In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the possible patterns. In finite rectangular domains, it is shown that a regular hexagonal pattern cannot occur if the aspect ratio is rational. In practice, it is ...

PURPOSE To determine the influence of age on central corneal thickness (CCT), endothelial cell density (ECD), average cell size, coefficient of variation in cell size, and percentage of regular hexagonal cells; and to estimate the average ECD and CCT in seven age groups. MATERIALS AND METHODS After obtaining informed consent, 211 Caucasian patients (358 eyes) were examined using a noncontact ...

This paper studies the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for hex...

This paper concerns the construction of highly symmetric compactly supported wavelets for hexagonal data/image and triangle surface multiresolution processing. Recently hexagonal image processing has attracted attention. Compared with the conventional square lattice, the hexagonal lattice has several advantages, including that it has higher symmetry. It is desirable that the filter banks for he...

This paper presents new methods for the generation of hexagonal patterns, based on cellular automata in smallsized regular hexagonal modular spaces. The patterns are intended to be used for procedural content generation in computer games, but could also be applied for diverse ends, such as logotype design and architecture.

Concave gold nanoplates are obtained in hexagonal liquid crystal (LLC) made of SDS (sodium dodecyl sulfate)/glycine/HAuCl(4) aqueous solution system where glycine plays the key role. All plates are single-crystals, characterized by {111} facets, with concave centers of regular hexagonal or triangular shapes, and with better electrocatalytic activity than gold nanoplates.

Image processing has traditionally involved the use of square operators on regular rectangular image lattices. For many years the concept of using hexagonal pixels for image capture has been investigated, and several advantages of such an approach have been highlighted. We present a design procedure for hexagonal gradient operators, developed within the finite element framework, for use on hexa...

OF THESIS Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science Computer Science The University of New Mexico Albuquerque, New Mexico