# 1. ## Fractal

In mathematics, a fractal is a subset of a Euclidean space for which the fractal dimension strictly exceeds the topological dimension. Fractals appear the same at different levels, as illustrated in successive magnifications of the Mandelbrot set; because of this, fractals are encountered ubiquitously in nature. Fractals exhibit similar patterns at increasingly small scales called self similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, it is called affine self-similar. Fractal geometry lies within the mathematical branch of topology.

## Fractal - Wikipedia

https://en.wikipedia.org/wiki/Fractal
2. ## Fractal - Wikipedia

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Images of fractals can be created by fractal generating programs. Because of the butterfly effect, a small change in a single variable can have an unpredictable outcome.
? Iterated function systems (IFS) – use fixed geometric replacement rules; may be stochastic or deterministic; e.g., Koch snowflake, Cantor set, Haferman carpet, Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-square, Menger sponge

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3. ## What are Fractals? – Fractal Foundation

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A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop.

4. fractal
名詞
fractals (復數名詞)
1. a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.
起源
1970s: from French, from Latinfract-‘broken’, from the verb frangere.
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5. ## Fractals | World of Mathematics

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Fractals are some of the most beautiful and most bizarre geometric shapes. They look the same at various different scales – you can take a small extract of the shape and it looks the same as the entire shape. This curious property is called self-similarity.To create a fractal, you can start with a simple pattern and repeat it at smaller scales, again and again, forever. In real life, of course, it is impossible to …
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6. ## How Fractals Work | HowStuffWorks

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Fractals are a paradox. Amazingly simple, yet infinitely complex. New, but older than dirt. What are fractals? Where did they come from? Why should I care? Unconventional 20th century mathematician Benoit Mandelbrot created the term fractal from …

7. ## Fractal art - Wikipedia

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Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media.Fractal art developed from the mid-1980s onwards. It is a genre of computer art and digital art which are part of new media art.The mathematical beauty of fractals lies at the intersection of generative art and computer art.

8. ## Fractals的圖片

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9. ## What Is A Fractal (and what are they good for)? - YouTube

Jun 11, 2015 · Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, a undergrad in Math at MIT, delves into their mysterious properties and how they can be found in ...

• 作者: MITK12Videos
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• ## Fractals at Amazon

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