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| has gloss | (noun) a set of complex numbers that has a highly convoluted fractal boundary when plotted; the set of all points in the complex plane that are bounded under a certain mathematical iteration Mandelbrot set |
| has gloss | eng: In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets. |
| has gloss | eng: The Mandelbrot set, named after Benoît Mandelbrot, is a famous example of a fractal. It begins with this equation: zn+1 = zn2 + c. Starting with z0=0, c is in the Mandelbrot set if the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets. |
| lexicalization | eng: Mandelbrot Set |
| subclass of | (noun) (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite" set |
| Meaning | |
|---|---|
| Arabic | |
| has gloss | ara: مجموعة ماندلبرو Mandelbrot set إحدى الأسكال الكسيرية المشهورة بشكل واسع حتى خارج مجال علماء الرياضيات لتداخلها مع ما يدعى الفن الكسيري حيث تعمد لتقديم صور فنية تتميز بالجمال والتجريدية. ما يميز مجموعة ماندلبرو هو البنية المعقدة التي تقدمها رغم بساطة تعريفها. |
| lexicalization | ara: مجموعة ماندلبرو |
| Catalan | |
| has gloss | cat: En matemàtiques, es defineix el conjunt de Mandelbrot M com el lloc geomètric de connexitat de la família uniparamètrica de polinomis quadràtics \f_c\colon\mathbb C\,\to\,\mathbb C\,\,|\,\,f_c(z)\,:=\,z^2+c\}_c\,\in\,\mathbb C}. És a dir, M és el subconjunt de punts c del pla complex per als quals el conjunt de Julia de f_c és connex. |
| lexicalization | cat: conjunt de Mandelbrot |
| Czech | |
| has gloss | ces: Mandelbrotova množina je jeden z nejznámějších fraktálů. Je definována jako množina komplexních čísel c, pro které \lim_n \rightarrow \infty}|z_n| \neq \infty, kde posloupnost z_0, z_1, z_2, ... je definována rekurzivním předpisem :z_0=0;\qquad z_n+1} = z_n^2 + c\,. Bod c tedy patří do Mandelbrotovy množiny právě tehdy, když uvedená limita neexistuje, nebo je konečná (např. c=0). |
| lexicalization | ces: Mandelbrotova množina |
| German | |
| has gloss | deu: Die Mandelbrot-Menge, im allgemeinen Sprachgebrauch oft auch Apfelmännchen genannt, ist eine fraktal erscheinende Menge, die in der Chaostheorie, und genauer in der komplexen Dynamik, eine bedeutende Rolle spielt. Sie wurde 1980 von Benoît Mandelbrot popularisiert und von Adrien Douady und John Hamal Hubbard in einer Reihe grundlegender mathematischer Arbeiten systematisch untersucht. Die ersten computergrafischen Darstellungen wurden 1978 von Brooks und Matelski vorgestellt. Die mathematischen Grundlagen dafür wurden bereits 1905 von dem französischen Mathematiker Pierre Fatou erarbeitet. Strenggenommen – und im Gegensatz zu häufig zu lesenden Meinungen – ist die Mandelbrot-Menge nicht selbstähnlich: Im Prinzip kann man jedem Ausschnitt des Randes in jeder Vergrößerung bei genügender Auflösung ansehen, von welchem Punkt er stammt. |
| lexicalization | deu: Mandelbrot-Menge |
| lexicalization | deu: Mandelbrotmenge |
| Persian | |
| lexicalization | fas: مجموعه مندلبرو |
| Finnish | |
| has gloss | fin: Mandelbrotin joukko eli Mandelbrotin fraktaali on eräs tunnetuimmista fraktaaleista. Joukko on nimetty puolalais-ranskalaisen matemaatikon Benoît Mandelbrotin mukaan, ja se perustuu kompleksilukufunktioon xn+1 = xn2 + c, jossa x ja c ovat kompleksilukuja. |
| lexicalization | fin: Mandelbrotin joukko |
| French | |
| has gloss | fra: Lensemble de Mandelbrot est une fractale qui est définie comme lensemble des points c du plan complexe pour lesquels la suite récurrente définie par : |
| lexicalization | fra: Ensemble de mandelbrot |
| Galician | |
| has gloss | glg: En Matemática, un conxunto de Mandelbrot é un fractal definido como o conxunto de puntos c no plano complexo para o cal a sucesión definida iterativamente: |
