M. Bubak et al. (Eds.): ICCS 2004, LNCS 3038, pp. 996–1003, 2004. © Springer-Verlag Berlin Heidelberg 2004 Using Indexed-Sequential Geometric Glyphs to Explore Visual Patterns Jim Morey and Kamran Sedig Cognitive Engineering Laboratory Department of Computer Science The University of Western Ontario, Canada {jmorey,sedig}@uwo.ca Abstract. This paper presents a visualization tool called PolygonR&D for exploring visual tiling patterns. To facilitate the exploration process, PolygonR&D uses dynamically-generated, interactive geometric glyph visualizations that intermediate reasoning between the sequential textual code and the parallel visual structure of the tilings. Sequential textual code generates indexed-sequential geometric glyphs. Not only does each glyph represent one procedure in the sequential code, but also a constituent element of the visual pattern. Users can reason with a sequence of glyphs to explore how tiling patterns are constructed. Alternatively, they can interact with glyphs to semantically unpack them. Glyphs also contain symbolic referents to other glyphs helping users see how all procedures work together to generate a tiling pattern. Experimenting with indexed-sequential glyphs in tools such as PolygonR&D can help us understand how to design interactive cognitive tools that support reciprocal reasoning between sentential and visual structures. 1 Introduction and Background Mathematics has been described as the science of patterns [1]. Visual tilings are an example of mathematical patterns that are all around us [1, 2]. One of the best ways to investigate many mathematical concepts is to interact with their representations using computational cognitive tools—interactive tools that support and enhance cognition in the process of reasoning and experimentation [3]. Gaining insight into many ideas involves reasoning with multiple forms of representations of those ideas and interacting with those representations using different interaction styles and methods [3, 4, 5]. This is true of mathematical patterns. Due to their flexibility, malleable form, and dynamic nature, computational tools can easily present users with different representational forms of mathematical ideas and various interaction styles, allowing for different reasoning [3, 5]. In this paper, we are interested in investigating how to explore geometric tiling patterns using different representational forms. Two forms of representation of geometric tilings include descriptive and visual [1, 2]. The first form is textual, sentential, and language-like; it is linear and sequential in nature; it linguistically describes how the tiling can be constructed. The second form is visual or diagrammatic; it is spatial and parallel in nature; it visually shows the structure of the tiling. These two forms of representation are informationally