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

```

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