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Fractal Complexity in Built and Game Environments
Daniel Della-Bosca, Dale Patterson, and Sean Costain
Griffith University, Gold Coast, Australia
{d.della-bosca,d.patterson,s.costain}@griffith.edu.au
Abstract.
Fractal patterns provide an automated mathematical method to create
rich and engaging visuals. These methods have been applied in the design of
physical and game spaces to only a limited extent. The current physical and vir-
tual game worlds are dominated by rectangles, squares and linear concepts. This
research studied the nature of fractal patterns and in particular the use of differ-
ing levels of fractal complexity to design physical and virtual environments.
The findings from the randomized trial identified differing levels of fractal
complexity and their aesthetic appeal to participants. These levels of fractal
complexity were then applied to spatial environments in games to create spaces
that were more or less appealing to the participant. The principle of using
fractal complexity as a design tool to make an environment more or less com-
fortable provided game and architectural designers an additional mechanism to
enhance spaces and levels of participant engagement.
Keywords:
fractal, surface, complexity, built environment, computer game.
1
Introduction
The world of computer games and their interactive environments is one filled with a
mixture of differing spatial locations. Much like the real world, each virtual location
features structural elements, both man made and natural. Every location and surface is
created geometrically and carefully designed to provide players with a particular visu-
al, ideally immersive, experience. The repetitive process, at heart of fractal mathemat-
ics, generates engaging, often uncannily natural patterns, images and objects [1,2,3].
The potential to use this fractal technique to enhance the surface textures and bump
maps in game spaces was the key focus of this project.
In aesthetic terms, 'An object is said to be self-similar if it looks "roughly" the
same at any scale' [1,2], an image is called fractal if it displays self-similarity, that is,
it can be broken into parts, each of which is (approximately) a reduced size copy of
the whole. The father of fractals, Benoit Mandelbrot, summarized his career as the
'ardent pursuit of the concept of roughness.' [1]. It is this “roughness” that creates the
link to natural surfaces, spaces and objects, where fractal patterns are comparatively
common [1], [3], [4], [5]. Analysis of architectural design also identifies fractal “cas-
cade of details” in many iconic structures such as the Sydney Opera House, Taj Mahal
and others, all applying fractal systems to positive impact [6,7,8].
Games design procedural techniques, including fractal systems have been used for
content generation to good effect [3],[4],[9]. Aesthetics are less clearly understood.
