An interesting solution to sparsify the positions of the phase centers maintaining at the same time a high aperture efficiency consists in filling the array aperture with a number of tiles characterized by a different orientation, most notably
polyominoes [6, 7].
Golomb,
Polyominoes, Puzzles, Patterns, Problems, And Packings, Princeton University Press, 1996.
It uses
polyominoes which are plane geometric figures formed by joining one or more equal squares edge to edge (refer Figure 1).
[RK:] In Conditions, there were sections that reminded me of cellular automata, like Conway's Game of Life (1) and others where it seemed that you were exploring symmetries of the 10 x 10 grid, or arrangements of
polyominoes. (2) I'm curious as to how much of this formal structure is pre-planned, and how much emerges organically from improvisations.
Do you happen to recall when and where he stated emphatically that the plural of "polyomino" is NOT "polyominos" but "
polyominoes"?
Coloring the cells of the grid, stereo learners revisit arithmetic and algebra, meet tessellations,
polyominoes, moires, affine transformations, cellular automata, methods of computer graphics and animation.
Yuan, Lee, and Wang (2010) examined the effects of using virtual manipulatives and physical manipulatives in the study of
polyominoes on junior high school students.
One of the
polyominoes requires a more sophisticated version of the priority strategy called history dependent priority strategy.
Gessel has shown [6] that the coefficients count convex
polyominoes. Finally, for general m, the coefficients have a combinatorial interpretation in the work of V.
Pentominoes are a particular group of
polyominoes, a mathematical generalisation of the idea of a domino.
Urs, Dice, and
Polyominoes: Topics in the Theory of Groups, Residues, Primes, & Probability is an anthology of brain-teasing mathematical puzzles and solutions, written by expert mathematician and instructor Barr McCutcheon.
Polyominoes. Washington, D.C.: Mathematical Association of America, 1991.