"010", "100" and "101". Being also non-periodic, it is then of "minimal complexity", and hence a Sturmian word, with slope . The infinite Fibonacci word is the standard word generated by the directive sequence (1,1,1,....). The infinite Fibonacci word is recurrent; that is, every subword occurs infinitely often. If is a subword of the infinite Fibonacci word, then so is its reversal, denoted . If is a subword of the infinite Fibonacci word, then the least period of is a Fibonacci number. The concatenation of two successive Fibonacci words is "almost commutative". and differ only by their last two letters. The number 0.010010100..., whose digits are built with the digits of the infinite Fibonacci word, is transcendental. The letters "1" can be found at the positions given by the successive values of the Upper Wythoff sequence : The letters "0" can be found at the positions given by the successive values of the Lower Wythoff sequence : The distribution of points on the unit circle, placed consecutively clockwise by the golden angle , generates a pattern of two lengths on the unit circle. Although the above generating process of the Fibonacci word does not correspond directly to the successive division of circle segments, this pattern is if the pattern starts at the point nearest to the first point in clockwise direction, whereupon 0 corresponds to the long distance and 1 to the short distance. The infinite Fibonacci word contains repetitions of 3 successive identical subwords, but none of 4. The critical exponent for the infinite Fibonacci word is . It is the smallest index (or critical exponent) among all Sturmian words. The infinite Fibonacci word is often cited as the worst case for algorithms detecting repetitions in a string. The infinite Fibonacci word is a morphic word, generated in {0,1}* by the endomorphism 0 → 01, 1 → 0. The nth element of a Fibonacci word, , is 1 if the Zeckendorf representation (the sum of a specific set of Fibonacci numbers) of n includes a 1, and 0 if it does not include a 1. The digits of the Fibonacci word may be obtained by taking the sequence of fibbinary numbers modulo 2. Applications Fibonacci based constructions are currently used to model physical systems with aperiodic order such as quasicrystals, and in this context the Fibonacci word is also called the Fibonacci quasicrystal. Crystal growth techniques have been used