We show how one-dimensional cellular automata can be dynamically simulated by DNAbased tiles within the Active Abstract Tile Assembly Model (Active aTAM). The Active aTAM is a tile model for self assembly where tiles are able to transfer signals and change identities according to the signals received. We give a brief description of the model with the dynamics of tile attachment and signal passi...

T he interplay between local constraints and global structure of mathematical and physical systems is both subtle and important. The macroscopic physical properties of a system depend heavily on its global symmetries, but these are often difficult to predict given only information about local interactions between the components. A rich history of work on tilings of the Euclidean plane and highe...

This paper describes an exploration of visual and sonic texture. These textures are linked by a swarm of “tech-tiles”, where each tech-tile is a rectangular element of an image or a sequence of audio samples. An entire image can be converted to a single tech-tile, which can be performed as a composition, or a swarm of small tiles can fly over the image, generating a sonic improvisation. In each...

In this survey paper, I describe three applications of tilings to music theory: the representation of tuning systems and chord relationships by lattices, modeling voice leading by tilings of n-dimensional space, and the classification of rhythmic tiling canons, which are essentially one-dimensional tilings.

Traditional physical rehabilitation techniques are based mainly on mechanical structures and passive materials. This has certain limitations, which can be overcome by applying interactive technologies. As a team of designers, technologists and medical researchers and practitioners, we have developed an interactive sensor floor tile system for rehabilitation exercises, as part of an interactive ...

The results we introduce in this work lead to get an algorithm which produces aperiodic sets of tiles using Voronoi diagrams. This algorithm runs in optimal worst-case time O(n log n). Since a wide range of new examples can be obtained, it could shed some new light on non-periodic tilings. These examples are locally isomorphic and exhibit the 5-fold symmetry which appears in Penrose tilings and...

This chapter focuses on multiple tilings associated with substitutive dynamical systems. We recall that a substitutive dynamical system (Xσ, S) is a symbolic dynamical system where the shift S acts on the set Xσ of infinite words having the same language as a given infinite word which is generated by powers of a primitive substitution σ. We restrict to the case where the inflation factor of the...

We prove the computational intractability of rotating and placing n square tiles into a 1 × n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NPhard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying th...

In this paper we describe a hierarchical method for procedurally generating maps using Markov chains. Our method takes as input a collection of human-authored two-dimensional maps, and splits them into high-level tiles which capture large structures. Markov chains are then learned from those maps to capture the structure of both the high-level tiles, as well as the low-level tiles. Then, the le...

The creation of realistic, complex, and diversified virtual worlds is of utmost importance for video games. Unfortunately the amount of time required to create 3D scene contents can be extremely tedious to graphic artists. While procedural modeling can alleviate this task, it has mostly been developed for specific contexts. In this paper, we study tiling for synthetic worlds, taking into accoun...