## 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.https://**en.wikipedia.org**/wiki/**Fractal**數據來源: Wikipedia## Fractal - Wikipedia

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 spongeWikipedia · CC-BY-SA 許可下的文字## What are Fractals? – Fractal Foundation

- fractal名詞
**fractals**(復數名詞)- 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.更多信息fractal將 fractal 翻譯為找不到翻譯。Powered by Oxford Dictionaries · 必應在線翻譯 ## Fractals | World of Mathematics

## How Fractals Work | HowStuffWorks

## Fractal art - Wikipedia

## Fractals的圖片

bing.com/images## What Is A Fractal (and what are they good for)? - YouTube