--- title: "Meaning & Key Takeaway of: I claim that many patterns of Nature are…" description: "\"I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid-a term used in this work to denote all of standard geo..." image: "https://sms4smile.com/quotes/i/281/benoit-mandelbrot-7685_challenges_i-claim-that-many-patterns-of-nature-are_3098550.jpg" --- # I claim that many patterns of Nature are so irregular and… ![“I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid-a term used in this work to denote all of standard geometry-Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us…” quote by Benoit Mandelbrot](https://sms4smile.com/quotes/i/281/benoit-mandelbrot-7685_challenges_i-claim-that-many-patterns-of-nature-are_3098550.jpg) [Download](https://sms4smile.com/quotes/i/281/benoit-mandelbrot-7685_challenges_i-claim-that-many-patterns-of-nature-are_3098550.jpg) [Open image](https://sms4smile.com/quotes/i/281/benoit-mandelbrot-7685_challenges_i-claim-that-many-patterns-of-nature-are_3098550.jpg) > “I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid-a term used in this work to denote all of standard geometry-Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."” [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) ## About This Quote This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation. Natural patterns often defy simple Euclidean geometry, showing irregular, fragmented complexity that requires new mathematical approaches beyond traditional forms. **In simple terms:** Nature’s shapes are irregular and need new math. Key Takeaway Explore non‑Euclidean models for complex natural forms. Themes complexity geometry nature mathematics Mood inquisitive analytical Type scientific mathematical When to use this quote - modeling coastlines - analyzing clouds - designing antennas Key Concepts fractal theory morphology Questions to Reflect On - How can fractal concepts improve your field? - What natural patterns seem “formless” to you? A Different Perspective Traditional geometry may miss crucial details. ★ ★ ★ ★ ★ No ratings yet [Challenges](https://sms4smile.com/quotes/about/challenges/) [Complexity](https://sms4smile.com/quotes/about/complexity/) [Euclid](https://sms4smile.com/quotes/about/euclid/) [Existence](https://sms4smile.com/quotes/about/existence/) [Geometry](https://sms4smile.com/quotes/about/geometry/) [Mathematics](https://sms4smile.com/quotes/about/mathematics/) [Morphology](https://sms4smile.com/quotes/about/morphology/) [Nature](https://sms4smile.com/quotes/about/nature/) [Patterns](https://sms4smile.com/quotes/about/patterns/) [Science](https://sms4smile.com/quotes/about/science/) ## Related quotes > [A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales.](https://sms4smile.com/quotes/benoit-mandelbrot/a-fractal-is-a-mathematical-set-or-concrete-object-that-is-irregular/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the…](https://sms4smile.com/quotes/benoit-mandelbrot/i-conceived-and-developed-a-new-geometry-of-nature-and-implemented/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining…](https://sms4smile.com/quotes/benoit-mandelbrot/one-of-the-high-points-of-my-life-was-when-i-suddenly-realized-that/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [ The existence of these patterns \[fractals\] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the… ](https://sms4smile.com/quotes/benoit-mandelbrot/the-existence-of-these-patterns-fractals-challenges-us-to-study-forms/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [There are patterns in everything, in the whole of Nature, from the way the stars turn in the heavens to the whorl of a…](https://sms4smile.com/quotes/celia-rees/there-are-patterns-in-everything-in-the-whole-of-nature-from-the-way/) [Celia Rees](https://sms4smile.com/quotes/author/celia-rees/) > [ What is striking is these things \[patterns in nature, e.g. fish stripes\] do look like something that has been crafted. We are conditioned to… ](https://sms4smile.com/quotes/philip-ball/what-is-striking-is-these-things-patterns-in-nature-e-g-fish-stripes/) [Philip Ball](https://sms4smile.com/quotes/author/philip-ball/) > [“No very good sense can be given to the idea that the elements of Euclidean geometry may be found in nature because either everything…](https://sms4smile.com/quotes/david-berlinski/no-very-good-sense-can-be-given-to-the-idea-that-the-elements-of/) [David Berlinski](https://sms4smile.com/quotes/author/david-berlinski/) > [“Straight lines evidently belonged only to geometry, not to nature and life.”](https://sms4smile.com/quotes/hermann-hesse/straight-lines-evidently-belonged-only-to-geometry-not-to-nature-and/) [Hermann