Gallery :

Sensitivity to Rounding-Off Errors

[Galerie : Sensibilité aux Erreurs d'Arrondi]

Jean-François COLONNA
www.lactamme.polytechnique.fr
jean-francois.colonna@polytechnique.edu
CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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

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

[more information]

The Verhulst Dynamics [la Dynamique de Verhulst] :

Real numbers do not exist for a computer

Real numbers do not exist for a computer.

Bidimensional display of the rounding-off errors when computing the Verhulst dynamics

Bidimensional display of the rounding-off errors when computing the Verhulst dynamics.

Tridimensional display of the rounding-off errors when computing the Verhulst dynamics

Tridimensional display of the rounding-off errors when computing the Verhulst dynamics.

The Lorenz Attractor [l'Attracteur de Lorenz] :

Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one : sensitivity to rounding-off errors)

Computation of the Lorenz attractor on three different computers (the Red one, the Green one and the Blue one : sensitivity to rounding-off errors).

Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers

Rotation about the X axis of the Lorenz attractor (1000 iterations), computed simultaneously on two different computers.

Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers

Rotation about the X axis of the Lorenz attractor (5000 iterations), computed simultaneously on two different computers.

The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-

The Lorenz attractor -sensitivity to initial conditions (displayed as the central point of each frame)-.

The Lorenz attractor -sensitivity to initial conditions (the Red one, the Green one and the Blue one)-

The Lorenz attractor -sensitivity to initial conditions (the Red one, the Green one and the Blue one)-.

The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-

The Lorenz attractor -sensitivity to integration methods used (Red=Euler, Green=Runge-Kutta/2nd order, Blue=Runge-Kutta/4th order)-.

Pendulum Systems [Systèmes de Pendules] :

more information about Pendulum Systems

The three pendulums and three magnets problem computed on three different computers (the Red one, the Green one and the Blue one : sensitivity to rounding-off errors)

The three pendulums and three magnets problem computed on three different computers (the Red one, the Green one and the Blue one : sensitivity to rounding-off errors).

The N-Body Problem [le Problème des N-Corps] :

more information about the N-Body Problem

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 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)

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=4 : one star, one heavy planet and one light planet with a satellite)-sensitivity to initial conditions-

N-body problem integration (N=4 : one star, one heavy planet and one light planet with a satellite) -sensitivity to initial conditions-.

Bidimensional Billiards [Billards Bidimensionnels] :

The irreversibility of the numerical bidimensional billiard

The irreversibility of the numerical bidimensional billiard.

Copyright (c) Jean-François Colonna, 2000-2013.
Copyright (c) CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2000-2013.