Bulletin of the Society for Science on Form 

About: Bulletin of the Society for Science on Form is an academic journal. The journal publishes majorly in the area(s): Space group & Geometric algebra. It has an ISSN identifier of 0915-6089. Over the lifetime, 29 publications have been published receiving 593 citations.

P systems for array generation and application to kolam patterns

Abstract: In the area of membrane computing, a new computability model, now called P system was introduced by PAUN (2002) inspired from the cell structure and its functioning. One area of P systems deals with string objects and rewriting rules. Recently, array P systems with array objects and array rewriting rules were introduced. Here we introduce a new class of array P systems called sequential/parallel rectangular array P systems generating pictures of rectangular arrays. These P systems have rectangular arrays as objects in the membranes and rules in the membranes are either context-free or regular with sequential horizontal rewriting or right-linear rules with vertical rewriting in parallel as in the two-dimensional (2D) matrix grammars (SIROMONEY et al., 1972). These P systems have more generative power and accordingly, they can generate kolam patterns that cannot be handled by 2D matrix grammars.

Fundamental Study on Design System of Kolam Pattern

Abstract: Kolam" is a kind of string/knot pattern seen primarily in Tamilnadu state of South India, which has a very attractive system of pattern formation, that is to say, countless complicated Kolam patterns can be drawn following extremely simple elements and drawing rules. In this paper, the fundamental characteristic of Kolam patterns' designing system is considered by converting these patterns into numbers and linear diagrams. Further discussions on the drawing methods to create new Kolams will also be given.

Three Vector Generation of Crystal Space Groups in Geometric Algebra

Abstract: This paper focuses on the symmetries of crystal space lattices. All two dimensional (2D) and three dimensional (3D) point groups of 2D and 3D crystal cells are exclusively described by vectors (two in 2D, three in 3D for one particular cell) taken from the physical cells. Geometric multiplication of these vectors completely generates all symmetries, including reflections, rotations, inversions, rotary-reflections and rotary-inversions. We then extend this treatment to 3D space groups by including translations, glide reflections and screw rotations. We focus on the monoclinic case as an example. A software demonstration shows the spacegroup visualizer.