Gallery:

Didactical Pictures

[Galerie: Images didactiques]

Didactical Pictures [Images didactiques]:

Didactical Pictures [Images didactiques]:

Mathematics [Mathématiques]:

[More pictures about Mathematics]




An equilateral triangle.

A right-angled triangle.

A demonstration of the Pythagoras' theorem.

A demonstration of the Pythagoras' theorem.

Two sets.

A bijection.

A bijection.

To count the members of a set.

A set 'E'.

Two subsets 'SE1' and 'SE2' of a set 'E'.

Two sets 'SE1' and 'SE2'.

A set 'F' with two elements 'SE1' and 'SE2'.

The 20 first digits {1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6} of 'pi' displayed on an helix -orange-.

The 20 first digits {1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6} of 'pi' displayed on an helix -orange-.

The four first power sets {P(E),P(P(E)),P(P(P(E))),P(P(P(P(E))))} of a one-element set E.

The Continuum Hypothesis (CH).

The Continuum Hypothesis (CH).

Generation of the 63 first Conway's surreal numbers.

Generation of the 63x63 first Conway's surreal complex numbers.

The continuity.

The differentiability.

Definition of a tangent -orange- by means of a secant -red-.

The continuity.

The differentiability.

Definition of a tangent -yellow- by means of a secant -orange-.

The volume of a cube K -U being the unity cube-.

A point.

A 0-cube -a point-.

A 1-cube -a segment-.

A 2-cube -a square-.

A 3-cube -a cube-.

A 4-cube -an hypercube-.

A 0-cube -a point-.	A 1-cube -a segment-.	A 2-cube -a square-.	A 3-cube -a cube-.	A 4-cube -an hypercube-.
A distorded -for the sake of display- 5-cube -an hyperhypercube-.

The Golden Rectangle.

Recursive subdivision of the Golden Rectangle by means of the Golden Ratio -phi-.

The two subdivisions of the 'flat' Golden Triangle.

The 'flat' Golden Triangle.

One of the two subdivisions of the 'flat' Golden Triangle.

One of the two subdivisions of the 'flat' Golden Triangle.

The two subdivisions of the 'sharp' Golden Triangle.

The 'sharp' Golden Triangle.

One of the two subdivisions of the 'sharp' Golden Triangle.

One of the two subdivisions of the 'sharp' Golden Triangle.

Tridimensional representation of our familiar tridimensional space.

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?.

A cylinder -a bidimensional manifold-.

A cylinder -a bidimensional manifold-.

Bidimensional cross-sections of a cylinder.	Bidimensional cross-sections of a cylinder.	Bidimensional cross-sections of the Klein bottle.	Bidimensional cross-sections of the Klein bottle.	Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.
Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle.	Bidimensional cross-sections of the Jeener unilateral node.	Bidimensional cross-sections of the Jeener unilateral node.

To add two numbers.

To multiply two numbers.

The abelian -commutative- group defined on elliptic curves.

Bidimensional localization of a point P its distances to the three vertices of a triangle ABC being known, the four points being coplanar.

Tridimensional localization of a point P its distances to the four vertices of a tetrahedron ABCD being known.







Fractal Geometry [Géométrie Fractale]:

[More pictures about Deterministic Fractal Geometry]
[More pictures about Non Deterministic Fractal Geometry]




The construction process of the von Koch curve -the starting point: a segment-.	The construction process of the von Koch curve -iteration 1: an equilateral triangle-.	The construction process of the von Koch curve -iteration 1: the removing of the base of the equilateral triangle-.	The construction process of the von Koch curve -iteration 2: four equilateral triangles-.	The construction process of the von Koch curve -iteration 2: the removing of the bases of the four equilateral triangles-.
The construction process of the von Koch curve -iteration 3-.	The construction process of the von Koch curve -iteration 3-.	The first two iterations of the construction of the von Koch curve.	The construction of the von Koch curve.	The construction process of the von Koch curve.

The length of the first two iterations of the construction of the von Koch curve.

About the length of the von Koch curve.

About the length of the von Koch curve.

About the length of the von Koch curve.

About the length of the von Koch curve.

The self-similarity of the von Koch curve.

The self-similarity of the von Koch curve displayed by means of a zoom in with a ratio that is equal to 3.

About the fractal dimension with the first two iterations -red and green respectively- of the construction of the von Koch curve.

About the fractal dimension with the first two iterations -red and magenta respectively- of the construction of the von Koch curve.

A perfect bidimensional fractal tree and the self-similarity.

A perfect bidimensional fractal tree and the self-similarity.

The self-similarity of a perfect bidimensional fractal tree.

A random bidimensional fractal tree and the self-similarity.

The self-similarity of a random bidimensional fractal tree.

The Cantor triadic set -iterations 0 to 5-.

The Sierpinski carpet -iteration 1-.	The Sierpinski carpet -iteration 2-.	The Sierpinski carpet -iteration 3-.	The Sierpinski carpet -iteration 4-.	The Sierpinski carpet -iteration 5-.
The construction process of the Sierpinski carpet.

The Menger sponge -iteration 1-.	The Menger sponge -iteration 2-.	The Menger sponge -iteration 3-.	The Menger sponge -iteration 4-.	The Menger sponge -iteration 5-.
The construction process of the Menger sponge.

