1,576 research outputs found
Generation of 3D Fractal Images for Mandelbrot and Julia Sets
Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of self-similarity, scale invariance, and dimensionality. Images such as coastlines, terrains, cloud mountains, and most interestingly, random shapes composed of curves, sets of curves, etc. present a multivaried spectrum of fractals usage in domains ranging from multi-coloured, multi-patterned fractal landscapes of natural geographic entities, image compression to even modelling of molecular ecosystems. Fractal geometry provides a basis for modelling the infinite detail found in nature. Fractals contain their scale down, rotate and skew replicas embedded in them. Many different types of fractals have come into limelight since their origin. This paper explains the generation of two famous types of fractals, namely the Mandelbrot Set and Julia Set, the3D rendering of which gives a real-world look and feel in the world of fractal images
Visualising Volumetric Fractals
Fractal images have for many years been a richsource of exploration by those in computer science who also havean interest in graphics. They often served as a way of testing theperformance of new computing hardware and to explore thecapabilities of emerging display technologies. While there havebeen forays by some into 3D geometric fractals, the 3Dequivalents of the Mandelbrot set have been largely ignored. Thisis largely due to the lack of suitable tools for rendering these setsexcept perhaps as isosurfaces, a rather unsatisfactory and limitedrepresentation. The following will illustrate the application ofGPU based raycasting, a now relatively standard approach tovolume rendering, to the representation of volumetric fractals.Leveraging existing software that has been designed for generalvolume visualisation allows the interested 3D fractal explorer tofocus on the mathematical generation of the volume data ratherthan reinventing the entire volume rendering pipeline
Texture descriptor combining fractal dimension and artificial crawlers
Texture is an important visual attribute used to describe images. There are
many methods available for texture analysis. However, they do not capture the
details richness of the image surface. In this paper, we propose a new method
to describe textures using the artificial crawler model. This model assumes
that each agent can interact with the environment and each other. Since this
swarm system alone does not achieve a good discrimination, we developed a new
method to increase the discriminatory power of artificial crawlers, together
with the fractal dimension theory. Here, we estimated the fractal dimension by
the Bouligand-Minkowski method due to its precision in quantifying structural
properties of images. We validate our method on two texture datasets and the
experimental results reveal that our method leads to highly discriminative
textural features. The results indicate that our method can be used in
different texture applications.Comment: 12 pages 9 figures. Paper in press: Physica A: Statistical Mechanics
and its Application
Fractal-based autonomous partial discharge pattern recognition method for MV motors
On-line partial discharge (PD) monitoring is being increasingly adopted to improve the asset management and maintenance of medium-voltage (MV) motors. This study presents a novel method for autonomous analysis and classification of motor PD patterns in situations where a phase-reference voltage waveform is not available. The main contributions include a polar PD (PPD) pattern and a fractal theory-based autonomous PD recognition method. PPD pattern that is applied to convert the traditional phase-resolved PD pattern into a circular form addresses the lack of phase information in on-line PD monitoring system. The fractal theory is then presented in detail to address the task of discrimination of 6 kinds of single source and 15 kinds of multi-source PD patterns related to motors, as outlined in IEC 60034. The classification of known and unknown defects is calculated by a method known as centre score. Validation of the proposed method is demonstrated using data from laboratory experiments on three typical PD geometries. This study also discusses the application of the proposed techniques with 24 sets of on-site PD measurement data from 4 motors in 2 nuclear power stations. The results show that the proposed method performs effectively in recognising not only the single-source PD but also multi-source PDs
The Inverse Iteration Method for Julia Sets in the 3-Dimensional Space
In this article, we introduce the adapted inverse iteration method to
generate bicomplex Julia sets associated to the polynomial map . The
result is based on a full characterization of bicomplex Julia sets as the
boundary of a particular bicomplex cartesian set and the study of the fixed
points of . The inverse iteration method is used in particular to
generate and display in the usual 3-dimensional space bicomplex Julia sets that
are dendrites.Comment: 16 pages, 4 figure
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