Rings on a matrix
- To: mathgroup at smc.vnet.net
- Subject: [mg108512] Rings on a matrix
- From: mokambo <alexandrepassosalmeida at gmail.com>
- Date: Sun, 21 Mar 2010 02:05:52 -0500 (EST)
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