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:
“I am a dreamer of words, of written words. I think I am reading; a word stops me. I leave the page. The syllables of the word begin to move around. Stressed accents begin to invert. The word abandons its meaning like an overload which is too heavy and prevents dreaming. Then words take on other meanings as if they had the right to be young. And the words wander away, looking in the nooks and crannies of vocabulary for new company, bad company.”
—Gaston Bachelard (1884–1962)