fractals – Quanta Magazine https://www.quantamagazine.org Illuminating science Mon, 16 Sep 2024 14:10:47 -0400 en-US hourly 1 https://wordpress.org/?v=6.2 Number of Distances Separating Points Has a New Bound https://www.quantamagazine.org/number-of-distances-separating-points-has-a-new-bound-20240409/ https://www.quantamagazine.org/number-of-distances-separating-points-has-a-new-bound-20240409/#respond Tue, 09 Apr 2024 15:28:12 +0000 https://www.quantamagazine.org/?p=136956 The post Number of Distances Separating Points Has a New Bound first appeared on Quanta Magazine

]]> Scatter three points in a plane, then measure the distances between every pair of them. In all likelihood, you’ll find three different distances. But if you arrange the points in an equilateral triangle, then every distance is the same. In a plane, this is impossible to do with four points. The smallest number of distances you can engineer is 2 — the edges and diagonals of a square.

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]]> https://www.quantamagazine.org/number-of-distances-separating-points-has-a-new-bound-20240409/feed/ 0 ‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules https://www.quantamagazine.org/entropy-bagels-and-other-complex-structures-emerge-from-simple-rules-20240227/ https://www.quantamagazine.org/entropy-bagels-and-other-complex-structures-emerge-from-simple-rules-20240227/#respond Tue, 27 Feb 2024 15:49:38 +0000 https://www.quantamagazine.org/?p=135768 The post ‘Entropy Bagels’ and Other Complex Structures Emerge From Simple Rules first appeared on Quanta Magazine

]]> Repetition doesn’t always have to be humdrum. In mathematics, it is a powerful force, capable of generating bewildering complexity. Even after decades of study, mathematicians find themselves unable to answer questions about the repeated execution of very simple rules — the most basic “dynamical systems.” But in trying to do so, they have uncovered deep connections between those rules and other...

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]]> https://www.quantamagazine.org/entropy-bagels-and-other-complex-structures-emerge-from-simple-rules-20240227/feed/ 0 The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/ https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/#respond Fri, 26 Jan 2024 16:46:49 +0000 https://www.quantamagazine.org/?p=134276 The post The Quest to Decode the Mandelbrot Set, Math’s Famed Fractal first appeared on Quanta Magazine

]]> In the mid-1980s, like Walkman cassette players and tie-dyed shirts, the buglike silhouette of the Mandelbrot set was everywhere. Students plastered it to dorm room walls around the world. Mathematicians received hundreds of letters, eager requests for printouts of the set. (In response, some of them produced catalogs, complete with price lists; others compiled its most striking features into...

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]]> https://www.quantamagazine.org/the-quest-to-decode-the-mandelbrot-set-maths-famed-fractal-20240126/feed/ 0 Mathematicians Cross the Line to Get to the Point https://www.quantamagazine.org/mathematicians-cross-the-line-to-get-to-the-point-20230925/ https://www.quantamagazine.org/mathematicians-cross-the-line-to-get-to-the-point-20230925/#respond Mon, 25 Sep 2023 14:05:13 +0000 https://www.quantamagazine.org/?p=130590 The post Mathematicians Cross the Line to Get to the Point first appeared on Quanta Magazine

]]> Imagine an endless piece of blank paper covered with a smattering of lines pointing every which way. A gust of wind comes and sprinkles dust on top of the paper — in effect covering the lines with points. Say a helpful mathematician tells you how much dust covers any one line. Based on that one piece of information, can you figure out how much dust is there in total? While there isn’t enough...

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]]> https://www.quantamagazine.org/mathematicians-cross-the-line-to-get-to-the-point-20230925/feed/ 0 New Proof Threads the Needle on a Sticky Geometry Problem https://www.quantamagazine.org/new-proof-threads-the-needle-on-a-sticky-geometry-problem-20230711/ https://www.quantamagazine.org/new-proof-threads-the-needle-on-a-sticky-geometry-problem-20230711/#respond Tue, 11 Jul 2023 14:44:31 +0000 https://www.quantamagazine.org/?p=127713 The post New Proof Threads the Needle on a Sticky Geometry Problem first appeared on Quanta Magazine

]]> In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an infinitely thin, inch-long needle on a flat surface, then rotate it so that it points in every direction in turn. What’s the smallest area the needle can sweep out? If you simply spin it around its center, you’ll get a circle. But it’s possible to move the needle...

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