Hesse](https://sms4smile.com/quotes/author/hermann-hesse/) > [Mathematics is the science of patterns, and nature exploits just about every pattern that there is.](https://sms4smile.com/quotes/ian-stewart/mathematics-is-the-science-of-patterns-and-nature-exploits-just-about/) [Ian Stewart](https://sms4smile.com/quotes/author/ian-stewart/) > [For most of the history of our species we were helpless to understand how nature works. We took every storm, drought, illness and comet…](https://sms4smile.com/quotes/ann-druyan/for-most-of-the-history-of-our-species-we-were-helpless-to-understand/) [Ann Druyan](https://sms4smile.com/quotes/author/ann-druyan/) > [“You must know in what way you are going to use the morphology and syntax to build your 'how”](https://sms4smile.com/quotes/frederick-vanderbuilt/you-must-know-in-what-way-you-are-going-to-use-the-morphology-and/) [Frederick Vanderbuilt](https://sms4smile.com/quotes/author/frederick-vanderbuilt/) > [“The starting point of Darwin 's theory of evolution is precisely the existence of those differences between individual members of a race or species…](https://sms4smile.com/quotes/karl-pearson/the-starting-point-of-darwin-s-theory-of-evolution-is-precisely-the/) [Karl Pearson](https://sms4smile.com/quotes/author/karl-pearson/) > [When I think of organizations, I think of the capabilities an organization has more than its morphology or structure. The ability of an organization…](https://sms4smile.com/quotes/dave-ulrich/when-i-think-of-organizations-i-think-of-the-capabilities-an/) [Dave Ulrich](https://sms4smile.com/quotes/author/dave-ulrich/) > [We are bored in the city, there is no longer any Temple of the Sun. Between the legs of the women walking by, the…](https://sms4smile.com/quotes/ivan-chtcheglov/we-are-bored-in-the-city-there-is-no-longer-any-temple-of-the-sun/) [Ivan Chtcheglov](https://sms4smile.com/quotes/author/ivan-chtcheglov/) > [ We did not purify... We saw some particles but they did not have the morphology \[shape\] typical of retroviruses. They were very different... What… ](https://sms4smile.com/quotes/luc-montagnier/we-did-not-purify-we-saw-some-particles-but-they-did-not-have-the/) [Luc Montagnier](https://sms4smile.com/quotes/author/luc-montagnier/) ## More by Benoit Mandelbrot > [Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities,…](https://sms4smile.com/quotes/benoit-mandelbrot/regular-geometry-the-geometry-of-euclid-is-concerned-with-shapes/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made…](https://sms4smile.com/quotes/benoit-mandelbrot/it-was-astonishing-when-at-one-point-i-got-the-idea-of-how-to-make/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.](https://sms4smile.com/quotes/benoit-mandelbrot/pictures-were-completely-eliminated-from-mathematics-in-particular/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of…](https://sms4smile.com/quotes/benoit-mandelbrot/in-mathematics-and-science-definition-are-simple-but-bare-bones-until/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [One of the high points of my life was when I suddenly realized that this dream I had in my late adolescence of combining…](https://sms4smile.com/quotes/benoit-mandelbrot/one-of-the-high-points-of-my-life-was-when-i-suddenly-realized-that/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and…](https://sms4smile.com/quotes/benoit-mandelbrot/my-life-has-been-extremely-complicated-not-by-choice-at-the-beginning/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may…](https://sms4smile.com/quotes/benoit-mandelbrot/the-extraordinary-fact-is-that-the-first-idea-i-had-which-motivated/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [Most economists, when modeling market behavior, tend to sweep major fluctuations under the rug and assume they are anomalies. What I have found is…](https://sms4smile.com/quotes/benoit-mandelbrot/most-economists-when-modeling-market-behavior-tend-to-sweep-major/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [I don't seek power and do not run around](https://sms4smile.com/quotes/benoit-mandelbrot/i-don-t-seek-power-and-do-not-run-around/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the…](https://sms4smile.com/quotes/benoit-mandelbrot/i-conceived-and-developed-a-new-geometry-of-nature-and-implemented/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by,…](https://sms4smile.com/quotes/benoit-mandelbrot/if-you-look-at-a-shape-like-a-straight-line-what-s-remarkable-is-that/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [When I first began studying prices, it wasn't a topic that mathematicians were working on. Purely by accident, I saw a set of data…](https://sms4smile.com/quotes/benoit-mandelbrot/when-i-first-began-studying-prices-it-wasn-t-a-topic-that/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.](https://sms4smile.com/quotes/benoit-mandelbrot/the-rare-scholars-who-are-nomads-by-choice-are-essential-to-the/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [Science would be ruined if (like sports) it were to put competition above everything else, and if it were to clarify the rules of…](https://sms4smile.com/quotes/benoit-mandelbrot/science-would-be-ruined-if-like-sports-it-were-to-put-competition/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) > [Many painters had a clear idea of what fractals are. Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial…](https://sms4smile.com/quotes/benoit-mandelbrot/many-painters-had-a-clear-idea-of-what-fractals-are-take-a-french/) [Benoit Mandelbrot](https://sms4smile.com/quotes/author/benoit-mandelbrot/) [Explore all 88 Benoit Mandelbrot quotes ](https://sms4smile.com/quotes/author/benoit-mandelbrot/) ## More Challenges quotes > [I know for my wife and I, we always loved the idea of being young parents. 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It can be that hard, and it can take…](https://sms4smile.com/quotes/dragos-bratasanu/doing-the-work-to-transform-your-dreams-into-reality-is-like-walking/) [Dragos Bratasanu](https://sms4smile.com/quotes/author/dragos-bratasanu/) > [I want to be perceived as a guy who played his best in all facets, not just scoring. A guy who loved challenges.](https://sms4smile.com/quotes/michael-jordan/i-want-to-be-perceived-as-a-guy-who-played-his-best-in-all-facets-not/) [Michael Jordan](https://sms4smile.com/quotes/author/michael-jordan/) > [People in great groups have blinders on. Their work is all they see. They value failures as learning opportunities. They are optimistic, not realistic,…](https://sms4smile.com/quotes/warren-g-bennis/people-in-great-groups-have-blinders-on-their-work-is-all-they-see/) [Warren G. Bennis](https://sms4smile.com/quotes/author/warren-g-bennis/) > [If, as I anticipate, a wide array of personal, portable information/communication devices becomes increasingly important and widespread for information-intensive users, it will be a…](https://sms4smile.com/quotes/tom-peters/if-as-i-anticipate-a-wide-array-of-personal-portable-information/) [Tom Peters](https://sms4smile.com/quotes/author/tom-peters/) > [“Two powerful, little words I've learned to use when facing challenges, fears, and doubts— so what? ”](https://sms4smile.com/quotes/richelle-e-goodrich/two-powerful-little-words-i-ve-learned-to-use-when-facing-challenges/) [Richelle E. Goodrich](https://sms4smile.com/quotes/author/richelle-e-goodrich/) > [It's a challenge to work a character's arc into a format in which you only have a very limited amount of time to grow…](https://sms4smile.com/quotes/ginnifer-goodwin/it-s-a-challenge-to-work-a-character-s-arc-into-a-format-in-which-you/) [Ginnifer Goodwin](https://sms4smile.com/quotes/author/ginnifer-goodwin/) > [I personally think if something's not a challenge, there's no point doing it, because you're not gonna learn much.](https://sms4smile.com/quotes/anonymous/i-personally-think-if-something-s-not-a-challenge-there-s-no-point/) [Anonymous](https://sms4smile.com/quotes/author/anonymous/) > [Men want a challenge, but they want a challenge they can win.](https://sms4smile.com/quotes/whitney-gaskell/men-want-a-challenge-but-they-want-a-challenge-they-can-win/) Whitney Gaskell > [Growing up with a parent in the army, I saw firsthand the challenges our service members face when transitioning to new jobs after time…](https://sms4smile.com/quotes/sharice-davids/growing-up-with-a-parent-in-the-army-i-saw-firsthand-the-challenges/) [Sharice Davids](https://sms4smile.com/quotes/author/sharice-davids/) > [Nobody challenges me. I challenge myself.](https://sms4smile.com/quotes/shakuntala-devi/nobody-challenges-me-i-challenge-myself/) [Shakuntala Devi](https://sms4smile.com/quotes/author/shakuntala-devi/) > [Challenging is good, like good conversation, yes? Who wants to have dinner with the same old easy listening music sounding friends all the time?](https://sms4smile.com/quotes/hilton-als/challenging-is-good-like-good-conversation-yes-who-wants-to-have/) [Hilton Als](https://sms4smile.com/quotes/author/hilton-als/) [Browse all 8,851 Challenges quotes ](https://sms4smile.com/quotes/about/challenges/) ```json { "@context": "https://schema.org", "@graph": [ { "@type": "Quotation", "text": "I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid-a term used in this work to denote all of standard geometry-Nature exhibits not simply a higher degree but an altogether different level of complexity ... 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