Gallery (119 different pictures):

Animations

[Galerie (119 images différentes) : Animations]

Animations [Animations]:

Animations [Animations]:

Deterministic Fractal Geometry [Géométrie Fractale Déterministe]:

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

The construction of the bidimensional Hilbert Curve -iteration 3-.

The construction of the bidimensional Hilbert Curve -iteration 4-.

The construction of the tridimensional Hilbert Curve -iteration 3-.

The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-.

The construction of a tridimensional Hilbert-like Curve defined with {X3(...),Y3(...),Z3(...)} and based on an 'open' 3-foil torus knot -iteration 3-.

The construction of the Klein bottle described by means of a Bidimensional Hilbert Curve -iteration 7-.

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

Bidimensional zoom in on the Mandelbrot set with display of the arguments.

Bidimensional zoom in on the Mandelbrot set with display of the arguments.

Bidimensional zoom in on the Mandelbrot set with display of the arguments.

Bidimensional zoom in on the Mandelbrot set.

Bidimensional zoom in on the Mandelbrot set.

Tridimensional zoom in on the Mandelbrot set.

A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.

A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments.

Along the border of the Mandelbrot set.

Quaternionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-.	Pi/2 rotation about the X axis of a pseudo-quaternionic Julia set ('MandelBulb' like: a 'JuliaBulb') -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 0 to pi rotation about the X axis -tridimensional cross-section-.	Pseudo-octonionic Julia sets along the border of the Mandelbrot set -tridimensional cross-sections-.	Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.
Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) -tridimensional cross-section-.	Zoom in on a pseudo-octonionic Julia set ('MandelBulb' like: a 'JuliaBulb') computed with A=(-0.581514...,+0.635888...,0,0,0,0,0,0) with a (4xO+1)/(1xO-1) conformal transformation in the octonionic space -tridimensional cross-section-.

A tridimensional billiard starting with a Menger Sponge -iteration 2-.

Cauliflowers, seaweeds, shells,....




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

Light cloud dynamics.

Light cloud dynamics -this sequence being periodical-.

Dynamical mountains (bird's-eye view).

Mountains and light cloud dynamics -this sequence being periodical-.

Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-.

Erosion of a bidimensional random (with large scale correlations) island.




Deterministic Chaos [Chaos Déterministe]:

David versus Goliath: there is a war between Ukraine and Russia.

David versus Goliath: there is a war between Ukraine and Russia.

The Road to Chaos -06/19/2022-.

The Road to Chaos -06/19/2022-.

On the Road to Chaos again -07/07/2024-.

On the Road to Chaos again -07/07/2024-.

The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with cluster(s), with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- without confinement -300 particles-, with a zero death rate and with a 50% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a tridimensional epidemic -the COVID-19 coronavirus?- without confinement -1430 particles-, with a zero death rate and with a 100% infection, starting with just one infected person -red particle on bottom left picture-.	The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 50% infection, starting with just one infected person -red particle on bottom left picture-.
The 'exponential' spreading of a bidimensional epidemic -the COVID-19 coronavirus?- with partial confinement -201 particles-, with a zero death rate and a 100% infection, starting with just one infected person -red particle on bottom left picture-.

Bidimensional domino effect.

The numerical reversibility of the bidimensional billiard -192 particles-.

The numerical irreversibility of the bidimensional billiard -336 particles-.

The numerical irreversibility of the bidimensional billiard -768 particles-.

The numerical irreversibility of the bidimensional billiard -1376 particles-.

The numerical reversibility of the bidimensional billiard -192 particles-.

The numerical irreversibility of the bidimensional billiard -336 particles-.

The numerical irreversibility of the bidimensional billiard -768 particles-.

The numerical irreversibility of the bidimensional billiard -1376 particles-.

The dynamics of the diffusion process in a bidimensional medium obtained by means of a random walk process.




Statistical Mechanics and Particle Systems [Mécanique Statistique et Systèmes de Particules]:

Bidimensional rectangular billiard.

The bidimensional brownian motion of 891 light particles.

The bidimensional brownian motion of 846 light particles and 45 heavier ones.

The bidimensional brownian motion of 846 light particles and 45 heavier ones.

The bidimensional brownian motion of 846 light particles and 45 heavier ones.

The bidimensional brownian motion of 891 particles.

The tridimensional brownian motion of 1815 light particles.

The tridimensional brownian motion of 1738 light particles and 77 heavier ones.

The tridimensional brownian motion of 1738 light particles and 77 heavier ones.

