The Unit Cell
| Whole pattern | Off Diagonal Elements |
|---|---|
 |
 |
The Off Diagonal cells are generated by the sequences starting (3, 1), (3, 2) and (6, 2).
The Pattern
A number of unit cells are tiled to show the overall pattern.
The pattern composed from just the Off Diagonal cells.
The Numbers
The points are generated using an algorithm where the only input is the number of cells across the pattern. The resulting series for N=11 are shown below.
| Seed | Sequence | No. |
|---|---|---|
| (0,0) | [0], [0], [0], [0], ... | 1 |
| (1,1) | [1, 1, 2, 3, 5, 8, 2, 10, 1, 0], [1, 1, 2, 3, ... | 10 |
| (2,2) | [2, 2, 4, 6, 10, 5, 4, 9, 2, 0], [2, 2, 4, 6, ... | 10 |
| (3,3) | [3, 3, 6, 9, 4, 2, 6, 8, 3, 0], [3, 3, 6, 9, ... | 10 |
| (4,4) | [4, 4, 8, 1, 9, 10, 8, 7, 4, 0], [4, 4, 8, 1, ... | 10 |
| (5,5) | [5, 5, 10, 4, 3, 7, 10, 6, 5, 0], [5, 5, 10, 4, ... | 10 |
| (6,6) | [6, 6, 1, 7, 8, 4, 1, 5, 6, 0], [6, 6, 1, 7, ... | 10 |
| (7,7) | [7, 7, 3, 10, 2, 1, 3, 4, 7, 0], [7, 7, 3, 10, ... | 10 |
| (8,8) | [8, 8, 5, 2, 7, 9, 5, 3, 8, 0], [8, 8, 5, 2, ... | 10 |
| (9,9) | [9, 9, 7, 5, 1, 6, 7, 2, 9, 0], [9, 9, 7, 5, ... | 10 |
| (10,10) | [10, 10, 9, 8, 6, 3, 9, 1, 10, 0], [10, 10, 9, 8, ... | 10 |
| (3,1) | [3, 1, 4, 5, 9], [3, 1, 4, 5, 9], ... | 5 |
| (3,2) | [3, 2, 5, 7, 1, 8, 9, 6, 4, 10], [3, 2, 5, 7, ... | 10 |
| (6,2) | [6, 2, 8, 10, 7], [6, 2, 8, 10, 7], ... | 5 |
| Total | 121 | |
The Art Gallery
The following picture is an example of effects that can be obtained by taking the original rather sterile tiled picture and putting it through some effects in Paintshop Pro.
