A Virtual Machine for Exploring Space-Time and Beyond [Une Machine Virtuelle à explorer l'Espace-Temps et au-delà] A Gateway Between Science and Art with 10583 Pictures and Animations [Un Pont entre la Science et l'Art avec 10583 Images et Animations]

Foreword [Avant-Propos]:

Often considered useless, Mathematics, without being always aware of it, are omnipresent in everyday life (LED's, cell phone, digital picture, GPS , Artificial Intelligence,...). But they are above all the Language of Science and Industry and their formidable efficiency in this field is perhaps a revealer of their deep nature. Today, powerfully assisted by computers, they can also be considered, alongside the microscope and the telescope, as a virtual optical instrument which every day unveils new and mysterious aspects of our Universe -including ourselves- and beyond...



Contents of this site [Contenu de ce site]:

The 40 most recent pictures on display (among 10583) on 03/19/2026 [Les 40 Images mises en exposition le plus récemment (parmi 10583) le 19/03/2026]:

+ [Click here to display the 500 most recent pictures on display [Cliquez ici pour accéder aux 500 Images mises en exposition le plus récemment]]

Best Of:

+ [Click here to access more Best Of information [Cliquez ici pour accéder à plus d'informations sur le Best Of]]

Contents of this site [Contenu de ce site]:

01 The Most Interesting Pages [Les pages les plus intéressantes]	02 Picture Galleries [Galeries d'Images]	03 Exhibitions [Expositions]	04 Slide Shows [Diaporamas]	05 Virtual Experimentation [L'Expérimentation Virtuelle]
06 Virtual Space-Time Travel [Le Voyage Virtuel dans l'Espace-Temps]	07 Mathematics [Les Mathématiques]	08 Generative Artificial Intelligences [Les Intelligences Artificielles Génératives]	09 Chaos [Les Chaos]	10 Fractal Geometry [La Géométrie Fractale]
11 Software Engineering [Le Génie Logiciel]	12 Year 2000 Bug [Le Bug de l'An 2000]	13 Picture Synthesis [Synthèse d'Image]	14 Comments, Definitions and more [Commentaires, Définitions et autres sujets]	15 Art and Science [Art et Science]
16 Lectures [Présentations]	17 Miscellaneous [Divers]	18 Thematic Picture Search [Recherche Thématique d'Images]	19 About this Site [A propos de ce Site]	20 The Most Recently Created/Updated Pages [Les pages créées/mises à jour le plus récemment]


(370 main pages inside 20 chapters [370 pages principales regroupées dans 20 chapîtres])





01-The Most Interesting Pages [Les pages les plus intéressantes]:

