fractal
Sign in to savethumb|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
AI overview
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.
Article
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