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Images des Mathématiques (IdM/CNRS)

[Galerie d'images présentées (72 images différentes) : Images des Mathématiques (IdM/CNRS)]

Jean-François Colonna
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www.lactamme.polytechnique.fr

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France

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Mathematics [Mathématiques]	A Tribute to Patrice Jeener [Hommage à Patrice Jeener]	Deterministic Fractal Geometry [Géométrie Fractale Déterministe]	Non Deterministic Fractal Geometry [Géométrie Fractale Non Déterministe]	Tilings [Pavages]
Celestial Mechanics [Mécanique Céleste]	Quantum Mechanics [Mécanique Quantique]	Miscellaneous [Divers]

Mathematics [Mathématiques]:

The relief -modulus- of the function e^1/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-.	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-.	Tridimensional representation of a quadridimensional Calabi-Yau manifold described by means of 5x5 Bidimensional Hilbert Curves -iteration 5-.

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]:

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-.

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