01.001 A Quoi Servent (et Que Sont) les Mathématiques? Où sont les Mathématiques? Les Mathématiques, de la vie courante à la recherche fondamentale. Les Mathématiques, une fenêtre ouverte sur l'Univers et au-delà.	01.002 Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15 ---------- Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15	01.003 The Y2038 bug ---------- The Y2038 bug	01.004 From Euclid to GPS ---------- From Euclid to GPS	01.005 Quelques Remarques concernant la Nature des Mathématiques
01.006 Universe, Multiverse and Simulation (A few remarks regarding the Multiverse) ---------- Universe, Multiverse and Simulation (A few remarks regarding the Multiverse)	01.007 Some questions regarding the Hugh Everett's Multiverse ---------- Some questions regarding the Hugh Everett's Multiverse	01.008 Mouvements Relatifs et Observations Astronomiques (le géocentrisme revisité)	01.009 Gallery: Numbers and Light (Mathematics as a virtual optical instrument) [Galerie : Les Nombres et la Lumière (Les Mathématiques, un Instrument d'Optique Virtuel)]	01.010 Gallery: Numbers and Light (Mathematics as a virtual optical instrument) -"light" version- [Galerie : Les Nombres et la Lumière (Les Mathématiques, un Instrument d'Optique Virtuel) -version "légère"-]
01.011 Are we alone in the Universe? The Fermi Paradox: Definition, some Solutions,... ---------- Are we alone in the Universe? The Fermi Paradox: Definition, some Solutions,...	01.012 God and the Science ---------- Dieu et la Science	01.013 Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds	01.014 Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds	01.015 About the Countability of the Algebraic Numbers (Polynomials with integer coefficients, Prime Numbers, Rational Numbers and Transcendent Numbers) ---------- About the Countability of the Algebraic Numbers (Polynomials with integer coefficients, Prime Numbers, Rational Numbers and Transcendent Numbers)
01.016 Transcendental Numbers ---------- Transcendental Numbers	01.017 N-Dimensional Deterministic Fractal Sets using Quaternions, Octonions and more (MandelBulb, JuliaBulbs and beyond...) ---------- N-Dimensional Deterministic Fractal Sets using Quaternions, Octonions and more (MandelBulb, JuliaBulbs and beyond...)	01.018 Definition and Animation of Bi- and Tridimensional Manifolds by Means of Pseudo-Projections, Picture Self-Transformations ---------- Definition and Animation of Bi- and Tridimensional Manifolds by Means of Pseudo-Projections, Picture Self-Transformations	01.019 Generation and Animation of Intertwinings, Larsen Effects and more ---------- Generation and Animation of Intertwinings, Larsen Effects and more	01.020 Are Floating Point Computations Reliable? or again Is a Computer a Perfect Computing Machine? ---------- Are Floating Point Computations Reliable? or again Is a Computer a Perfect Computing Machine?
01.021 Arithmétique et Ordinateur	01.022 Is a Computer a Perfect Computing Machine? ---------- Is a Computer a Perfect Computing Machine?	01.023 On the Irreversibility of Digital Time ---------- On the Irreversibility of Digital Time	01.024 From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata ---------- From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata	01.025 Impossible Structures ---------- Impossible Structures
01.026 The Many Names of Chaos	01.027 Software Engineering	01.028 Du Modèle à l'Image: un Parcours semé d'Embûches	01.029 About the digits of 'pi'	01.030 La Fractale Ultime: un Hommage à Benoît Mandelbrot (1924-2010)
01.031 Géométrie fractale et phénomènes naturels ("Dessine-moi un nuage")




02-Picture Galleries [Galeries d'Images]:

02.001 Gallery: The 500 Most Recent Pictures on display on Thursday March 19 2026 [Galerie : Les 500 Images les plus récemment mises en exposition à la date du Jeudi 19 Mars 2026]

02.002 Gallery: Best Of

02.003 Gallery: Deterministic Fractal Geometry [Galerie : Géométrie Fractale Déterministe]	02.004 Gallery: Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Galerie : Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]	02.005 Gallery: Deterministic Chaos [Galerie : Chaos Déterministe]	02.006 Gallery: Sensitivity to Rounding-Off Errors [Galerie : Sensibilité aux Erreurs d'Arrondi]	02.007 Gallery: Statistical Mechanics and Particle Systems [Galerie : Mécanique Statistique et Systèmes de Particules]
02.008 Gallery: Fluid Mechanics [Galerie : Mécanique des Fluides]	02.009 Gallery: Quantum Mechanics [Galerie : Mécanique Quantique]	02.010 Gallery: Celestial Mechanics [Galerie : Mécanique Céleste]	02.011 Gallery: Astrophysics and Cosmology [Galerie : Astrophysique et Cosmologie]	02.012 Gallery: Number Theory and much more (Cellular Automata, Complex Functions, Fractals, Great Conjectures, Hyperbolic Geometry, Knots, Meshings, Tilings, Trees, ...) [Galerie : Théorie des Nombres et beaucoup d'autres sujets (Arbres, Automates Cellulaires, Fractales, Géométrie Hyperbolique, Grandes Conjectures, Maillages, Nœuds, Pavages, ...)]
02.013 Gallery: Pi [Galerie : Pi]	02.014 Gallery: Numbers and Light (Mathematics as a virtual optical instrument) [Galerie : Les Nombres et la Lumière (Les Mathématiques, un Instrument d'Optique Virtuel)]	02.015 Gallery: Numbers and Light (Mathematics as a virtual optical instrument) -"light" version- [Galerie : Les Nombres et la Lumière (Les Mathématiques, un Instrument d'Optique Virtuel) -version "légère"-]	02.016 Gallery: Signal Processing [Galerie : Traitement du Signal]	02.017 Gallery: Texture Synthesis [Galerie : Synthèse de Textures]

