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fractal
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Mandelbrot setDuring the late 20th century, Polish mathematician Benoit Mandelbrot helped popularize the fractal that bears his name. The fundamental set contains all complex numbers C such that the iterative equation Zn + 1 = Zn2 + C stays finite for all n starting with Z0 = 0. As shown here, the set of points that remain finite through all iterations is white, with darker colours showing how quickly other values diverge to infinity. The fractal edge between points that remain finite and those that diverge to infinity is extremely complicated, with self-repeating features that can be seen at all scales. Sierpiński gasketPolish mathematician Wacław Sierpiński described the fractal that bears his name in 1915, although the design as an art motif dates at least to 13th-century Italy. Begin with a solid equilateral triangle, and remove the triangle formed by connecting the midpoints of each side. The midpoints of the sides of the resulting three internal triangles are connected to form three new triangles that are then removed to form nine smaller internal triangles. The process of cutting away triangular pieces continues indefinitely, producing a region with a Hausdorf dimension of a bit more than 1.5 (indicating that it is more than a one-dimensional figure but less than a two-dimensional figure).
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fractal: References & Edit History

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Article History

Type Description Contributor Date
Add new Web site: IBM - Fractal geometry. Oct 30, 2026
Add new Web site: Frontiers - Frontiers in Psychology - Aesthetics and Psychological Effects of Fractal Based Design. Apr 12, 2026
Add new Web site: Khan Academy - Koch snowflake fractal. Dec 20, 2025
Add new Web site: UNI ScholarWorks - Introduction to fractal geometry: Definition, concept, and applicationsapplications (PDF). Jan 31, 2025
Add new Web site: Cornell University - Department of Mathematics - An Introduction to Dimension Theory and Fractal Geometry GEOMETRY: Fractal Dimension and Measure. Dec 06, 2024
Add new Web site: The University of Utah - Department of Mathematics - Fractal Geometry and its Applications. Oct 25, 2024
Add new Web site: CORE - The New Role of Fractal Mathematics in Creating Human Friendly (PDF). Aug 15, 2024
Add new Web site: Nature - Emergence of fractal geometries in the evolution of a metabolic enzyme. May 20, 2024
Add new Web site: Academia - Fractals in the Mathematics Classroom: The Case of Infinite Geometric Series (PDF). Jan 05, 2024
Add new Web site: WebMD - What is Pizza Made of? Aug 18, 2023
Add new Web site: California State University - Fractals. Feb 18, 2023
Add new Web site: Mathematics LibreTexts - Fractals. Sep 19, 2022
Added new Web site: Sekino's Fractal Gallery. Jun 19, 2006
Added new Web site: The Geometry Section. Jun 07, 2006
Added new Web site: The Geometry Section. Jun 07, 2006
Article revised. Sep 02, 2004
Article revised. Feb 16, 2001
Article added to new online database. Jul 20, 1998
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