| lexicalization | glg: conxunto de Mandelbrot |
| Serbo-Croatian | |
| has gloss | hbs: Mandelbrotov skup je skup točaka c kompleksne ravnine za koje je Julijin skup (u užem smislu) povezan. Dobio je ime po francusko-američkom Benoîtu Mandelbrotu. |
| lexicalization | hbs: Mandelbrotov skup |
| Hebrew | |
| has gloss | heb: קבוצת מנדלברוט היא קבוצה של מספרים מרוכבים אשר הגבול של ייצוגן הגאומטרי מהווה את אחת הדוגמאות המוכרות ביותר של פרקטלים במתמטיקה. קבוצת מנדלברוט הומצאה על ידי בנואה מנדלברוט בשנת 1979. |
| lexicalization | heb: קבוצת מנדלברוט |
| Croatian | |
| has gloss | hrv: Mandelbrotov skup je skup točaka c kompleksne ravnine za koje je Julijin skup (u užem smislu) povezan. Dobio je ime po francusko-američkom Benoîtu Mandelbrotu. |
| lexicalization | hrv: Mandelbrotov skup |
| Hungarian | |
| has gloss | hun: A matematikában a Mandelbrot-halmaz azon c komplex számokból áll (a „komplex számsík” azon pontjainak mértani helye, halmaza), melyekre az alábbi (komplex szám értékű) x_n} rekurzív sorozat: |
| lexicalization | hun: Mandelbrot-halmaz |
| Icelandic | |
| has gloss | isl: Mandelbrot mengið er stærðfræðilegt mengi sem lýsir brotamynd. Það er skilgreint sem mengi allra punkta c í tvinntölusléttunni þar sem að runan Z_n+1} = Z_n^2 + C fyrir öll Z, C \isin \mathbbC} þar sem að Z_0 = 0 og Z_n hneigist ekki að óendanleika. |
| lexicalization | isl: Mandelbrot mengið |
| Italian | |
| has gloss | ita: Linsieme di Mandelbrot è definito come linsieme dei numeri complessi c\,\! tale per cui non è divergente la successione definita da: :z_n+1} = z_n}^2 + c\,\! con :z_0 = 0\,\!. Linsieme è un frattale e, nonostante la semplicità della definizione, ha una forma non banale. Solo con lavvento del computer è stato possibile visualizzarla. |
| lexicalization | ita: insieme di Mandelbrot |
| lexicalization | ita: Insieme di Mandelbrot |
| Japanese | |
| has gloss | jpn: マンデルブロ集合（まんでるぶろしゅうごう、Mandelbrot set）とは、 複素平面上の集合が作り出すフラクタルである。 定義 |
| lexicalization | jpn: マンデルブロ集合 |
| Korean | |
| has gloss | kor: 만델브로 집합(Mandelbrot set)은 브누아 만델브로가 고안한 프랙탈의 일종이다. |
| lexicalization | kor: 만델브로 집합 |
| Latvian | |
| has gloss | lav: Mandelbrota kopa ir punktu kopa kompleksajā plaknē, kuras robeža ir fraktālis (šo robežu sauc par Mandelbrota līkni). Mandelbrota kopa ir nosaukta par godu franču / amerikāņu matemātiķim Benuā Mandelbrotam. Formāli to definē kā tādu punktu c kopu kompleksajā plaknē, kuriem, iterējot jeb atkārtoti izpildot : z_n+1} = z_n^2 + c \, ar sākuma nosacījumu z0 = 0, iegūtā virkne zn ir ierobežota. Tas nozīmē, ka komplekss skaitlis c pieder Mandelbrota kopai tad, ja eksistē tāds reāls skaitlis r (kas var būt atkarīgs no c), ka virknes zn locekļu absolūtā vērtība nekad nekļūst lielāka par r. |
| lexicalization | lav: Mandelbrota kopa |
| Dutch | |
| has gloss | nld: De Mandelbrotverzameling is een fractal die een belangrijke rol speelt in de chaostheorie. De verzameling is genoemd naar Benoît Mandelbrot, een Pools-Franse wiskundige die de fractal in 1980 voor het eerst met de behulp van een computer onderzocht. De verzameling werd echter al in 1905 onderzocht door Pierre Fatou, een Franse wiskundige die zich specialiseerde in de studie van recursieve vergelijkingen. |
| lexicalization | nld: Mandelbrot-verzameling |
| lexicalization | nld: Mandelbrotverzameling |
| Norwegian | |
| has gloss | nor: Mandelbrotmengden er en fraktal, oppkalt etter den franske matematikeren Benoît Mandelbrot. |
| lexicalization | nor: Mandelbrot-mengden |
| lexicalization | nor: mandelbrotmengden |
| Polish | |
| has gloss | pol: Zbiór Mandelbrota (żuk Mandelbrota) - podzbiór płaszczyzny zespolonej, którego brzeg jest jednym ze sławniejszych fraktali. Nazwa tego obiektu została wprowadzona dla uhonorowania jego odkrywcy, francuskiego matematyka Benoit Mandelbrota. |