02.018 Gallery: Tributes [Galerie : Hommages]

02.019 Gallery: Art and Science [Galerie : Art et Science]

02.020 Gallery: Artistic Creation [Galerie : Création Artistique]

02.021 Gallery: Self-Portraits [Galerie : Auto-Portraits]

02.022 Gallery: Generalities about Visualization [Galerie : Généralités sur la Visualisation]

02.023 Gallery: Didactical Pictures [Galerie : Images didactiques]

02.024 Gallery: Animations [Galerie : Animations]

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03-Exhibitions [Expositions]:

03.001 Exposition: Ecole Polytechnique, 2005 Année Mondiale de la Physique	03.002 Exposition: Ecole Polytechnique, Fête de la Science 09/2013	03.003 Exposition: Ecole Polytechnique, Fête de la Science 10/2015	03.004 Exposition: Ecole Polytechnique, Fête de la Science 10/2018	03.005 Exposition: Ecole Polytechnique, Fête de la Science 10/2019
03.006 Exposition: Ecole Polytechnique, Fête de la Science 10/2025	03.007 Exposition: Opéra de Massy, 12/12/2019-25/01/2020	03.008 Exposition: Mairie du cinquième arrondissement de Paris, 29/01/2020-07/02/2020	03.009 Exposition: Célébration à l'Ecole Polytechnique du centenaire de la naissance de Benoît Mandelbrot (1924-2010)

03.010 Miscellaneous Exhibitions ---------- Exposition Diverses

03.011 Expositions, de 1978 à aujourd'hui

03.012 Images encadrées actuellement disponibles

03.013 Gallery: RCM GALERIE [Galerie : RCM GALERIE]

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04-Slide Shows [Diaporamas]:

04.001 Full set of randomized Slide Shows.

04.002 Full set of randomized Slide Shows: Fractales.

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05-Virtual Experimentation [L'Expérimentation Virtuelle]:

05.001 Foreword ---------- Foreword

05.002 Images du Virtuel

05.003 Comprendre L'Expérimentation Virtuelle jusqu'à ses Limites

05.004 Virtual Experimentation [the place where Art and Science meet together]

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06-Virtual Space-Time Travel [Le Voyage Virtuel dans l'Espace-Temps]:

06.001 S'il-vous-plaît... dessine moi l'infini (d'après Antoine de Saint-Exupéry): Voyages de l'infiniment petit à l'infiniment grand

06.002 From the Infinitely Small to the Infinitely Big

06.003 De l'Infiniment Petit à l'Infiniment Grand (les Mathématiques, un Instrument d'Optique)

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07-Mathematics [Les Mathématiques]:

07.001 Gallery: Number Theory and much more (Cellular Automata, Complex Functions, Fractals, Great Conjectures, Hyperbolic Geometry, Knots, Meshings, Tilings, Trees, ...) [Galerie : Théorie des Nombres et beaucoup d'autres sujets (Arbres, Automates Cellulaires, Fractales, Géométrie Hyperbolique, Grandes Conjectures, Maillages, Nœuds, Pavages, ...)]	07.002 Gallery: Pi [Galerie : Pi]	07.003 Gallery: Numbers and Light [Galerie : Nombres et Lumière]	07.004 Gallery: Numbers and Light (Mathematics as a virtual optical instrument) [Galerie : Les Nombres et la Lumière (Les Mathématiques, un Instrument d'Optique Virtuel)]	07.005 Gallery: Numbers and Light (Mathematics as a virtual optical instrument) -"light" version- [Galerie : Les Nombres et la Lumière (Les Mathématiques, un Instrument d'Optique Virtuel) -version "légère"-]
07.006 S'il-vous-plaît... dessine moi l'infini (d'après Antoine de Saint-Exupéry): Voyages de l'infiniment petit à l'infiniment grand	07.007 S'il-vous-plaît... dessine moi l'infini	07.008 Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15 ---------- Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15

