Fibonacci Word
In analogy to its numerical counterpart, the Fibonacci word is defined by:
where + denotes the concatenation of two strings. The sequence of Fibonacci strings starts:
- b, a, ab, aba, abaab, abaababa, abaababaabaab, …
The length of each Fibonacci string is a Fibonacci number, and similarly there exists a corresponding Fibonacci string for each Fibonacci number.
Fibonacci strings appear as inputs for the worst case in some computer algorithms.
If "a" and "b" represent two different materials or atomic bond lengths, the structure corresponding to a Fibonacci string is a Fibonacci quasicrystal, an aperiodic quasicrystal structure with unusual spectral properties.
Read more about this topic: Generalizations Of Fibonacci Numbers
Famous quotes containing the word word:
“Denotation by means of sounds and markings is a remarkable abstraction. Three letters designate God for me; several lines a million things. How easy becomes the manipulation of the universe here, how evident the concentration of the intellectual world! Language is the dynamics of the spiritual realm. One word of command moves armies; the word liberty entire nations.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)