This special issue aims to highlight recent research, development and applications of fractals and fractal-based methods. Fractal-based techniques lie at the heart of multiscale modelling, as fractals are inherently multiscale objects. Fractals have increasingly become a useful tool in real-world applications; they very often describe such phenomena better than traditional mathematical models.
Fractal-based methods attempt to discover and exploit inter-scale relationships for modeling, prediction and control of phenomena. Fractal-based image compression was popularized by Barnsley, but research in imaging has moved beyond compression to other types of image processing (denoising, edge detection, deblurring, watermarking, information hiding, etc.) and to the broader notion of multiscale image analysis. Fractal-based methods have also been used to solve a wide variety of inverse problems arising in models described by systems of differential equations in both deterministic and stochastic settings.
Papers relevant to the scope of the special issue should include, but are not limited to, the following areas:
- Analysis on fractals
- Fractals, V-variable fractals, superfractals and self-similar objects
- Fractal geometry
- Fractal-based image analysis
- Inverse problems using fractal-based analysis
- Applications to biology, economics, engineering, finance, physics
Manuscript submission: 30 August, 2011
Notification of acceptance: 31 October, 2011
Revised final manuscript submission: 15 December, 2011
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