07.009 Quelques Remarques concernant la Nature des Mathématiques

07.010 A Quoi Servent et Que Sont les Mathématiques?

07.011 A Quoi Servent et Que Sont les Mathématiques? (les Mathématiques, une fenêtre ouverte sur l'Univers et au-delà)

07.012 A Quoi Servent (et Que Sont) les Mathématiques? Où sont les Mathématiques? Les Mathématiques, de la vie courante à la recherche fondamentale. Les Mathématiques, une fenêtre ouverte sur l'Univers et au-delà.

07.013 Why do we Need Real Numbers?

07.014 From Euclid to GPS ---------- From Euclid to GPS	07.015 From Parallel Axiom to GPS ---------- From Parallel Axiom to GPS	07.016 God and the Science ---------- Dieu et la Science	07.017 Do Martians Do Mathematics (And Do They Believe in God)? ---------- Do Martians Do Mathematics (And Do They Believe in God)?	07.018 Are we alone in the Universe? The Fermi Paradox: Definition, some Solutions,... ---------- Are we alone in the Universe? The Fermi Paradox: Definition, some Solutions,...
07.019 Universe, Multiverse and Simulation (A few remarks regarding the Multiverse) ---------- Universe, Multiverse and Simulation (A few remarks regarding the Multiverse)	07.020 Some questions regarding the Hugh Everett's Multiverse ---------- Some questions regarding the Hugh Everett's Multiverse	07.021 Occam's razor and Mathematics ---------- Occam's razor and Mathematics

07.022 Hilbert Curves and Infinite Knots ---------- Hilbert Curves and Infinite Knots

07.023 Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds

07.024 Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds

07.025 About the Countability of the Algebraic Numbers (Polynomials with integer coefficients, Prime Numbers, Rational Numbers and Transcendent Numbers) ---------- About the Countability of the Algebraic Numbers (Polynomials with integer coefficients, Prime Numbers, Rational Numbers and Transcendent Numbers)	07.026 Transcendental Numbers ---------- Transcendental Numbers	07.027 About the digits of 'pi'	07.028 The Syracuse Conjecture (the Syracuse sequence for the numbers 1 to 256)	07.029 The Syracuse Conjecture (the parities of the Syracuse sequence for the numbers 1 to 128)
07.030 Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15 ---------- Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15

07.031 From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata ---------- From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata

07.032 Definition and Animation of Bi- and Tridimensional Manifolds by Means of Pseudo-Projections, Picture Self-Transformations ---------- Definition and Animation of Bi- and Tridimensional Manifolds by Means of Pseudo-Projections, Picture Self-Transformations

07.033 The Ulam Spiral and its generalizations ---------- The Ulam Spiral and its generalizations

07.034 Golden Triangles and Plane non Periodical Penrose Tilings ---------- Golden Triangles and Plane non Periodical Penrose Tilings

07.035 Computer, Mathematics and Art	07.036 Mathematics and Art	07.037 Quelques souvenirs personnels à l'occasion du cinquantenaire du CMAP (1974-2014)	07.038 Ordinateur, Mathématiques et Art	07.039 La Fractale Ultime: un Hommage à Benoît Mandelbrot (1924-2010)
07.040 Mathematics and Representations ---------- Mathematics and Representations

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08-Generative Artificial Intelligences [Les Intelligences Artificielles Génératives]:

