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Shape Modeling with Fractals

2014
Fractal phenomena are a source of geometric detail that can be difficult to harness for general purpose shape modeling. We present a method for modeling surfaces by warping a fractal onto a given mesh. The warp is specified by the user as a coarse displacement field and interpolated by triharmonic radial basis functions. Efficient methods for rendering
Tim McGraw, Donald Herring
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Estimating fractal dimension with fractal interpolation function models

IEEE Transactions on Medical Imaging, 1997
Fractal dimension (fd) is a feature which is widely used to characterize medical images. Previously, researchers have shown that fd separates important classes of images and provides distinctive information about texture. We analyze limitations of two principal methods of estimating fd: box-counting (BC) and power spectrum (PS).
Alan I. Penn, Murray H. Loew
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Reservoir Variability and Modeling with Fractals

SPE Annual Technical Conference and Exhibition, 1990
ABSTRACT An important factor in the simulation of reservoir performance is the input reservoir parameters. Layers are often modeled with constant parameters (porosity, permeability, etc.) or with only minor variations. The failure to incorporate appropriate heterogeneity into reservoir performance predictions can be a significant problem.
S.D. Crane, K.M. Tubman
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A fractal model for erythrocyte sedimentation

Biorheology, 1994
The erythrocyte sedimentation test is a useful tool for studying the biophysical properties of red blood cells (RBCs) and the interactions between RBCs and bridging macromolecules in the suspending fluid. In our previous model of erythrocyte sedimentation formulated on the basis of a logistic growth equation of population dynamics (Kuo et al., 1989 ...
C D, Kuo, J J, Bai, S, Chien
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Filtered fractals in signal modeling

1993 IEEE International Symposium on Circuits and Systems, 2002
Filtered versions of fractionally differenced Gaussian noise (FDGN) processes are studied. Fractionally differenced Gaussian noise is a discrete-time equivalent of fractional Brownian motion. Filtered versions of such processes are ideally suited for modeling signals with both short-term and long-term correlation structures.
Mohamed A. Deriche, Ahmed H. Tewfik
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Fractal modelling of turbulent combustion

Combustion Theory and Modelling, 2000
In a previous paper we proposed a new model for turbulent flows, called the fractal model (FM), which is applicable both to RANS and LES formulations. Here, the model is extended to the reactive case with the goal of simulating turbulent flames, both premixed and non-premixed.
GIACOMAZZI E.   +2 more
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INHERENT FEATURES OF FRACTAL SETS AND KEY ATTRIBUTES OF FRACTAL MODELS

Fractals, 2022
The main goal of this work is to develop a robust framework for an exhaustive description of essential properties of a fractal object. For this purpose, the inherent features of fractal sets are scrutinized. The topological, metrological, morphological, and topographical attributes of fractal systems are delineated.
Balankin, Alexander S.   +2 more
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Ultrasonic characterization of fractal models

Proceedings of the IEEE, 1993
Ultrasonic scattering in inhomogeneous fluid media is examined. Of particular interest are those media having a compressibility that varies on a continuum of spatial scales. It is shown that the internal features of such media can be extracted by an analysis of the forward scattered field.
Kavitha Chandra, Charles Thompson
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Fractal model for disordered magnets

Physical Review B, 1988
Experimental results suggest that magnetic domains in disordered magnets have a topological fractal structure. Following Mandelbrot we build up a random fractal with properties consistent with neutron diffraction experiments. We show that the structure factor of the fractal provides all the forms used in the fit of experimental data.
, Gavoille, , Hubsch
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The Fractal Nature of an Ecological Model

Computer Graphics Forum, 1992
AbstractWith the help of computer graphics, the chaotic behaviour of an ecological model in the complex plane has been investigated. Convergence maps that show multi‐fractal characteristics (science) and beautiful patterns (art) are presented.
Wang Bennan, Shi Yin
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