The distribution of tiles in the regular lattices

There is a version of NXLCAU21 which can calculate de Bruijn diagrams up to ten generations in a reasonable time and with the available memory. These diagrams deliver shift periodic lattices whose unit cells already have the shift-period as one edge, but for which another edge must be extracted from the diagram. For superluminal combinations there is only one cycle, whose length is the horizontal dimension of the unit cell. The number of nodes in the de Bruijn diagram is an extreme limit on the length of cycles, which are usually quite small in comparison. However, an occasional encounter with a long cycle should be expected.

Unit cells can be arranged into more convenient shapes by choosing better edges, just as larger cells can be obtained by joining smaller cells in clumps. Consequently, the same lattice can appear several times in the de Bruijn map under variant forms.

Quite different lattices can coincide in their shift periods, opening the possibility of composite lattices. In the superluminal region this cannot happen, isolating each lattice in its own cycle. Otherwise composites are possible, and need to be noted in the map. Conversely, each different cycle is capable of producing its one superluminal variant, resulting in many lattices grouped around a common theme.

	10	9	8	7	6	5	4	3	2	1	0	1	2	3	4	5	6	7	8	9	10
1	.	.	.	.	.	.	.	.	.	*	.	*	.	.	.	.	.	.	.	.	.
2	.	.	.	.	.	.	.	.	*	.	.	.	*	.	.	.	.	.	.	.	.
3	.	.	.	.	.	.	.	*	.	.	.	.	.	*	.	.	.	.	.	.	.
4	.	.	.	.	.	.	*	.	.	.	.	.	.	.	*	.	.	.	.	.	.
5	.	.	.	.	.	*	.	.	.	.	.	.	.	.	.	*	.	.	.	.	.
6	.	.	.	.	*	.	.	.	.	.	.	.	.	.	.	.	*	.	.	.	.
7	.	.	.	*	.	.	.	.	.	.	.	.	.	.	.	.	.	*	.	.	.
8	.	.	*	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	*	.	.
9	.	*	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	*	.
10	*	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	.	*

The basic layout of the map is shown above. Rather than exhibiting one single, all inclusive map, less congestion arises from classifying the lattices according to the largest triangle contained within their primitive unit cell. In the region studied, two large triangles seldom sit in the same unit lattice cell.