Re: Rings on a matrix
- To: mathgroup at smc.vnet.net
- Subject: [mg108566] Re: Rings on a matrix
- From: mokambo <alexandrepassosalmeida at gmail.com>
- Date: Tue, 23 Mar 2010 05:52:21 -0500 (EST)
- References: <ho4gqd$jk0$1@smc.vnet.net> <ho778a$12k$1@smc.vnet.net>
On Mar 22, 7:46 am, "Sjoerd C. de Vries" <sjoerd.c.devr... at gmail.com>
wrote:
> 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, 1=
6,
> > 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
Thank you for your answer Sjoerd. But your solution gives a perfect ring
while what I was looking for has a different pattern. I managed to find
a solution involving a congruential inequality.
Alex