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Re: Rings on a matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108533] Re: Rings on a matrix
  • From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
  • Date: Mon, 22 Mar 2010 02:39:36 -0500 (EST)
  • References: <ho4gqd$jk0$1@smc.vnet.net>

Not sure I understand your problem, but would the difference of two
DiskMatrices be useful?

n = 10;
ArrayPlot[DiskMatrix[n, 2 n + 2] - DiskMatrix[n - 1, 2 n + 2], Mesh ->
All]

This generates one ring. You can get more if you add matrices with
samller or larger rings.

Cheers -- Sjoerd

On Mar 21, 9:11 am, mokambo <alexandrepassosalme... at gmail.com> wrote:
> I'm having a problem trying to find a procedure to generate rings in a
> matrix. Here are 3 steps of the algorithm (if it exists):
> Use ArrayPlot[%, Mesh -> True] for quick visualization.
>
> 1 ring at iteration 1:
> {{0, 0, 0, 0}, {0, 1, 1, 0}, {0, 1, 1, 0}, {0, 0, 0, 0}}
>
> 2 rings at iteration 2:
> {{0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 8, 8, 0, 0, 0},
> {0, 0, 8, 0, 0, 8, 0, 0}, {0, 8, 0, 8, 8, 0, 8, 0},
> {0, 8, 0, 8, 8, 0, 8, 0}, {0, 0, 8, 0, 0, 8, 0, 0},
> {0, 0, 0, 8, 8, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0}}
>
> 4 rings at iteration 3:
> {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 16,
>    16, 16, 16, 16, 16, 0, 0, 0, 0, 0}, {0, 0, 0, 16, 16, 16, 0, 0, 0,
>   0, 16, 16, 16, 0, 0, 0}, {0, 0, 16, 16, 16, 0, 0, 16, 16, 0, 0, 16,
>   16, 16, 0, 0}, {0, 0, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 16, 16, 0,
>    0}, {0, 16, 16, 0, 16, 16, 0, 16, 16, 0, 16, 16, 0, 16, 16, 0}, {0=
,
>    16, 0, 0, 16, 0, 16, 0, 0, 16, 0, 16, 0, 0, 16, 0}, {0, 16, 0, 16,
>   0, 16, 0, 16, 16, 0, 16, 0, 16, 0, 16, 0}, {0, 16, 0, 16, 0, 16, 0,
>   16, 16, 0, 16, 0, 16, 0, 16, 0}, {0, 16, 0, 0, 16, 0, 16, 0, 0, 16,
>   0, 16, 0, 0, 16, 0}, {0, 16, 16, 0, 16, 16, 0, 16, 16, 0, 16, 16, 0,
>    16, 16, 0}, {0, 0, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 16, 16, 0,
>   0}, {0, 0, 16, 16, 16, 0, 0, 16, 16, 0, 0, 16, 16, 16, 0, 0}, {0, 0,
>    0, 16, 16, 16, 0, 0, 0, 0, 16, 16, 16, 0, 0, 0}, {0, 0, 0, 0, 0,
>   16, 16, 16, 16, 16, 16, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0,
>   0, 0, 0, 0, 0, 0, 0}}
>
> I've tried just 1/4 of the problem (due to symmetries) and playing
> with the circle equation and measuring distances from
> points in a lattice. I've tried DiskMatrix but can't find a recursion
> to generate the examples. Any ideas, hints?
> Is there a way to solve this problem (Congruence equations perhaps?)
>
> Alex



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