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:
“The only chance for victory over the brainwash is the right of every man to have his ideas judged one at a time. You never get clarity as long as you have these packaged words, as long as a word is used by twenty-five people in twenty-five different ways. That seems to me to be the first fight, if there is going to be any intellect left.”
—Ezra Pound (1885–1972)