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The use of alpha channel based textures, with the sphinx hexiamond based tile pat-
tern, and a shader that transformed and re-combined them based on fractal dimension
provided the ability to utilize fractal tile patterns at varying levels of fractal complexi-
ty. This level of complexity can be varied by arranging tiles in differing patterns and
also by subdividing the tiles into greater levels of detail (see Figure 4 for examples).
Fig. 4. Laying tiles using differing methods to achieve differing fractal complexity levels
This implementation provided a practical method, using simple tile based elements,
to algorithmically create surfaces with differing levels of fractal complexity on de-
mand. When combined with the knowledge of aesthetic preference of fractal com-
plexity levels, this provides a means to create new surfaces of both aesthetically
pleasing (D 2.3-2.5), and, perhaps for some game scenarios, aesthetically undesirable
form (eg. 2.5+ for spaces to become more uncomfortable for players).
5
Conclusions and Discussion
Fractal patterns offer an automated mathematical mechanism to create rich patterns.
These rich patterns can be applied in interactive game environments and in many
cases can add a natural feel to the spaces in which they are used. The findings from
this study have identified that differing levels of fractal dimension and complexity in
a surface have a direct affect on the viewers comfort with that surface. Applied to
games design, through the use of texture and bump maps, applied using non-standard
shaders to construct the fractal complexity, this allows the designer to apply an auto-
mated mathematical approach to creating surfaces that can make the viewer more or
less comfortable with the space.
References
1. Mandelbrot, B.B.: The fractal geometry of nature. Macmillan, New York (1983)
2. Mandelbrot, B.B.: Fractals: Form, change and dimension. WH Freemann and Company,
San Francisco (1977)
3. Walsh, P., Prasad, G.: The use of an aesthetic measure for the evolution of fractal land-
scapes. In: 2011 IEEE Congress on Evolutionary Computation (CEC), pp. 1613-1619.
IEEE Press, New York (2011)
4. Fan, N.: Realistic Rendering of Three-Dimensional Ocean Waves Based on Fractal. Ad-
vanced Science Letters 11(1), 469-472 (2012)
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