08.001 Bard/Gemini "experimental" (2023): Myth and Reality ---------- Bard/Gemini "experimental" (2023): Myth and Reality	08.002 ChatGPT 3.5 (2023): Myth and Reality -season 1- ---------- ChatGPT 3.5 (2023): Myth and Reality -season 1-	08.003 Opinions (Pour La Science, 08/07/2023) Les élucubrations mathématiques de ChatGPT	08.004 Droit de réponse	08.005 ChatGPT 4o (2024), ChatGPT 5 (08/2025) and beyond: ---------- ChatGPT 4o (2024), ChatGPT 5 (08/2025) and beyond:
08.006 DeepSeek (2025): Myth and Reality	08.007 Le Chat -version bêta- (2024): Myth and Reality ---------- Le Chat -version bêta- (2024): Myth and Reality	08.008 Peut-on parler intelligemment et calmement de l'Intelligence Artificielle?	08.009 Generative Artificial Intelligences and Pictures Synthesis: The Museum of Babel The Virtual Museum of the 21th Century (A Tribute to a Universal Artist?) ---------- Generative Artificial Intelligences and Pictures Synthesis: The Museum of Babel The Virtual Museum of the 21th Century (A Tribute to a Universal Artist?)	08.010 Slide Show: I A Generatives Images.
08.011 Exposition: Ecole Polytechnique, Fête de la Science 10/2025




09-Chaos [Les Chaos]:

09.001 Gallery: Deterministic Chaos [Galerie : Chaos Déterministe]

09.002 Gallery: Sensitivity to Rounding-Off Errors [Galerie : Sensibilité aux Erreurs d'Arrondi]

09.003 The Many Names of Chaos ---------- The Many Names of Chaos	09.004 Arithmétique et Ordinateur	09.005 Are Floating Point Computations Reliable? or again Is a Computer a Perfect Computing Machine? ---------- Are Floating Point Computations Reliable? or again Is a Computer a Perfect Computing Machine?	09.006 Is a Computer a Perfect Computing Machine? ---------- Is a Computer a Perfect Computing Machine?	09.007 De la Perte de l'Associativité et de la Distributivité ou les Nombres Flottants ne sont pas des Rationnels et encore moins des Réels
09.008 On the Irreversibility of Digital Time ---------- On the Irreversibility of Digital Time

09.009 Mouvements Relatifs et Observations Astronomiques (le géocentrisme revisité)

09.010 Virtual (or Subjective) Chaos ---------- Virtual (or Subjective) Chaos

09.011 The Subjectivity of Computers

09.012 Kepler, Von Neumann and God [More Rounding-off Error Visualizations]

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10-Fractal Geometry [La Géométrie Fractale]:

10.001 Gallery: Deterministic Fractal Geometry [Galerie : Géométrie Fractale Déterministe]

10.002 Gallery: Non Deterministic Fractal Geometry and Natural Phenomenon Synthesis [Galerie : Géométrie Fractale Non Déterministe et Synthèse de Phénomènes Naturels]

10.003 Géométrie fractale et phénomènes naturels ("Dessine-moi un nuage")

10.004 Brève Histoire Illustrée des Fractales

10.005 Géométrie Fractale et Phénomènes Naturels (La Géométrie Fractale: un voyage dans les îles et les nuages)

10.006 Les Fractales ("Dessine-moi un nuage")

10.007 La Fractale Ultime: un Hommage à Benoît Mandelbrot (1924-2010)

10.008 Hilbert Curves and Infinite Knots ---------- Hilbert Curves and Infinite Knots

10.009 Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds

10.010 Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds

10.011 N-Dimensional Deterministic Fractal Sets using Quaternions, Octonions and more (MandelBulb, JuliaBulbs and beyond...) ---------- N-Dimensional Deterministic Fractal Sets using Quaternions, Octonions and more (MandelBulb, JuliaBulbs and beyond...)

