Fractal - Wikipedia
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.
What are Fractals? – Fractal Foundation
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.
Fractals | Brilliant Math & Science Wiki
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 ...
How Fractals Work | HowStuffWorks
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.
Fractal | Mathematics, Nature & Art | Britannica
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.
7.4: Fractals - Mathematics LibreTexts
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.
What is a fractal (and what are they good for)? - Khan Academy
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.
Fractals in Math - Definition, Types, & Examples
WEBJan 29, 2024 · 01. What are fractals? 02. Types of fractals: 03. Examples of Fractals. 04. Applications of Fractals. In this article, we’ll explain the definition, types, and applications of fractals. Let’s unravel the mysteries of this topic. What are fractals? Fractal is a pattern that never ends.
Fractal -- from Wolfram MathWorld
WEBApr 25, 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 ...
6.3.1: Fractal Dimension - Mathematics LibreTexts
WEB6.3.2 Learning Objectives. Determine the dimension of a fractal. In addition to visual self-similarity, fractals exhibit other interesting properties. For example, notice that each step of the Sierpinski gasket iteration removes one quarter of the remaining area.
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