Re: Cantor set

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg995] Re: [mg891] Cantor set*From*: Richard Mercer <richard at seuss.math.wright.edu>*Date*: Mon, 8 May 1995 03:38:22 -0400

> The ternary Cantor set can be constructed iteratively > from the interval [0,1] by removing at the n+1'th step > the middle third of each interval obtained in the n'th > step. Can anyone come up with a nice MMa formula for > calculating the beginning and end points of the k'th > interval (counted from left) in the n'th iteration? > > Thanks for any suggestions! > > -- Daniel > > > Fritz Haber Center for Molecular Dynamics Hebrew > University of Jerusalem E-mail: dani at batata.fh.huji.ac.il > Fax: 972-2-513742 > Daniel, As such thing go, this is easy. Are you sure you were really tryin? :) CantorEndPoints[0] = {{0,1}}; CantorEndPoints[n_]:= Join[CantorEndPoints[n-1]/3, CantorEndPoints[n-1]/3 + 2/3]; CantorEndPoints[3] 1 2 1 2 7 8 1 2 19 20 7 8 25 26 {{0, --}, {--, -}, {-, --}, {--, -}, {-, --}, {--, -}, {-, --}, {--, 1}} 27 27 9 9 27 27 3 3 27 27 9 9 27 27 If you want the kth interval, just take CantorEndPoints[n][[k]] Richard Mercer