Hypercubic billiard word: Difference between revisions

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	'''Hypercubic billiard words''', '''cutting sequences''' or '''cutting words'''<ref name="vuillon">Vuillon, L. (2003). Balanced words. Bulletin of the Belgian Mathematical Society-Simon Stevin, 10(5), 787-805.</ref> can be visualized by considering a point particle (a "billiard ball") bouncing off walls in a closed cubic room. The ratio between the numbers of the step sizes (associated with the direction of the billiard ball) may be rational (resulting in a periodic scale) or irrational (resulting in an aperiodic scale).		'''Hypercubic billiard words''', '''cutting sequences''', or '''cutting words'''<ref name="vuillon">Vuillon, L. (2003). Balanced words. Bulletin of the Belgian Mathematical Society-Simon Stevin, 10(5), 787-805.</ref> can be visualized by considering a point particle (a "billiard ball") bouncing off walls in a closed cubic room. The ratio between the numbers of the step sizes (associated with the direction of the billiard ball) may be rational (resulting in a periodic scale) or irrational (resulting in an aperiodic scale).

	Regarded as scales, they are called '''billiard scales''', which are one possible generalization of [[MOS]] scales to [[arity\|larger alphabets]].		Regarded as scales, they are called '''billiard scales''', which are one possible generalization of [[MOS]] scales to [[arity\|larger alphabets]].