منابع مشابه
Developing fractal curves
Many fractal curves can be produced as the limit of a sequence of polygonal curves, where the curves are generated via an iterative process, for example an L-system. One can visualise such a sequences of curves as an animation that steps through the sequence. A small part of the curve at one step of the iteration is close to a corresponding part of the curve at the previous step, and so it is n...
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Taking into account that the frequencies of Fourier expansions are integers it is not surprising that some arithmetical results play an important role in many theorems and examples in harmonic analysis. This relation is even clearer from the historical point of view and Hardy and Littlewood can be considered at the same time as founders of a substantial part of harmonic analysis and analytic nu...
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Fractal curves were generated on square initiators and rated in terms of complexity by eight viewers. The stimuli differed in fractional dimension, recursion, and number of segments in their generators. Across six stimulus sets, recursion accounted for most of the variance in complexity judgments, but among stimuli with the most recursive depth, fractal dimension was a respectable predictor. Si...
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We examine the dimension of the invariant measure for some singular circle homeomorphisms for a variety of rotation numbers, through both the thermodynamic formalism and numerical computation. The maps we consider include those induced by the action of the standard map on an invariant curve at the critical parameter value beyond which the curve is destroyed. Our results indicate that the dimens...
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The aim of our work is to specify and develop a geometric modeler, based on the formalism of iterated function systems with the following objectives: access to a new universe of original, various, aesthetic shapes, modeling of conventional shapes (smooth surfaces, solids) and unconventional shapes (rough surfaces, porous solids) by defining and controlling the relief (surface state) and lacunar...
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ژورنال
عنوان ژورنال: Communications of the Korean Mathematical Society
سال: 2005
ISSN: 1225-1763
DOI: 10.4134/ckms.2005.20.4.827