Related papers: Tatami Maker: A combinatorially rich mechanical ga…
We study the recursive structure of P-positions in the chocolate game $C_{m,m}$, an impartial game played on an $m \times m$ chocolate bar. We show that the set of P-positions exhibits self-similar patterns that can be described and…
Distributed Manipulator Systems, composed of arrays of robotic actuators necessitate dense actuator arrays to effectively manipulate small objects. This paper presents a system composed of modular 3-DoF robotic tiles interconnected by a…
The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials.…
Three dimensional (3D) structures composed of planar surfaces can be build out of accessible materials using easier fabrication technique with shorter fabrication time. To better design 3D structures with planar surfaces, realistic models…
In recent years, there has been an increasing interest in the use of robotic technology at home. A number of service robots appeared on the market, supporting customers in the execution of everyday tasks. Roughly at the same time, consumer…
Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of…
Metamaterials are a promising platform for a range of applications, from shock absorption to mechanical computing. These functionalities typically rely on floppy modes or mechanically frustrated loops, both of which are difficult to design.…
This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
In the Nikoli pencil-and-paper game Tatamibari, a puzzle consists of an $m \times n$ grid of cells, where each cell possibly contains a clue among +, -, |. The goal is to partition the grid into disjoint rectangles, where every rectangle…
Origami offers a versatile framework for designing morphable structures and soft robots by exploiting the geometry of folds. Tubular origami structures can act as continuum manipulators that balance flexibility and strength. However,…
The study of combinatorial games is intimately tied to the study of graphs, as any game can be realized as a directed graph in which players take turns traversing the edges until reaching a sink. However, there have heretofore been few…
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume…
Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…
Creating and evaluating games manually is an arduous and laborious task. Procedural content generation can aid by creating game artifacts, but usually not an entire game. Evolutionary game design, which combines evolutionary algorithms with…
We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences…
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about…
Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have…
Game boards are described in the Ludii general game system by their underlying graphs, based on tiling, shape and graph operators, with the automatic detection of important properties such as topological relationships between graph…
Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with colored cubes and bricks of $(2\times2\times n)$-board in three…