FRACTAL MAP GENERATORS: DEEP STRUCTURES FOR MULTI-SCALE TILE MAPS

Abstract

The evolution from flat square-tile games to flat hex-tile games was an enormous step forward for computer gaming. Transitioning to flat maps with hierarchical hidden structure and/or to deep maps with multi-scalar surface characteristics could be equally significant. Fractal map generators provide a procedural way to produce both. This paper presents the key algorithms for the challenging problem of neighbor-finding in hierarchical coordinate systems. Code and examples are provided in a sequence of increasing difficulty, for Fractal Map Generators with branching-factors (aperture) of 2, 3, 4, 9, and 7 (in that order). This project demonstrates that the rotational drift for fractal hexagonal tiling at aperture seven is 1/3 radians (~ 19.09859 degrees). High resolution fractal hex maps can be generated from low resolution hand-crafted maps, allowing for the combination of recognizable features at the macro scale, and re-playability on the micro scale. Potential multi-scalar game play is built into a single tree data structure. High-interest areas can be represented in unlimited detail, while low-interest areas stay at a lower level of detail, minimizing computational demands. When applied at the interaction level, multi-scalar tiles may improve the UX by enhancing focus on areas of higher relative importance.

Key Words Fractal Map, Map Generator, Iterated Function System, Region-of-Interest (ROI) rendering, foveation, multi-resolution tiling, multi-scale FEM, replayability, GIS and games, quadtree, bi-tree, tri-tree, nine-tree, hex-tree, Level-of-Detail (LOD) Management