The Menger sponge -iteration 1-.	The Menger sponge -iteration 2-.	The Menger sponge -iteration 3-.	The Menger sponge -iteration 4-.	The Menger sponge -iteration 5-.
The construction process of the Menger sponge.

Bidimensional Hilbert Curve -iteration 1-.	Bidimensional Hilbert Curve -iteration 2-.	Bidimensional Hilbert Curve -iteration 3-.	Bidimensional Hilbert Curve -iteration 4-.	Bidimensional Hilbert Curve -iteration 5-.
Bidimensional Hilbert Curve -iterations 1 to 5-.

Tridimensional Hilbert Curve -iteration 1-.

Tridimensional Hilbert Curve -iteration 2-.

Tridimensional Hilbert Curve -iteration 3-.

Tridimensional Hilbert Curve -iteration 4-.

Tridimensional Hilbert Curve -iterations 1 to 3-.

The Mandelbrot set.

Iterations in the complex plane.

Iterations in the complex plane: the computation of the Mandelbrot set.

A Douady rabbit -a complex Julia set computed with A=(-0.13,+0.77)- with display of the arguments.

Iterations in the complex plane: the computation of a Julia set.

Along the border of the Mandelbrot set.

The iterative process used to generate bidimensional fractal fields (large mesh).

Fractal diffusion front in a bidimensional medium obtained by means of a random walk process.







Celestial Mechanics [Mécanique Céleste]:

[More pictures about Celestial Mechanics]




The Ptolemaic system -without equant- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-.

The Ptolemaic system -without equant- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend- centered on the Earth -blue sphere-.

The Ptolemaic system with equant -grey circle above the Earth- and with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-.

The Ptolemaic system with equant -grey circle above the Earth- with a small light grey circle -the epicycle- whose center describes a larger dark grey circle -the deferend-.

N-body problem integration (N=2) displaying a perfect Keplerian orbit (an ellipse).

N-body problem integration (N=2) displaying a perfect Keplerian orbit.

display of the inclination of two elliptic trajectories.

N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on circular trajectories.

N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on elliptic trajectories.

The actual relative sizes of the Solar System bodies.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -Sun point of view-.

The non linear transformation of the coordinates in the Solar System.

N-body problem integration (N=10) displaying the actual Solar System during one plutonian year -the Sun point of view-.

Hodographs of 5 of the 9 planets of the Solar System during three plutonian years.

Hodographs -with display of a few velocity vectors- of 5 of the 9 planets of the Solar System during three plutonian years.

The velocity vectors -with a common origin- of the 9 planets of the Solar System during one plutonian year.

From Pluto to the Sun.

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







Astrophysics and Cosmology [Astrophysique et Cosmologie]:






Artistic view of gravitational waves.

Gravitation and space-time curvature.

Gravitation and space-time curvature.







Deterministic Chaos [Chaos Déterministe]:

[More pictures about Deterministic Chaos]
[More pictures about Statistical Mechanics]
[More pictures about Sensitivity to Rounding-Off Errors]




The Lorenz attractor.

Bidimensional visualization of the Verhulst dynamics -(grey,orange,red) display negative Lyapunov exponents, (yellow,green,blue) display positive Lyapunov exponents-.

Tridimensional high resolution visualization of the Verhulst dynamics -'Time Ships', a tribute to Stephen Baxter-.

Bidimensional rectangular billiard with 16 random particles, with collisions and display of their gravity center -white particle-.

Kasner billiard: Time-dependent billiard (from negative curvatures to positive curvature) with one accelerated particle.

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

Expansion of a gas inside a bidimensional circular box with display of velocity histograms.

A perfect bidimensional piston with following initial conditions: still piston, high temperature particles at left and low temperature particles at right, in a bidimensional box submitted to a vertical field of gravity.

Bidimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and its 'external border' -white-.

Tridimensional brownian motion -the colors used (magenta,red,yellow,green,cyan) are an increasing function of the time- and the 'external border' of its bidimensional projection -white-.

Brownian motion of a few heavy slow particles inside a gaz of fast light particles with increasing mass ratio (heavy/light=1,10,100,1000).

The irreversibility of the numerical bidimensional billiard.

N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite) computed on three different computers (the Red one, the Green one and the Blue one: sensitivity to rounding-off errors).

N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite) computed with 2 different optimization options on the same computer (sensitivity to rounding-off errors).







Miscellaneous [Divers]:

[More pictures about Visualization]




Free fall in the vacuum.

The rain (or the snow) is falling.

A childish Sun.

A color palette with an increasing luminance.

From cold to warm colors.

From cold to warm colors.

The same bidimensional scalar field displayed with 4 different color palettes.

The RGB cube and the additive synthesis of colors.

Anaglyphic glasses.

The 'Tapestry' effect applied to a right-angled triangle.

The 'CenterOf' effect applied to a right-angled triangle.

Clockwise.

Anticlockwise -trigonometric-.

Simple chessboard.

Simple chessboard.

Simple chessboard.

Simple chessboard.

CMAP.

Copyright (c) Jean-François Colonna, 2016-2020.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2016-2020.