Rendering computer-generated images is both memory and runtime intensive. This is particularly true in realtime computer graphics where large amounts of content have to be produced very quickly and from limited data. Tile-based methods offer a solution to this problem by generating large portions of a specific content out of a much smaller data set of tiles. This dissertation investigates the u...

Introduction Substitution tilings have been discussed now for at least twenty-five years, initially motivated by the construction of hierarchical non-periodic structures in the Euclidean plane [?, ?, ?, ?]. Aperiodic sets of tiles were often created by forcing these structures to emerge. Recently, this line was more or less completed, with the demonstration that (essentially) every substitution...

In any given fixed setting, say polygonal tiles in the hyperbolic plane, we can ask a variety of questions, such as: " Is there an aperiodic set of tiles? " In this talk, we'll look at an interlocked web of such questions and discuss a variety of conjectures and results, both old and new.

Electronic maps (E-maps) provide people with convenience in real-world space. Although web map services can display maps on screens, a more important function is their ability to access geographical features. An E-map that is based on raster tiles is inferior to vector tiles in terms of interactive ability because vector maps provide a convenient and effective method to access and manipulate we...

Algorithms and information, fundamental to technological and biological organization, are also an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Here we report the molecular realization, using two-dimensional self-assembly of DNA tiles, of a cellular automaton whose update rule computes the binary function XOR and thus fabricates a fractal pattern--a Si...

In solving problems people naturally seek to modify their external environment such that the physical space in which they work is more amenable or ‘congenial’ to achieving a desired outcome. Attempts to determine the effectiveness of certain artifacts or spatial reorganizations in aiding reasoners solve problems must be relativised to the difficulty of the task and the cognitive abilities of th...

The abstract Tile Assembly Model (aTAM) [3] is a mathematical model of self-assembly in which system components are four-sided Wang tiles with glue types assigned to each tile edge. Any pair of glue types are assigned some nonnegative interaction strength denoting how strongly the pair of glues bind. An aTAM system is an ordered triplet .T; ; / consisting of a set of tiles T , a positive intege...

Spectral reflection prediction models, although effective, are impractical for certain industrial applications such as self-calibrating devices and online monitoring because of the requirements imposed by their calibration. The idea emerged to make the calibration more flexible. Instead of requiring specific color-constant calibration patches, the calibration would rely on the information conta...

ÐThe semiconductor industry roadmap projects that advances in VLSI technology will permit more than one billion transistors on a chip by the year 2010. The MIT Raw microprocessor is a proposed architecture that strives to exploit these chip-level resources by implementing thousands of tiles, each comprising a processing element and a small amount of memory, coupled by a static two-dimensional i...