Information Technology Reference
In-Depth Information
2
Fractal Dimension, Complexity and Design
The concept of a fractal pattern being self-similar does not inherently require it to be
either complex or simple. There exists a range of possible levels of fractal complexity
within this mathematical space. For example the 2D fractal dimension (D value)
ranges anywhere between 1.0 and 2.0. A pattern that fills the plane in very simplistic
terms (a low order of roughness/irregularity) has a D value close to 1, and a pattern
that fills the plane with detailed and intricate structure will have a D value close to 2.
From a designers perspective this allows the ability to consider the fractal dimension
as a changeable variable to alter the visual and aesthetic nature of the fractal content
being created. For 3D objects the dimension ranges from 2.0-3.0.
Fig. 1.
Early experimental fractal forms from this project demonstrating natural features
Several research studies have measured the aesthetic preferences of participants
with regard to images with varying levels of fractal complexity, indicating
an average
aesthetic preference for a fractal complexity level in the range of 1.3 to 1.5 [10,11].
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Experimental Study of Fractal Complexity
Earlier studies of fractal dimension and complexity have dealt with mixed imagery
from both nature and digital systems, including variations in shape, color and pattern.
This research sought to reduce the amount of variables in the imagery studied and to
more specifically explore the link between fractal dimension and its aesthetic appeal.
The study included twenty-five participants from a range of cultures ranging in age
from 18 to 52 years.
Each participant was presented with a range of surface options,
these surfaces included a range of digitally created fractal surfaces and objects, each
with differing levels of fractal dimension. Fractal patterns can of course be extremely
complex and involve variations in color, depth, shape and pattern. To keep the expe-
riment to the simple focus of the fractal dimension, the surfaces produced were gener-
ated for their aesthetic neutrality (lack of association to natural or synthetic commonly
recognised form). Each surface was presented in consistent simple neutral color and
the base shape/function used to create the fractal pattern was consistent. The only
varying element was the dimension of fractal complexity in the surface patterns (see
Figure 2 for examples of some surfaces used (different levels of fractal dimension).