The tridimensional brownian motion of 1738 light particles and 77 heavier ones.

The tridimensional brownian motion of 1815 particles.

Bidimensional rectangular billiard with a central obstacle and an initial flow of rotating particles.

A bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle.

Tridimensional display of the particle density of a bidimensional periodical fluid with strictly identical initial velocities and with a vertically shifted central obstacle.

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

Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity.

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

Bidimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

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

Tridimensional fractal aggregate obtained by means of a 50% pasting process during collisions of particles submitted to an attractive central field of gravity.

Tridimensional fractal aggregates obtained by means of a 100% pasting process during collisions of particles submitted to a vertical field of gravity.

Tridimensional fractal aggregates obtained by means of a 50% pasting process during collisions of particles submitted to a vertical field of gravity.

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




Quantum Mechanics [Mécanique Quantique]:

Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation).

Rotation about the Y (vertical) axis of a tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation).

Rotation about the Y (vertical) axis of a tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation) that can also be viewed as a set of 4x3 stereograms.




Celestial Mechanics [Mécanique Céleste]:

N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on elliptic trajectories -'heliocentric' point of view, yellow body-.	N-body problem integration (N=3) displaying two planets with symmetrical initial conditions on elliptic trajectories -'geocentric' point of view, green body-.	N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite) computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions).	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).	N-body problem integration (N=5) displaying four planets with symmetrical initial conditions on elliptic trajectories -'geocentric' point of view, green body-.
N-body problem integration (N=5) displaying four planets with symmetrical initial conditions on elliptic trajectories -'heliocentric' point of view, yellow body-.

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- 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-.

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

From Mars to the Sun.

The journey of an Earth-like virtuel planet (green) from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-.

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

The distance {Earth-Mars} -millions of kilometers- starting on 01/01/1950 AD and during seven marsian years.

The distances {Sun-Jupiter,Sun-Saturn,Sun-Uranus,Sun-Neptune} during one neptunian year.

The distances Sun-Earth-Jupiter-Saturn-Uranus-Neptune during one neptunian year.

A succesful journey from the Earth to Mars starting on 01/01/1950 AD, velocity=27.900 m/s, duration=270 days.

A missed journey from the Earth to Mars starting on 01/01/1950 AD, velocity=10.000 m/s.




Astrophysics and Cosmology [Astrophysique et Cosmologie]:

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

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

Coalescence of 972 particles -black holes?- on a bidimensional rectangular billiard -a static, non relativistic and bounded universe- during 51.2 time units.	Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- during 51.2 time units.	Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- during 204.8 time units.	Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- with display of the dynamics of the mass histogram, during 204.8 time units.	Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- during 409.6 time units.
Coalescence of 40832 particles -black holes?- inside a tridimensional parallelepipedic billiard -a static, non relativistic and bounded universe- with display of the dynamics of the mass histogram, during 409.6 time units.

The random walk of photons escaping the Sun.




Miscellaneous [Divers]:

Bidimensional texture animation by means of the Generalized Product.

Tridimensional texture animation by means of the Generalized Product.

Bidimensional geometrical texture animation.

The Möbius strip.

The bidimensional John Conway's life game.

Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing.

Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing.

A 20x20 random bidimensional network.

A set of 4x3 stereograms displaying a tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps.

A set of 4x3 stereograms displaying a tridimensional pseudo-random walk defined by means of 'pi': 3.141592... -90.000 digits, -base 10- with 30.000 time steps.




Tests [Tests]:

N-body problem integration (N=4: one star, one heavy planet and one light planet with a satellite) computed with 2 slightly different sets of initial conditions (sensitivity to initial conditions). ISO Media, MPEG v4 system, version 1 ISO Media, MP4 Base Media v1 [IS0 14496-12:2003]

Erosion of a bidimensional random (with large scale correlations) island. MPEG sequence, v1, system multiplex MPEG sequence, v1, system multiplex

The random walk of photons escaping the Sun. RIFF (little-endian) data, AVI, video: FFMpeg MPEG-4 RIFF (little-endian) data, AVI, (...), video: FFMpeg MPEG-4

A Tribute to Benoît Mandelbrot (1924-2010): tridimensional zoom in on the Mandelbrot set with mapping of the arguments. RIFF (little-endian) data, AVI, video: Motion JPEG RIFF (little-endian) data, AVI, (...), video: Motion JPEG






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Copyright © Jean-François COLONNA, 2024-2025.
Copyright © CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2024-2025.