Picture Gallery (127 different pictures):

Images des Mathématiques (IdM/CNRS)

[Galerie d'images (127 images différentes) : Images des Mathématiques (IdM/CNRS)]

Images des Mathématiques (IdM/CNRS) [Images des Mathématiques (IdM/CNRS)]:

Displayed Pictures [Images exposées]:

Mathematics [Mathématiques]:

The relief -modulus- of the function e1/z with argument mapping.	Tridimensional display of the Riemann Zeta function inside [-50.0,+50.0]x[-50.0,+50.0] (bird's-eye view).	The Goldbach Conjecture -the Goldbach Comet or the Goldbach Rainbow- for the even numbers from 6 to 411678.	The Proth-Gilbreath Conjecture -display of the process for the 1600 prime numbers following 100215...-.	3-foil torus knot on its torus.
5-foil torus knot on its torus.	7-foil torus knot on its torus.	Generation of the 63 first Conway's surreal numbers.	Generation of the 63x63 first Conway's surreal complex numbers.	Causal set obtained by means of an homogeneous random meshing of a cube.
Wavelet transform of a bidimensional fractal field (bird's-eye view).




A Tribute to Patrice Jeener [Hommage à Patrice Jeener]:

The Jeener-Klein bottle loop 1.

The Jeener-Klein bottle loop 2.

The Jeener unilateral node.

The Jeener nautilus.




Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

The first four iterations of the construction of the von Koch snowflake.	The Sierpinski Carpet -iteration 1 to 5-.	The Menger Sponge -iteration 5-.	An amazing cross-section inside the Menger Sponge -iteration 5- with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-.	Bidimensional Hilbert Curve -iterations 1 to 5-.
Tridimensional Hilbert Curve -iterations 1 to 3-.	A Tridimensional Hilbert-like Curve base on an 'open' 3-foil torus knot -iteration 2-.	A sphere described by means of a Bidimensional Hilbert Curve -iteration 7-.	The Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-.	A Ball described by means of a Tridimensional Hilbert Curve -iteration 4-.
Visualization of the Newton's method when computing the roots of Z3=1.	Visualization of the Newton's method when computing the roots of Z5=1.	Along the border of the Mandelbrot set.	Tridimensional visualization of the Mandelbrot set with mapping of the arguments.	Tridimensional visualization of the Mandelbrot set with mapping of the arguments.
Tridimensional visualization of the Mandelbrot set with mapping of the arguments.	Tridimensional visualization of the Mandelbrot set with mapping of the arguments.	Tridimensional visualization of the Mandelbrot set with mapping of the arguments.	A foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis and with a tridimensional non linear transformation in the pseudo-octonionic space -tridimensional cross-section-.	Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a Tribute to Stephen Baxter-.	Close-up on a foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	A foggy pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0) and with a rotation about the Y axis -tridimensional cross-section-.




Non Deterministic Fractal Geometry [Géométrie Fractale Non Déterministe]:

A random tiling of a square domain using dominoes (1x2 rectangles) -line after line- with display of clusters of horizontal and vertical rectangles using the 4-connexity.	Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and its 'external border' -white-.	The 'island-peninsula' phenomenon of the fractal diffusion front in a bidimensional medium obtained by means of a random walk process.	Foggy seaboard.	Foggy island.
Mountains and fog.	Fractal landscape based on a bidimensional brownian motion.	An extended Menger Sponge -iteration 4- displaying the 53.919 first digits -base 2- of 'pi'.	An extended Menger Sponge -iteration 7- displaying the 211.210.335 first digits -base 2- of 'pi'.	Botticelli anomaly on the Moon.




Tilings [Pavages]:

An aperiodic Penrose tiling of the plane.	An aperiodic Penrose tiling of the plane -a Tribute to Piet Mondrian and Roger Penrose-.	The Penrose city.	The level 3 cluster made of 8 'Spectre' level 2 clusters with display of all the key-points making quadrilaterals (8 small and a big one).	A close-up of the 'EinStein' aperiodic 'Spectre' tiling.
A periodical tiling of the plane using 2 von Koch-like snowflakes -iteration 3-.	A periodical tiling of the plane using 3 von Koch-like snowflakes -iteration 3-.	A periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-.	Mapping on a sphere family of a finite subset of a periodical tiling of the plane using 4 von Koch-like snowflakes -iteration 3-.	The 500 first digits of π displayed as an Impossible Structure.




