On Graph Grammars and Games
Jayakrishna Vijayakumar, Lisa Mathew
TL;DR
The paper addresses automatic generation of solvable 2D game levels using directed, non-confluent graph grammars. It extends nc-eNCE into Directed Non-Confluent Edge and Node Controlled Embedding (Dnc-eNCE) and adds a jumping variant (Dnc-eNCE-JGG) to model directed puzzle graphs and platform layouts. Formal definitions, regular-control-based ordering, and a random plot generator enable countably infinite, solvable game plots, demonstrated through directed wheel and puzzle-graph constructions. This approach provides a structured, scalable framework for procedural content generation in 2D games with lock-and-key and platform elements, with future work on implementation and adaptive difficulty.
Abstract
Graph grammars form an interesting area of research because of their versatility in modelling diverse situations with graphs as the structures which are to be manipulated. A new class of graph grammars, nc-eNCE Graph Grammars has been introduced recently with an aim of restricting the order of application of graph production rules, thereby generating different graph classes using the same set of rules. On the other hand 2D game design using an algorithmic approach known as procedural content generation has been of interest recently. In this paper we modify the structure of nc-eNCE graph grammars with the aim of generating directed graphs. We show that employing these graph grammars simplifies the design of 2D games. We have also developed an algorithm which makes use of these graph grammars for generating random game level layouts ensuring that the players will get a different gaming experience each time they play.