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provide rich visuals, not only in the real natural world but also in the virtual space of
interactive computer games [10], [12]. In particular these mathematical patterns can
often provide more natural appearing shapes and three-dimensional structural forms
[5]. The use of fractal/recursive methods to automatically create complete structural
game environments has been explored in several projects and this offers potential to
address some issues regarding the scale of modern interactive computer games and
the need for increasing numbers of new spaces and environments [3], [13].
As the results from this study indicate, people find objects and surfaces that are too
simple (D values < 2.25) or too complex (D values > 2.75) to be less appealing. By
quantifying this through fractal dimension/complexity, this provided a mechanism
through which spaces could be designed to be more or less appealing. The second
phase of this research involved not simply understanding the nature of aesthetic re-
sponse to fractal dimension, but actively adjusting the fractal dimension for effect.
4.1
Fractal Surface Designs and Complexity in Game Environments
Applying fractal techniques to surfaces that require a more natural feel, and hence the
breakup of the simple linear nature of polygonal and flat textured surfaces, into richer
“self-similar” patterns has been explored in various forms. The most common exam-
ples of this include the use of fractal methods to add noise and natural disturbance to
fog, dust and water patterns [4], [14]. The key focus of these uses is in natural surfac-
es, although the principals have potential in other areas.
The second phase of this project addressed the application of fractal patterns in sur-
faces, but not those used in natural features like water and fog, but instead looked at
the use of fractal surfacing in the built environment. Stepping into the very heart of
the rectilinear world of bricks, tiles and pavers, this research applied the concepts and
knowledge gained in the earlier trials, on fractal complexity, to these built environ-
ment features. The focus of this work was on the use of surfacing techniques in the
form of texture and bump maps applied using a special shading mechanism based
around creating different levels of fractal complexity in the surface.
4.2
Fractal Surface Design and Implementation
To apply the concept of fractal complexity to the design of surfaces a tiling technique
was implemented. The fractal complexity was controlled through the use of tiled tex-
tures based on a simple equilateral triangle. These tiles were different to the normal
rectangular tiles used in texture maps and were instead sphinx hexiamond based tiles
(consisting of six equilateral triangles arranged as in Figure 3). These tiles can be
added together to make larger versions and also recursively subdivided to differing
levels of complexity in a classic fractal self-similar manner.
Fig. 3.
Sphinx hexiamond tiles and laying patterns
