On 11/29/2017 11:40 PM, Roger Hui wrote:
> 2.5 Cantor Set
>
> Write a function to compute the Cantor set of order n, n>:0.
>
> Cantor 0
> 1
> Cantor 1
> 1 0 1
> Cantor 2
> 1 0 1 0 0 0 1 0 1
> Cantor 3
> 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1
>
In Mathematica:
cantor[n_] := If[n == 0, {1},
cantor[n - 1] /. {0 -> Sequence[0, 0, 0], 1 -> Sequence[1, 0, 1]}]
I doubt J could do substantially better, but I'll leave that to you experts.
> 2.6 Sierpinski Carpet
>
> Write a function to compute the Sierpinski Carpet of order n, n>:0.
>
> SC 0
> 1
> SC 1
> 1 1 1
> 1 0 1
> 1 1 1
> SC 2
> 1 1 1 1 1 1 1 1 1
> 1 0 1 1 0 1 1 0 1
> 1 1 1 1 1 1 1 1 1
> 1 1 1 0 0 0 1 1 1
> 1 0 1 0 0 0 1 0 1
> 1 1 1 0 0 0 1 1 1
> 1 1 1 1 1 1 1 1 1
> 1 0 1 1 0 1 1 0 1
> 1 1 1 1 1 1 1 1 1
I believe Mathematica has no built in tiling function, so I wrote one.
tile[m_] := Join @@ ((Join @@@ #) & /@ (Transpose /@ m));
hole = {{1, 1, 1}, {1, 0, 1}, {1, 1, 1}};
zeros = Table[0, {3}, {3}];
sierpinski[n_] := If[n == 0, {{1}},
tile[sierpinski[n - 1] /. {1 -> hole, 0 -> zeros}]]
The tiling utilities in J are very nice.
Could give a reference for the extend H algorithm? I get the idea, but
I'm a little unclear about the details.
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