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.
What are Fractals? - Fractal Foundation
WEBFractals 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.
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.
How Fractals Work - HowStuffWorks
WEBOct 31, 2023 — You can create fractals with mathematical equations and algorithms, but there are also fractals in nature. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex.
Fractals | Brilliant Math & Science Wiki
WEBFractals are fundamental to understanding many chaotic systems, and have many applications in sciences. They are also beautiful and mesmerizing objects, as we have seen with the Mandelbrot and Julia sets. In this section, we collect examples of fractals in all scales in nature.
Fractals in Math - Definition, Types, & Examples
WEBJan 29, 2024 — Fractal is a pattern that never ends. It elaborates mathematical constructs that exhibit self-similarity, meaning they display similar patterns or structures when zoomed in or out. This self-similarity occurs at many levels of magnification, revealing elaborate details that are replicated at every scale.
Fractals – Mathigon
WEBIn mathematics, we call this property self-similarity, and shapes that have it are called fractals. They are some of the most beautiful and most bizarre objects in all of mathematics. To create our own fractals, we have to start with a simple pattern and then repeat it over and over again, at smaller scales.
15.1: Fractals - Mathematics LibreTexts
WEBJul 18, 2022 — Fractals 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.
Fractal -- from Wolfram MathWorld
WEB3 days ago — 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.
Fractal Geometry - Yale University
WEBHere we introduce some basic geometry of fractals, with emphasis on the Iterated Function System (IFS) formalism for generating fractals. In addition, we explore the application of IFS to detect patterns, and also several examples of architectural fractals.
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