GrameStation: Specifying Games with Graphs

This paper presents a platform for creating games using graphs. The proposed game engine is based on a mathematical formalism called Graph Grammar. It aims to rescue, within computer science education, the stage of specification, that precedes programming. The proposal is aligned to the trends of the problem-solving focus, development of computational thinking, use of visual languages, game-related environments and the maker movement. The structure of the platform and the creation/execution of an example game are described and a brief discussion about specification in computer science education is given.

A Computational Design Synthesis Method for the Generation of Rigid Origami Crease Patterns

Today most origami crease patterns employed in technical applications are selected from a handful of well-known origami principles. Computational algorithms capable of generating novel crease patterns either target artistic origami, focus on quadrilateral creased paper, or do not incorporate direct knowledge for the purposeful design of crease patterns tailored to engineering applications. The lack of computational methods for the generative design of crease patterns for engineering applications arises from a multitude of geometric complexities intrinsic to origami, such as rigid foldability and rigid body modes, many of which have been addressed by recent work of the authors. Based on these findings, in this paper we introduce a Computational Design Synthesis method for the generative design of novel crease patterns to develop origami concepts for engineering applications. The proposed method first generates crease pattern graphs through a graph grammar that automatically builds the kinematic model of the underlying origami and introduces constraints for rigid foldability. Then, the method enumerates all design alternatives that arise from the assignment of different rigid body modes to the internal vertices. These design alternatives are then automatically optimized and checked for intersection to satisfy the given design task. The proposed method is generic and applied here to two design tasks that are a rigidly foldable gripper and a rigidly foldable robotic arm.

Shopping Around and One-Off Graphs

Given explicit recognition between ~1915 and the 1930s that certain artifact types display unimodal frequency distributions over time, archaeologists initially presented tables of those frequencies but by the 1930s were experimenting with different types of graphs to present visual images of culture change. The lack of familiarity with graph theory and graph grammar meant numerous kinds of graph were published, often only once each as researchers sought effective (readily deciphered) and efficient (minimal ink and space) graph forms. These experimental graph types range from fairly simplistic to complex and virtually indecipherable. Lack of decipherability and errors in some graphs reflect poor understanding of the principles of graph construction and the precise nature of what a graph type is meant to illustrate. The analytical focus on culture history and recognition that artifact form varied along both time and geographic space led to some efforts to incorporate all three dimensions—form, time, space—into some graphs. It is not surprising that in the search for a useful graph type, the one-off graphs variously implied transformational, variational, and a combination of variational and transformational evolutionary change.

Observations on Graphing Prehistory

Despite years of graphing culture change using different types and styles of diagram, there is minimal discussion of graph grammar—how to construct an effective and efficient graph, and how to decipher a graph of change. Part of the difficulty attending graph decipherment resided in (and continues to reside in) unclear distinction of transformational change from variational change. Models reflecting the former tend to be commonsensical and are similar to Petrie’s classic sequence dating graphs. The difficulty of graph decipherment is exacerbated by parsing temporally continuous variation into discontinuous spatio-temporally bounded units known as artifact types, cultures, phases, periods, stages, etc. These units are reified and (implicitly) conceived as real entities to be discovered for want of a well-developed theory of change and an attendant ontology of how continuously variable phenomena should be parsed into types for analysis. Archaeologists did perfect models of diffusion—the movement of culture traits (ideas or norms manifest as artifact types) across space over time—and built models of how it should be reflected in the archaeological record. A majority of introductory archaeology textbooks published since 1965 typically present graphs of culture change in the form of a spindle graph but with minimal discussion of graph grammar. Texts on regional or continental prehistory typically summarize culture change in spatio-temporal rectangle diagrams, which for pedagogical reasons may be reasonable. A few spindle graphs have been published in other disciplines and, like archaeological spindles, display temporally shifting frequencies.

Materials and Methods

To determine the origin of archaeological spindle graphs, and to track the frequency of use of each of several types of graph used to diagram culture change, a sample of North American archaeological literature was examined. Numerous series of monographs and volumes of journals in both the archaeological and the paleontological literature were inspected. If a graph of biological (paleontological) or cultural (archaeological) change was included in a publication, that piece of literature was recorded along with the type of graph included. To record such data, a classification of graph types was developed based on categories of statistical graphs (e.g., bar graph, line graph, pie graph, time range, spatio-temporal rectangle). More than 900 pieces of literature on North American archaeology published between ~1880 and ~1960 were inspected, and more than 450 pieces of literature on paleontology were inspected. Because different graph types are constructed under different guidelines, they require an understanding of graph grammar—the rules for constructing, deciphering, and interpreting graphs.

Graphing Culture Change in North American Archaeology

Documentation, analysis, and explanation of culture change have long been goals of archaeology. The earliest archaeological spindle graphs appeared in the 1880s and 1890s, but had no influence on subsequent archaeologists. Line graphs showing change in frequencies of specimens in each of several artifact types were used in the 1910s and 1920s. Seriograms or straight-sided spindles diagraming interpretations of culture change were published in the 1930s, but were seldom subsequently mimicked. Spindle graphs of centered and stacked columns of bars, each column representing a distinct artifact type, each bar the empirically documented relative frequency of specimens in an assemblage, were developed in the 1940s, became popular in the 1950s and 1960s, and are often used to illustrate culture change in textbooks published during the twentieth century. Graphs facilitate visual thinking, different graph types suggest different ontologies and theories of change, and particular techniques of parsing temporally continuous morphological variation of artifacts into types influence graph form. Line graphs, bar graphs, spindle diagrams, and phylogenetic trees of artifacts and cultures indicate archaeologists often mixed elements of Darwinian variational evolutionary change with elements of Midas-touch-like transformational change. Today there is minimal discussion of graph theory or graph grammar in both introductory archaeology textbooks and advanced texts, and elements of the two theories of evolution are often mixed. Culture has changed, and despite archaeology’s unique access to the totality of humankind’s cultural past, there is minimal discussion on graph theory, construction, and decipherment in the archaeological literature.

Parallel graph-grammar-based algorithm for the longest-edge refinement of triangular meshes and the pollution simulations in Lesser Poland area

In this paper, we propose parallel graph-grammar-based algorithm for the longest-edge refinements and the pollution simulations in Lesser Poland area. We introduce graph-grammar productions for Rivara’s longest-edged algorithm for the local refinement of unstructured triangular meshes. We utilize the hyper-graph to represent the computational mesh and the graph-grammar productions to express the longest-edge mesh refinement algorithm. The parallelism in the original Rivara’s longest edge refinement algorithm is obtained by processing different longest edge refinement paths in different three ads. Our graph-grammar-based algorithm allows for additional parallelization within a single longest-edge refinement path. The graph-grammar-based algorithm automatically guarantees the validity and conformity of the generated mesh; it prevents the generation of duplicated nodes and edges, elongated elements with Jacobians converging to zero, and removes all the hanging nodes automatically from the mesh. We test the algorithm on generating a surface mesh based on a topographic data of Lesser Poland area. The graph-grammar productions also generate the layers of prismatic three-dimensional elements on top of the triangular mesh, and they break each prismatic element into three tetrahedral elements. Next, we propose graph-grammar productions generating element matrices and right-hand-side vectors for each tetrahedral element. We utilize the Streamline Upwind Petrov–Galerkin (SUPG) stabilization for the pollution propagation simulations in Lesser Poland area. We use the advection–diffusion-reaction model, the Crank–Nicolson time integration scheme, and the graph-grammar-based interface to the GMRES solver.