Towards realistic modeling and rendering of 3-D escape-time deterministic fractal shapes

Karam, Hussein; Nakajima, M.

doi:10.1109/vsmm.2001.969714

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…In equation (11), the parameter l = k log(2) is constant, therefore complete the proof. Table (2), illustrates the complexity rendering time comparison between our algorithm and other proposed techniques [10,24,22] for some fractal patterns.…”

Section: Resultsmentioning

confidence: 62%

Automatic Generation of 3-D Linear Fractal Shapes with Quadratic Map Basins Animation

Karam

Nakajima

2003

The Journal of the Society for Art and Science

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Quadratic map basins is a method used to generate the images of Julia and Mandelbrot sets and has been applied to visualize the attractors of iterated function systems (IFS). Three dimensional extension of such mapping with animation is an aspiring goal and a challenging task. In this paper an extension algorithm of quadratic map basin for classifying points in the complement of a 3-D linear fractal shapes are discussed. Such extension produces fractal surfaces that exhibit self-similarity and suggest smooth evolution under animation. The proposed technique has fast computations and simple representation whereby a computer can automatically select parameters and generate a large collection of aesthetically appealing 3-D fractal patterns. The simple representation and the speed of computation of our algorithm make 3-D fractal patterns reliable for interactive machine.

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Section: Resultsmentioning

confidence: 62%

Automatic Generation of 3-D Linear Fractal Shapes with Quadratic Map Basins Animation

Karam

Nakajima

2003

The Journal of the Society for Art and Science

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“…The process of building a fractal model is rapid as it is based on recursive algorithms. For instance, an array of 50000 pixels requires less than 8 seconds to be built using the IFS method and rendering algorithms for various FM methods are constantly optimized for productivity (Gröller, 1994;Karam and Nakajima, 2001;Martyn, 2010).…”

Section: Introduction Of a Fractal Classification Of Enps Aggregate Smentioning

confidence: 99%

Improving the prediction of environmental fate of engineered nanomaterials by fractal modelling

Avilov

Lamon

Hristozov

et al. 2017

Environment International

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A critical analysis of the available engineered nanomaterials (ENMs) environmental fate modelling approaches indicates that existing tools do not satisfactorily account for the complexities of nanoscale phenomena. Fractal modelling (FM) can complement existing kinetic fate models by including more accurate interpretations of shape and structure, density and collision efficiency parameters to better describe homo- and heteroaggregation. Pathways to including hierarchical symmetry concepts and a route to establishing a structural classification of nanomaterials based on FM are proposed.

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Towards realistic modeling and rendering of 3-D escape-time deterministic fractal shapes

Cited by 2 publications

References 17 publications

Automatic Generation of 3-D Linear Fractal Shapes with Quadratic Map Basins Animation

Automatic Generation of 3-D Linear Fractal Shapes with Quadratic Map Basins Animation

Improving the prediction of environmental fate of engineered nanomaterials by fractal modelling

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