Exempel på tiling

• Local characteristics, entropy and limit theorems for spanning trees and domino tilings via transfer-impedances.

• Proposition 3.15 allows us to assume that the basic regions come equipped with an approximately alternating grid tiling.

• Then by symmetry you get exactly half the possible tilings, so double the final answer.

• Only the last one can be made into a genuine self-similar tiling, although all variants are closely related.

• If a tiling is given, the atomic arrangement can be formed by placing atoms at the vertices.

• To get an idea of what these tiling spaces look like, consider the substitution on two letters given by (1) = 12, (2) = 122.

• We investigate the consequences of assuming one or the other of these notions of isomorphism for such tilings.

• For substitution minimal systems, flow equivalence is equivalent to the existence of an orientation preserving homeomorphism of the associated tiling spaces.

• Roughly speaking, two tilings are close if they have the same pattern in a large neighborhood of the origin, up to a small translation.

• We therefore have to show that a real set of steps can't be built by tiling according to our rules.

• That means finding a way to generate each possible tiling just once.

• A point in the inverse limit is then a consistent prescription for constructing a tiling out to infinity.

• We might want a tree of tilings or some other structure to represent the set of possible tilings.

• How does the tiling behavior of astrocytes contribute to their interconnectivity?

• Limits and boundaries of word and tiling substitutions.