10.012 Quelques Remarques concernant le Calcul et la Visualisation des Objets Fractals

10.013 Animation of Fractal Objects

10.014 From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata ---------- From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata

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11-Software Engineering [Le Génie Logiciel]:

11.001 Software Engineering

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12-Year 2000 Bug [Le Bug de l'An 2000]:

12.001 Are you Ready for the Year 2000? [2000: A Data Processing Odyssey]

12.002 The Y2038 bug ---------- The Y2038 bug

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13-Picture Synthesis [Synthèse d'Image]:

13.001 Definition and Animation of Bi- and Tridimensional Manifolds by Means of Pseudo-Projections, Picture Self-Transformations ---------- Definition and Animation of Bi- and Tridimensional Manifolds by Means of Pseudo-Projections, Picture Self-Transformations

13.002 Generation and Animation of Intertwinings, Larsen Effects and more ---------- Generation and Animation of Intertwinings, Larsen Effects and more

13.003 Animation of Fractal Objects

13.004 From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata ---------- From Monodimensional Binary Cellular Automata to Monodimensional "Quasi-Continuous" Cellular Automata, (Random) Perturbations of Cellular Automata

13.005 Are Autostereograms Useful for Computer Graphics and Scientific Visualization?

13.006 Stéréogrammes et Autostéréogrammes

13.007 Tridimensional Dispaly

13.008 Visualizing with Spheres

13.009 The staging of numbers ---------- The staging of numbers

13.010 Impossible Structures ---------- Impossible Structures

13.011 Creativity and Simplicity

13.012 Labyrinths ---------- Labyrinths

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14-Comments, Definitions and more [Commentaires, Définitions et autres sujets]:

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15-Art and Science [Art et Science]:

15.001 Hilbert Curves and Infinite Knots ---------- Hilbert Curves and Infinite Knots

15.002 Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Hilbert and Peano Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds

15.003 Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds ---------- Space filling Curves and Beyond: From Squares and Cubes to Surfaces (bidimensional Manifolds) and tridimensional Manifolds

15.004 Images du Virtuel

15.005 A la Frontière de l'Art et de la Science: la Visualisation Scientifique (l'Exemple de l'Attracteur de Lorenz)

15.006 Art and Science, 1971-1991

15.007 Computer, Mathematics and Art

15.008 Mathematics and Art

15.009 Quelques souvenirs personnels à l'occasion du cinquantenaire du CMAP (1974-2014)

15.010 Ordinateur, Mathématiques et Art

15.011 Guided Tours of Buried Galleries (inside a Computer) ---------- Guided Tours of Buried Galleries (inside a Computer)

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16-Lectures [Présentations]:

16.001 A Quoi Servent (et Que Sont) les Mathématiques? Où sont les Mathématiques? Les Mathématiques, de la vie courante à la recherche fondamentale. Les Mathématiques, une fenêtre ouverte sur l'Univers et au-delà.	16.002 A Quoi Servent et Que Sont les Mathématiques? (les Mathématiques, une fenêtre ouverte sur l'Univers et au-delà)	16.003 Du Modèle à l'Image: un Parcours semé d'Embûches	16.004 Quelques Questions et Remarques sur la Recherche, les Chercheurs et les Ingénieurs	16.005 Pourquoi faut-il faire de la Recherche (en particulier en Mathématiques)?
16.006 Les Nombres et la Lumière	16.007 Quelques souvenirs personnels à l'occasion du cinquantenaire du CMAP (1974-2014)	16.008 De L'Enseignement Assisté par Ordinateur à L'Expérimentation Virtuelle	16.009 Faire des Mathématiques, se poser les bonnes questions	16.010 Faire connaître et faire aimer les Mathématiques
16.011 Les Mathématiques: Langage du grand Livre de la Nature	16.012 Les Fractales ("Dessine-moi un nuage")	16.013 S'il-vous-plaît... dessine moi l'infini (d'après Antoine de Saint-Exupéry): Voyages de l'infiniment petit à l'infiniment grand	16.014 S'il-vous-plaît... dessine moi l'infini

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17-Miscellaneous [Divers]:

17.001 God and the Science ---------- Dieu et la Science	17.002 Universe, Multiverse and Simulation (A few remarks regarding the Multiverse) ---------- Universe, Multiverse and Simulation (A few remarks regarding the Multiverse)	17.003 Some questions regarding the Hugh Everett's Multiverse ---------- Some questions regarding the Hugh Everett's Multiverse	17.004 Are we alone in the Universe? The Fermi Paradox: Definition, some Solutions,... ---------- Are we alone in the Universe? The Fermi Paradox: Definition, some Solutions,...	17.005 Quelques Remarques sur le Cerveau
17.006 Les Apprentis-Dieux (Tout est Information)	17.007 Welcome to Mars ---------- Welcome to Mars

