Tiles made of joined unions of squares. Such tilings were introduced and studied in [Golomb:P not found].
Also known as ‘table tiling’. In [Sol97] was shown that its dynamical spectrum has a continuous component. Thus it cannot be a cut and project tiling. The same was shown in [Rob99] , where a topological model of the dynamical system of the domino tilings is obtained.
Polyomio Tiling Finite Rotations Polyomio Tilings Rep Tiles Self Similar Substitution
A simple variant of the domino tilings (aka table tilings). C. Goodman-Strauss pointed out in [Goo98] the following. B. Solomyak proved in Sol98, that for each nonperiodic substitution tiling the substitution rule is invertible: One can tell from $\sigma(T)$ its predecessor $T$ uniquely. But this is true only if the prototiles have the same symmetry group as the first order supertiles. By using decorated tiles this can always be achieved. (And now Chaims remark:) Here we see a case where such a decoration is necessary.
Finite Rotations P Adic Windowed Tiling Polytopal Tiles Parallelogram Tiles Polyomio Tiling Rep Tiles Self Similar Substitution
A generalization of the domino substitution. There are several possibilities to play with 1x2 rectangles (dominos) in order to generate non-periodic tilings. The decorative lining shows here how the prototile gets turned and mirrored for this example. The two rules are actually exactly the same. For decoration the horizontal tile was colored purple.
Finite Rotations Polytopal Tiles Polyomio Tiling Rep Tiles Self Similar Substitution