Gallery (17 different pictures):

Sensitivity to Rounding-Off Errors

[Galerie (17 images différentes) : Sensibilité aux Erreurs d'Arrondi]

Jean-François COLONNA
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CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
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Sensitivity to Rounding-Off Errors [Sensibilité aux Erreurs d'Arrondi]:

The Mandelbrot Set [L'ensemble de Mandelbrot]	The Verhulst Dynamics [La Dynamique de Verhulst]	The Lorenz Attractor [L'Attracteur de Lorenz]	Pendulum Systems [Systèmes de Pendules]	The N-Body Problem [Le Problème des N-Corps]
Bidimensional Billiards [Billards Bidimensionnels]

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

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The Mandelbrot Set [L'ensemble de Mandelbrot]:

The Mandelbrot set computed using 32/64 bit arithmetics (discrepancies between two computations).

The Verhulst Dynamics [La Dynamique de Verhulst]:

Real numbers do not exist for a computer.

Bidimensional 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).

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.

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 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 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 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-.

Bidimensional Billiards [Billards Bidimensionnels]:

The numerical irreversibility of the bidimensional billiard.

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

[More information and visual access to more Sensitivity to Rounding-Off Errors pictures [Plus d'informations et accès visuel à plus d'images de Sensibilité aux Erreurs d'Arrondi]]

Copyright © Jean-François COLONNA, 2000-2024.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 2000-2024.