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fractal
Sign in to saveAlso known as fractals, fractal set, fractal sets
thumb|Sierpiński carpet|Sierpiński Carpet - Infinite perimeter and zero area thumb|Highly magnified area on the boundary of the Mandelbrot set thumb|The Mandelbrot set: its boundary is a fractal curve with [[Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)|200x200px]] thumb|Mandelbrot set with 12 encirclements
A fractal is a geometric shape that displays the same patterns when viewed at different levels of magnification, such as the infinitely complex boundary of the Mandelbrot set or the Sierpiński carpet. Fractals matter because they appear throughout nature and mathematics, helping us understand and describe complex patterns that traditional geometry cannot easily explain.
AI-generated from the Wikipedia summary — may contain errors.
Research
17,170 papers- Fractal Analysis in Clinical Neurosciences: An Overview.ReviewAdvances in neurobiology · 2024Di Ieva ADOI: 10.1007/978-3-031-47606-8_13
- Fractal Analysis in MATLAB: A Tutorial for Neuroscientists.ReviewAdvances in neurobiology · 2024Ruiz de Miras JDOI: 10.1007/978-3-031-47606-8_41
- Fractal Time Series: Background, Estimation Methods, and Performances.ReviewAdvances in neurobiology · 2024Porcaro C, Moaveninejad S, D'Onofrio V et al.DOI: 10.1007/978-3-031-47606-8_5
- Fractal Dimension Analysis in Neurological Disorders: An Overview.ReviewAdvances in neurobiology · 2024Díaz Beltrán L, Madan CR, Finke C et al.DOI: 10.1007/978-3-031-47606-8_16
- The Fractal Viewpoint of Tumors and Nanoparticles.ReviewCurrent medicinal chemistry · 2023Alexiou A, Tsagkaris C, Chatzichronis S et al.DOI: 10.2174/0929867329666220801152347
- Fractal Neurodynamics.Advances in neurobiology · 2024Armonaite K, Conti L, Tecchio FDOI: 10.1007/978-3-031-47606-8_33
- The fractal brain: scale-invariance in structure and dynamics.ReviewCerebral cortex (New York, N.Y. : 1991) · 2023Grosu GF, Hopp AV, Moca VV et al.DOI: 10.1093/cercor/bhac363
- Fractal nature of human gastrointestinal system: Exploring a new era.ReviewWorld journal of gastroenterology · 2023Grizzi F, Spadaccini M, Chiriva-Internati M et al.DOI: 10.3748/wjg.v29.i25.4036
via PubMed
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Encyclopedic overview
17 sectionsContents
- Etymology
- Introduction
- History
- Definition and characteristics
- Common techniques for generating fractals
- Applications
- Simulated fractals
- Natural phenomena with fractal features
- Fractals in cell biology
- In creative works
- Physiological responses: Fractal Fluency
- Applications in technology
- See also
- Notes
- References
- Further reading
- External links
thumb|Sierpiński carpet|Sierpiński Carpet - Infinite perimeter and zero area thumb|Highly magnified area on the boundary of the Mandelbrot set thumb|The Mandelbrot set: its boundary is a fractal curve with [[Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)|200x200px]] thumb|Mandelbrot set with 12 encirclements
thumb|Zooming into the boundary of the Mandelbrot set|200x200px
Excerpted from Wikipedia’s “fractal” article, available under the CC BY-SA 4.0 licence.
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