve, dragon curve, Fibonacci fractal, among others. Then we obtain new fractal patterns. Moreover, we generalize the method called circle inversion fractal be means of the p-circle inversion.
6 citations
Posted Content•
TL;DR: A family of infinite words that generalize the Fibonacci word are introduced and their combinatorial properties are studied and they are double squares polyominoes, i.e., tile the plane by translation in exactly two distinct ways.
Abstract: In this paper we introduce a family of infinite words that generalize the Fibonacci word and we study their combinatorial properties. Moreover, we associate to this family of words a family of curves, which have fractal properties, in particular these curves have as attractor the Fibonacci word fractal. Finally, we describe an infinite family of polyominoes (double squares) from the generalized Fibonacci words and we study some of their geometric properties. These last polyominoes generalize the Fibonacci snowflake.
6 citations
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Journal Article•
TL;DR: What do you do to start reading automatic sequences theory applications generalizations?
Abstract: What do you do to start reading automatic sequences theory applications generalizations? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this automatic sequences theory applications generalizations.
305 citations
01 Jun 2015
TL;DR: In this paper, the k-Fibonacci and k-Lucas quaternions were defined and the generating functions and Binet formulas for these quaternians were investigated.
Abstract: Abstract In this paper, we define the k-Fibonacci and the k-Lucas quaternions. We investigate the generating functions and Binet formulas for these quaternions. In addition, we derive some sums formulas and identities such as Cassini’s identity.
47 citations
TL;DR: In this article, the authors introduce a family of infinite words that generalize the Fibonacci word and study their combinatorial properties, such as perimeter and area, and describe an infinite family of polyominoes.
18 citations
TL;DR: A new selection method for evolutionary computation algorithms that defines a better balance between elitism and diversity of the selection strategy and achieves the best performance over other selection algorithms, in terms of its solution quality and convergence speed.
Abstract: During millions of years, nature has developed patterns and processes with interesting characteristics. They have been used as inspiration for a significant number of innovative models that can be extended to solve complex engineering and mathematical problems. One of the most famous patterns present in nature is the Golden Section (GS). It defines an especial proportion that allows the adequate formation, selection, partition, and replication in several natural phenomena. On the other hand, Evolutionary algorithms (EAs) are stochastic optimization methods based on the model of natural evolution. One important process in these schemes is the operation of selection which exerts a strong influence on the performance of their search strategy. Different selection methods have been reported in the literature. However, all of them present an unsatisfactory performance as a consequence of the deficient relations between elitism and diversity of their selection procedures. In this paper, a new selection method for evolutionary computation algorithms is introduced. In the proposed approach, the population is segmented into several groups. Each group involves a certain number of individuals and a probability to be selected, which are determined according to the GS proportion. Therefore, the individuals are divided into categories where each group contains individual with similar quality regarding their fitness values. Since the possibility to choose an element inside the group is the same, the probability of selecting an individual depends exclusively on the group from which it belongs. Under these conditions, the proposed approach defines a better balance between elitism and diversity of the selection strategy. Numerical simulations show that the proposed method achieves the best performance over other selection algorithms, in terms of its solution quality and convergence speed.
17 citations
TL;DR: This paper studies the growth order and digit sum of the Fibonacci sequence and gives several decompositions of $\mathbf{F}$ using singular words.
Abstract: The infinite Fibonacci sequence $\mathbf{F}$, which is an extension of the classic Fibonacci sequence to the infinite alphabet $\mathbb{N}$, is the fixed point of the morphism $\phi$: $(2i)\mapsto (2i)(2i+1)$ and $(2i+1)\mapsto (2i+2)$ for all $i\in\mathbb{N}$. In this paper, we study the growth order and digit sum of $\mathbf{F}$ and give several decompositions of $\mathbf{F}$ using singular words.
9 citations