| lexicalization | pol: Zbiór Mandelbrota |
| Portuguese | |
| has gloss | por: Em Matemática, conjunto de Mandelbrot é um fractal definido como o conjunto de pontos c no plano complexo para o qual a seqüência (sucessão, em Portugal) definida iterativamente: |
| lexicalization | por: Conjunto de mandelbrot |
| Moldavian | |
| has gloss | ron: Mulţimea lui Mandelbrot este un fractal care a devenit cunoscut în afara matematicii atât pentru estetica sa, cât şi pentru structura complicată, care are la bază o definiţie simplă. Acest lucru se datorează în mare parte eforturilor lui Benoît Mandelbrot şi ale altora de a populariza acest domeniu al matematicii. Mulţimea lui Mandelbrot se defineşte ca fiind mulţimea acelor puncte c din planul complex pentru care aplicând în mod repetat polinomul complex z2 + c (pornind de la z = 0) rezultatul rămâne în interiorul unui disc de rază finită. |
| lexicalization | ron: mulţimea lui Mandelbrot |
| lexicalization | ron: Mulțimea lui Mandelbrot |
| Russian | |
| has gloss | rus: В математике мно́жество Мандельбро́та — это фрактал, определённый как множество точек c\! на комплексной плоскости, для которых итеративная последовательность |
| lexicalization | rus: Множество мандельброта |
| Slovak | |
| has gloss | slk: Mandelbrotova množina (pomenovaná po matematikovi Benoîtovi Mandelbrotovi) je jeden z najznámejších fraktálov. Je definovaná ako množina komplexných čísel c, pre ktoré platí :\lim_n \rightarrow \infty}|z_n| \neq \infty, kde postupnosť z_0, z_1, z_2, ... je definovaná rekurzívnym predpisom :z_0=0;\qquad z_n+1} = z_n^2 + c\,. Bod c teda patrí do Mandelbrotovej množiny práve vtedy, ak uvedená limita neexistuje, alebo je konečná (napr. c = 0). |
| lexicalization | slk: Mandelbrotova množina |
| Castilian | |
| has gloss | spa: El conjunto de Mandelbrot es el más conocido de los conjuntos fractales, y el más estudiado. Se conoce así en honor al científico Benoît Mandelbrot, que investigó sobre él en la década de los setenta del siglo XX. |
| lexicalization | spa: conjunto de Mandelbrot |
| Swedish | |
| has gloss | swe: Mandelbrotmängden är en berömd fraktal uppkallad efter den franske matematikern Benoît B. Mandelbrot. |
| lexicalization | swe: mandelbrotmängden |
| lexicalization | swe: Mandelbrotmängd |
| Telugu | |
| has gloss | tel: మేండెల్బ్రాట్ సెట్ ఒక . గణితములో నే కాకుండా బైట కూడా ఇది చాలా ప్రముఖమైనది. చాలా చిన్న కంప్యూటర్ ప్రోగ్రామ్ తో క్రింద ఇవ్వబడిన కంప్యూటర్ గ్రాఫిక్స్ ను సృష్టించవచ్చును. కొత్త జేమ్స్బాండ్ సినిమా (2006), టైటిల్స్ లో తుపాకీ లోంచి వచ్చే పొగను, కళావరు పేకముక్కల క్రింద మేండల్బ్రాట్ సెట్ క్రింద చూపించడము జరిగింది. |
| lexicalization | tel: మేండెల్బ్రాట్ సెట్ |
| Thai | |
| has gloss | tha: เซตมานดัลบรอ คือ เซตของจุดในระนาบเชิงซ้อนที่เรียงตัวเป็นแฟร็กทัล ในทางคณิตศาสตร์นิยามเซตมานดัลบรอ คือ เซตของค่าจำนวนเชิงซ้อน c ซึ่งให้ทางเดินของ 0 ภายใต้การส่งวนซ้ำของ ฟ้งก์ชันกำลังสอง (quadratic function) z2 + c มีค่าจำกัด |
| lexicalization | tha: เซตมานดัลบรอ |
| Turkish | |
| has gloss | tur: Mandelbrot kümesi, Benoit Mandelbrot'un teorisidir. Matematikte Mandelbrot kümesi, fraktal şekli oluşturan sınırları belirleyen, karmaşık düzlemdeki sayılar kümesidir. Fraktallar doğada, ağaçların yapraklarının diziliminde ve akciğerlerin damarlarının dallanmasında olduğu gibi bir çok alanda doğal olarak bulunur. |
| lexicalization | tur: Mandelbrot kümesi |
| Ukrainian | |
| lexicalization | ukr: Множина Мандельброта |
| Chinese | |
| has gloss | zho: 曼德布洛特集合（Mandelbrot set）是在复平面上组成分形的点的集合。 |
| lexicalization | zho: 曼德勃羅集合 |
| Links | |
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| similar | c/Mandelbrot set (featured picture set) |
| similar | e/Mandelbrot set |
| similar | e/simple/Mandelbrot set |
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