Texture is one of the main visual attributes for describing patterns found in nature. Several
methods of texture analysis have been used as a powerful tool for real applications
involving image analysis and computational vision. However, existing methods can not
successfully discriminate the complexity of texture patterns. Such methods disregard the
possibility of describing image structures through measures such as the fractal dimension.
Measures based on fractality allow a non-integer geometric interpretation that has
applications in areas such as Mathematics, Physics, Biology, etc. In recent years, fractal
analysis has emerged as a promising approach to capturing self-similarities in textures.
Based on the fractal analysis, many successful approaches to texture classification were
proposed. The basic idea of these methods is to use fractal dimension to summarize the
spatial distribution of image patterns. In this paper the algorithm proposed by Shier and
Bourke which uses, in an empirical way, ideas and some procedures of Fractal Geometry,
was analyzed and implemented. Besides the application in the generation of textures for
computer graphics in general, it has been investigated the use of the algorithm in two
special situations: space filling and artistic texture. This algorithm that aims to fill a
specific region using shapes whose distribution obeys a Power Law ruled by the Hurwitz
zeta function, in this way these shapes are inserted ad infinitum. As a final result images
with self-similar textures that resembles the Apollonian fractal (when using circles) are
displayed. As a final product of the monograph it was developed a tool, called Mosaico
Fractal, which is able to fill a two-dimensional region with geometric figures and generate
artistic textures. An important feature of this paper is the interactions between Computer
Science, Mathematics and Art, allowing an interdisciplinary view of the subject.
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