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<dc:subject>Fractals</dc:subject>
<dc:subject>Approximation algorithms</dc:subject>
<dc:subject>Data structures</dc:subject>
<dc:subject>Displays</dc:subject>
<dc:subject>Graphics</dc:subject>
<dc:subject>Particle measurements</dc:subject>
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<dc:title>Rendering algorithms for deterministic fractals</dc:title>
<dc:date>1995</dc:date>
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<dc:title>Makie.jl: Flexible high-performance data visualization for Julia</dc:title>
<dcterms:abstract>Makie.jl is a cross-platform plotting ecosystem for the Julia programming language (Bezanson et al., 2012), which enables researchers to create high-performance, GPU-powered, interactive visualizations, as well as publication-quality vector graphics with one unified interface. The infrastructure based on Observables.jl allows users to express how a visualization depends on multiple parameters and data sources, which can then be updated live, either programmatically, or through sliders, buttons and other GUI elements. A sophisticated layout system makes it easy to assemble complex figures. It is designed to avoid common difficulties when aligning nested subplots of different sizes, or placing colorbars or legends freely without spacing issues. Makie.jl leverages the Julia type system to automatically convert many kinds of input arguments which results in a very flexible API that reduces the need to manually prepare data. Finally, users can extend every step of this pipeline for their custom types through Julia’
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<dcterms:abstract>The computation of the fractal dimension is straightforward using the box-counting method. However, this approach may require very long computation times. If the Julia set is the connected common boundary of two or more basins of attraction, then a recursive version of the box-counting method can be made storage- and time-efficient. The method is also suitable for the computation of the Julia sets. We apply the method to verify a result of D. Ruelle regarding the dimension of Julia sets of R(z)= z2+c for small c∈C, to Newton's method for complex polynomials of degree 3 and to a sequence of Julia sets from the renormalization transformation for hierarchical lattices. We also discuss the computation of Julia sets and their information dimension by the inverse iteration method. In all examples tested we find that the information dimension is less than the fractal dimension.</dcterms:abstract>
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<bib:pages>358-370</bib:pages>
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