17.008 Mathématiques et Cinématographe

17.009 A Web Server: a New Tool for Scientific Communication?

17.010 About the Backup of the Virtual Patrimony of the Humananity

17.011 Faire connaître et faire aimer les Mathématiques en 2020

17.012 Faire connaître et faire aimer les Mathématiques en 2022

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18-Thematic Picture Search [Recherche Thématique d'Images]:

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19-About this Site [A propos de ce Site]:

19.001 Everything is 'home made' [Tout est 'fait maison']

19.002 Main Topics, Available Pages on this Site and Search [Sujets Principaux, Pages Disponibles sur ce Site et Recherche]

19.003 The private Librairies and most of the Programs

19.004 Whole Visual Picture Catalog (alphabetical order)

19.005 About this Site and Whole Contents of Available Items

19.006 Whole Visual Picture Catalog (chronological order)

19.007 Downloading [Téléchargement]

19.008 Visitor Log (CMAP Site)

19.009 Web Mail [Courrier Électronique]

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20-The Most Recently Created/Updated Pages [Les pages créées/mises à jour le plus récemment]:

20.1-The Most Recently Created Pages [Les pages créées le plus récemment]:

20.1.001 The Brownian Motion ---------- The Brownian Motion	20.1.002 From Euclid to GPS ---------- From Euclid to GPS	20.1.003 From Parallel Axiom to GPS ---------- From Parallel Axiom to GPS	20.1.004 Exposition: Ecole Polytechnique, Fête de la Science 10/2025	20.1.005 Welcome to Mars ---------- Welcome to Mars
20.1.006 Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15 ---------- Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15	20.1.007 Opinions (Pour La Science, 08/07/2023) Les élucubrations mathématiques de ChatGPT	20.1.008 Droit de réponse	20.1.009 Peut-on parler intelligemment et calmement de l'Intelligence Artificielle?	20.1.010 The Y2038 bug ---------- The Y2038 bug




20.2-The Most Recently Updated Pages [Les pages mises à jour le plus récemment]:

20.2.001 Are you Ready for the Year 2000? [2000: A Data Processing Odyssey] ---------- Are you Ready for the Year 2000? [2000: A Data Processing Odyssey]	20.2.002 The Y2038 bug ---------- The Y2038 bug	20.2.003 Bard/Gemini "experimental" (2023): Myth and Reality	20.2.004 ChatGPT 3.5 (2023): Myth and Reality -season 1-	20.2.005 ChatGPT 4o (2024), ChatGPT 5 (08/2025) and beyond:
20.2.006 DeepSeek (2025): Myth and Reality	20.2.007 Le Chat -version bêta- (2024): Myth and Reality	20.2.008 S'il-vous-plaît... dessine moi l'infini	20.2.009 Peut-on parler intelligemment et calmement de l'Intelligence Artificielle?	20.2.010 Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15 ---------- Proth-Gilbreath Conjecture Beat the Andrew Odlyzko Record G(Pi(1013))=635 (1993) G(Pi(1014))=693 on 10/05/2025 at 20:59:18 G(Pi(2.8000*1014))=788 on 11/08/2025 at 17:46:01 G(Pi(6.1500*1014))=800 on 12/13/2025 at 17:24:56 G(Pi(1015))=800 on 01/23/2026 at 18:41:08 G(Pi(1.0025*1015))=806 on 01/24/2026 at 00:51:08 G(Pi(1.2075*1015))=809 on 02/15/2026 at 02:58:42 G(Pi(1.2125*1015))=811 on 02/15/2026 at 21:50:58 Verification up to 1.5x10^15

Copyright © Jean-François COLONNA, 1994-2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 1994-2026.