We first prove that solving Mahjong Solitaire boards with peeking is NPcomplete, even if one only allows isolated stacks of the forms aab and abb. We subsequently show that layouts of isolated stacks of heights one and two can always be solved with peeking, and that doing so is in P, as well as finding an optimal algorithm for such layouts without peeking. Next, we describe a practical algorith...

We give a simple set of two tiles that can only tile aperiodically | that is no tiling with these tiles is invariant under any in nite cyclic group of isometries. Although general constructions for producing aperiodic sets of tiles are nally appearing, simple aperiodic sets are fairly rare. This set is among the smallest sets ever found. A tiling is non-periodic if there is no in nite cyclic gr...

A new aperiodic tile set containing 11 Wang tiles on 4 colors is presented. This tile set is minimal in the sense that no Wang set with less than 11 tiles is aperiodic, and no Wang set with less than 4 colors is aperiodic. Wang tiles are square tiles with colored edges. A tiling of the plane by Wang tiles consists in putting a Wang tile in each cell of the grid Z so that contiguous edges share ...

Many complex signals, such as point distributions and textures, cannot efficiently be synthesized and stored. In this work we present tile-based methods to solve this problem. Instead of synthesizing a complex signal when needed, the signal is synthesized on forehand over a small set of tiles. Arbitrary large amounts of that signal can then efficiently be generated when needed by generating a s...

Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the cla...

In this article, glaze with different colorants was applied to tile specimens manufactured by incinerated sewage sludge ash (ISSA) and clay. Improvements using different amounts of colorants, and glaze components and concentrations on tile bodies were investigated. Four different proportions of clay (by weight ratio) were replaced by ISSA. Tiles of size 12 cm x 6 cm x 1 cm were made and left in...

A model of a kinematic system consisting of moveable tiles in a two dimensional discrete space environment is presented. Neighbouring tiles repel one another, some tiles are fixed in place. A dual-rail logic gate is constructed in this system.

By introducing a mean-field version of the tile automaton model introduced in earlier works, growth of molecules through chemical reaction networks is studied with explicit consideration for molecule shape as a “tile”. Tiles are picked up randomly to collide, and with a certain rule they react to form new tiles. A non-trivial growth pattern, called joint growth is found, with which tiles grow b...