Characterization by a cutting sequence with a line of slope or , with the golden ratio.
Fibonacci curves made from the 10th and 17th Fibonacci words[1]
A Fibonacci word is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition.
It is a paradigmatic example of a Sturmian word and specifically, a morphic word.
The name "Fibonacci word" has also been used to refer to the members of a formal language L consisting of strings of zeros and ones with no two repeated ones. Any prefix of the specific Fibonacci word belongs to L, but so do many other strings. L has a Fibonacci number of members of each possible length.
A Fibonacciword is a specific sequence of binary digits (or symbols from any two-letter alphabet). The Fibonacciword is formed by repeated concatenation...
The Fibonacciword fractal is a fractal curve defined on the plane from the Fibonacciword. This curve is built iteratively by applying the Odd–Even Drawing...
Fibonacci (/ˌfɪbəˈnɑːtʃi/; also US: /ˌfiːb-/, Italian: [fiboˈnattʃi]; c. 1170 – c. 1240–50), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo...
mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are...
integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely...
the θ-coding of x. A famous example of a (standard) Sturmian word is the Fibonacciword; its slope is 1 / ϕ {\displaystyle 1/\phi } , where ϕ {\displaystyle...
The Fibonacci numbers are a sequence of integers, starting with 0, 1 and continuing 1, 2, 3, 5, 8, 13, ..., each new number being the sum of the previous...
calculations of pentagons and decagons; his writings influenced that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry...
words, the largest possible palindromic density is achieved by the Fibonacciword, which has density 1/φ, where φ is the Golden ratio. A palstar is a...
from the original on 15 October 2012. Retrieved 2 October 2006. The Fibonacciword fractal Theiler, James (1990). "Estimating fractal dimension" (PDF)...
assemblies of tiles called rhombs, illustrates scaling symmetry. A Fibonacciword can be used to build an aperiodic tiling, and to study quasicrystals...
these include the Baum–Sweet sequence, Ehrenfeucht–Mycielski sequence, Fibonacciword, Kolakoski sequence, regular paperfolding sequence, Rudin–Shapiro sequence...
attributed to his technique. Fractal image generated by Electric Sheep A Fibonacciword fractal A 3D Mandelbulb fractal generated using Visions of Chaos 3D...
The Fibonaccis were an American art rock band formed in 1981 in Los Angeles.[citation needed] The band consisted of songwriters John Dentino (keyboards)...
example is the Fibonacciword. More generally, a Sturmian word over an alphabet of size k is one with complexity n+k−1. An Arnoux-Rauzy word over a ternary...
1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for helping popularize Arabic numerals in Europe...
computer words. The worst-case space usage of a suffix tree is seen with a fibonacciword, giving the full 2 n {\displaystyle 2n} nodes. An important choice when...
endomorphism 0 → 01, 1 → 10. The Fibonacciword is generated over {a,b} by the endomorphism a → ab, b → a. The tribonacci word is generated over {a,b,c} by...
critical exponent of the Fibonacciword is (5 + √5)/2 ≈ 3.618. The critical exponent of the Thue–Morse sequence is 2. The word contains arbitrarily long...
words. Fibonacciword Kolakoski sequence Levi's lemma Partial word Shift space Word metric Word problem (computability) Word problem (mathematics) Word problem...
properties of binary numbers and Fibonacci numbers: The number of fibbinary numbers less than any given power of two is a Fibonacci number. For instance, there...
Global Information
