Keyword Analysis & Research: fractal


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  • Fractal - Wikipedia

    wikipedia.org

    https://en.wikipedia.org/wiki/Fractal

    WEBIn mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set.

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  • What are Fractals? – Fractal Foundation

    fractalfoundation.org

    https://fractalfoundation.org/resources/what-are-fractals/

    WEBA 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. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos.

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  • Fractals | Brilliant Math & Science Wiki

    brilliant.org

    https://brilliant.org/wiki/fractals/

    WEBWell, a fractal, by definition, is 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 ...

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  • Fractal | Mathematics, Nature & Art | Britannica

    britannica.com

    https://www.britannica.com/science/fractal

    WEBfractal, in mathematics, any of a class of complex geometric shapes that commonly have “fractional dimension,” a concept first introduced by the mathematician Felix Hausdorff in 1918. Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth.

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  • How Fractals Work | HowStuffWorks

    howstuffworks.com

    https://science.howstuffworks.com/math-concepts/fractals.htm

    WEBOct 31, 2023 · At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex. Contents. Background on Fractals. Fractal Terminology. Before They Were Fractals. Math Behind the Beauty. Practical Fractals. How to Make Your Own Fractal. Background on Fractals.

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  • Fractal -- from Wolfram MathWorld

    wolfram.com

    https://mathworld.wolfram.com/Fractal.html

    WEBApr 13, 2024 · Fractal. Download Wolfram Notebook. A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a ...

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  • 7.4: Fractals - Mathematics LibreTexts

    libretexts.org

    https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100%3A_Liberal_Arts_Mathematics_(Saburo_Matsumoto)/07%3A_Mathematics_and_the_Arts/7.04%3A_Fractals

    WEBSep 12, 2020 · Fractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties. We’ll explore what that sentence means through the rest of this section. For now, we can begin with the idea of self-similarity, a characteristic of most fractals.

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  • What is a fractal (and what are they good for)? - Khan Academy

    khanacademy.org

    https://www.khanacademy.org/partner-content/mit-k12/mit-k12-math-and-engineering/mit-math/v/what-is-a-fractal-and-what-are-they-good-for

    WEBWhat is a fractal (and what are they good for)? Google Classroom. About. Transcript. Fractals are complex, never-ending patterns created by repeating mathematical equations. Yuliya, an undergrad in Math at MIT, delves into their mysterious properties and how they can be found in technology and nature. Questions. Tips & Thanks.

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  • Fractals – Mathigon

    mathigon.org

    https://mathigon.org/course/fractals/introduction

    WEBFractal Coastlines. One of the key characteristics of all the fractals we’ve seen so far is that you can “zoom in” forever and always find new patterns. Around 1920, the British mathematician Lewis Fry Richardson realised that the same is true for the border or coastline of many countries.

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  • 15: Fractals - Mathematics LibreTexts

    libretexts.org

    https://math.libretexts.org/Bookshelves/Applied_Mathematics/Math_in_Society_(Lippman)/15%3A_Fractals

    WEBFractals are mathematical sets, usually obtained through recursion, that exhibit interesting dimensional properties. We’ll explore what that sentence means through the rest of the chapter. For now, we can begin with the idea of self-similarity, a characteristic of most fractals. 15.2: Iterated Fractals.

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