Generation of Sierpinski Triangles: A Case Study for Graph Transformation Tools

Customizing grgen.net for model transformation

“…In contrast, GrGen.NET seamlessly integrates the production of the output into the rule language. Comparisons [21] show that the mixed visual and textual modeling language is quite verbose, while GReAT's execution speed is rather low. Most notably, no DSL for UML with comparable coverage is available for GReAT to the knowledge of the authors.…”

Parallelism in AGREE Transformations

“…A Sierpinski triangle is a well-known fractal in which an equilateral triangle is divided into smaller equilateral triangles in a controlled way, given by a rule like the one depicted in Figure 2(a). Applying this rule repeatedly and fairly a convenient number of times leads to shapes like the ones shown in Figure 2 In [16] the generation of Sierpinski triangles was used as a case study to compare di↵erent graph transformation tools. There, a triangle was modeled as a graph with three nodes and three edges, and each step of the generation deleted edges and created new nodes and edges.…”

A Reference Interpreter for the Graph Programming Language GP 2

“…Sierpinski triangles pose a hard challenge for graph transformation: generating the n-th triangle requires space and a number of rule applications exponential in n. This problem was part of the 2007 tool contest for graph transformation, where the goal was to generate triangles of generation numbers as high as possible and as fast as possible [19].…”