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MathGroup Archive 1995

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Re: Cantor set

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg924] Re: Cantor set
  • From: steve at tweedledee.ucsb.edu (Steve Trainoff)
  • Date: Wed, 3 May 1995 00:03:09 -0400
  • Organization: University of California, Santa Barbara

In article <3nkc8n$mq8 at news0.cybernetics.net> "Hamburger Dani"  
<dani at espresso.fh.huji.ac.il> writes:
> 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 lef 
t) in the n'th iteration?
> 
> Thanks for any suggestions!
> 
Sure, just write a recursive function to compute it.  MMA is great for things like this.

In[1]:= h[x_,0] = x;                            (* Recursive Anchor *)

In[2]:= h[{a_,b_}, n_Integer] := {h[{a, a+(b-a)/3},n-1], h[{a+2(b-a)/3, b},n-1]}

In[3]:= Partition[Flatten[h[{0,1},2]],2]

             1    2  1    2  7    8
Out[3]= {{0, -}, {-, -}, {-, -}, {-, 1}}
             9    9  3    3  9    9

--

..STeve
------------------------------------
Insert pithy maxim here...
steve at tweedledee.ucsb.edu (NeXT mail)


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