Celestial Mechanics [Mécanique Céleste]:

The journey of an Earth-like planet (green) in the Solar System -point of view of the virtual planet-.




Quantum Mechanics [Mécanique Quantique]:

Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-.

Artistic view of the space-time structure at the Planck scale in the context of the super-string theory.




Miscellaneous [Divers]:

The same bidimensional scalar field displayed with 4 different color palettes.	Two identical grey rectangles in front of a grey scale.	display of π with 1.000 digits -base 10- on an helix -good point of view-.	A tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps.	The Mathematics are the key of the Multiverse.
The Mathematics are the key of the Multiverse.	Periodical impossible structure.	Quadruple impossible staircase built by means of a paradoxal structure -a Tribute to Maurits Cornelis Escher-.

Excluded Pictures [Images exclues]:

Mathematics [Mathématiques]:

The Legendre Conjecture with 0 < n < 201.

The Syracuse Conjecture for U(0)={5,6,7,8,...,132} -'pseudo-ramdom walk' display: 'The Syracuse Pulsar'-.

8 evenly distributed points on a sphere by means of simulated annealing.




Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

Tridimensional fractal cross -iteration 5-.

Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-.

A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.

A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-.




Non Deterministic Fractal Geometry [Géométrie Fractale Non Déterministe]:

Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.




Tilings [Pavages]:




Celestial Mechanics [Mécanique Céleste]:




Quantum Mechanics [Mécanique Quantique]:

Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-.




Miscellaneous [Divers]:

Submitted Pictures [Images soumises]:

Mathematics [Mathématiques]:

Visualization of the Proth-Gilbreath Conjecture process for G(Pi(6.0213x10^27))=1935..	Tridimensional Visualization of the Proth-Gilbreath Conjecture process for G(Pi(1.0025x10^15))=806..	An elementary monodimensional binary cellular automaton -110- with 1 white starting point -bottom right-.	A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of the square root of 2 (414213...) -base 10- with 33.333 time steps.	A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'phi' -the golden ratio- (618033...) -base 10- with 33.333 time steps.
A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'e' (718281...) -base 10- with 33.333 time steps.	A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...) -base 10- with 33.333 time steps.	A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of 'pi' (141592...) with 492 more digits defining a helix -base 10- with 33.497 time steps.	A tridimensional pseudo-random walk -spherical coordinates- defined by means of the 999 first decimals of the Champernowne number (1 2 3 4 5 6 7 8 9 10 11 12...) -base 10- with 333 time steps.	A tridimensional pseudo-random walk -cartesian coordinates- defined by means of the 99.999 first decimals of an arbitrary random number (190496...) -base 10- with 33.333 time steps.




Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

Tridimensional fractal cross -iteration 5-.	An amazing cross-section inside the Menger Sponge -iteration 5-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.
A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A foggy pseudo-octonionic Mandelbrot set (a 'MandelBulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set (a 'MandelBulb') -'children's corner' or 'the consciousness emerging from Mathematics'- -tridimensional cross-section-.	Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-.	A pseudo-octonionic Mandelbrot set -tridimensional cross-section-.
A pseudo-octonionic Mandelbrot set -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-.	The quaternionic Julia set -degree=2- computed -pseudo-addition and pseudo-multiplication in C- with A=(-0.581514...,+0.635888...,0,0) -tridimensional cross-section-.	A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.
A foggy pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) and with a rotation about the X axis -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.	Close-up on a foggy pseudo-quaternionic Mandelbrot set with a 1/O conformal transformation in the octonionic space -tridimensional cross-section-.




Non Deterministic Fractal Geometry [Géométrie Fractale Non Déterministe]:

Tridimensional fractal aggregate obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.	Tridimensional display of the particle trajectories of bidimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to an attractive central field of gravity.	Bidimensional closed self-avoiding brownian motion on an ellipsoide.	Bidimensional closed self-avoiding brownian motion on a torus.	Bidimensional closed self-avoiding brownian motion on the Möbius strip.
Bidimensional closed self-avoiding brownian motion on the Klein bottle.	Bidimensional closed self-avoiding brownian motion on the Boy surface.	Tridimensional fractal surface (bird's-eye view).	Mountains and fog.	Monument Valley at sunrise.
Snowy Monument Valley.




A Tribute to Patrice Jeener [Hommage à Patrice Jeener]:




Tilings [Pavages]:

The level 2 cluster made of 8 'Spectre' level 1 clusters with display of all the key-points making quadrilaterals (8 small and a big one).




Celestial Mechanics [Mécanique Céleste]:




Quantum Mechanics [Mécanique Quantique]:

Tridimensional representation of quadridimensional Calabi-Yau manifolds -Calabi-Yau manifolds attached to every point of a fractal tridimensional space-.




Miscellaneous [Divers]:

display of 'pi' with 100 digits {3.141592...} on an helix -grey-.

My papers -en français/in french- [Mes articles -en français/in french-]:

• 01 - 17/02/2010 - images.math.cnrs.fr/billets/physique-et-nombres-reels/. See the original page: Physique et nombres réels.


• 02 - 28/04/2010 - images.math.cnrs.fr/un-ordinateur-est-il-une-parfaite-machine-a-calculer/. See the original page: Un ordinateur est-il une parfaite machine à calculer?.


• 03 - 24/06/2010 - images.math.cnrs.fr/pseudo-projections-de-surfaces/. See the original page: Pseudo-projections de surfaces.


• 04 - 23/08/2010 - images.math.cnrs.fr/ensembles-fractals-deterministes-n-dimensionnels/. See the original page: Ensembles fractals déterministes n-dimensionnels.


• 05 - 12/09/2010 - images.math.cnrs.fr/quelques-remarques-personnelles-concernant-la-nature-des-mathematiques/. See the original page: Quelques remarques personnelles concernant la nature des Mathématiques.


• 06 - 02/06/2023 - images.math.cnrs.fr/billets/chatgpt-du-mythe-a-la-realite/. See the original pages: ChatGPT 3.5: du mythe à la réalité and ChatGPT 4o, 5 et au-delà: du mythe à la réalité.


• 07 - 07/06/2023 - images.math.cnrs.fr/billets/courbes-remplissantes-et-varietes-bi-et-tridimensionnelles/. See the original page: Courbes remplissantes et variétés bi-et tridimensionnelles.


• 08 - 05/07/2024 - images.math.cnrs.fr/billets/intelligences-artificielles-generatives/. See the original page: Intelligences artificielles génératives et synthèse d'images.


• 09 - 08/11/2024 - images.math.cnrs.fr/billets/de-chatgpt-3-5-a-chatgpt-4o-un-petit-pas-pour-lhomme-un-grand-pas-pour-lhumanite/. See the original pages: De ChatGPT 3.5 à ChatGPT 4o: un petit pas pour l'Homme, un grand pas pour l'Humanité? and De ChatGPT 3.5 à ChatGPT 4o: un petit pas pour l'Homme, un grand pas pour l'Humanité?.


• 10 - 18/11/2024 - images.math.cnrs.fr/billets/celebration-a-lecole-polytechnique-du-centenaire-de-la-naissance-de-benoit-mandelbrot-1924-2010/. See the original page: Exposition: célébration à l'Ecole polytechnique du centenaire de la naissance de Benoît Mandelbrot (1924-2010).


• 11 - 25/03/2025 - images.math.cnrs.fr/billets/de-lirreversibilite-du-temps-numerique/. See the original page: De l'irréversibilité du temps numérique.


• 12 - 05/04/2025 - images.math.cnrs.fr/billets/billard-de-kasner/. See the original page: Billard de Kasner.


• 13 - 12/04/2025 - images.math.cnrs.fr/billets/le-mouvement-brownien/. See the original page: Le mouvement brownien.


• 14 - 19/04/2025 - images.math.cnrs.fr/billets/de-laxiome-des-paralleles-au-gps/. See the original page: De l'axiome des parallèles au GPS.


• 15 - 26/04/2025 - images.math.cnrs.fr/billets/mouvements-relatifs-et-observations-astronomiques/. See the original page: Mouvements relatifs et observations astronomiques.


• 16 - 20/11/2025 - images.math.cnrs.fr/billets/la-conjecture-de-proth-gilbreath/. See the original page: La conjecture de Proth-Gilbreath.


• 17 - 20/07/2026 - images.math.cnrs.fr/billets/de-la-visualisation-des-nombres-reels/. See the original page: De la visualisation des nombres réels.


• 18 - 27/07/2026 - images.math.cnrs.fr/billets/de-la-denombrabilite-des-nombres-algebriques/. See the original page: De la Dénombrabilité des Nombres Algébriques.

Copyright © Jean-François Colonna, 2025-2026.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2025-2026.