Bidimensional display of the integration of the Lorenz attractor system for 448500 different initial conditions [Visualisation bidimensionnelle de l'intégration du système de l'attracteur de Lorenz pour 448500 conditions initiales différentes].




Each {X,Y} point of this picture encodes a particular Lorenz attractor (there are 448500 different ones). Each one of them is caracterized with its initial conditions chosen as follows:
                    x  = X scaled within [-30.0,+30.0],
                     0
                    y  = Y scaled within [-30.0,+30.0],
                     0
                    z  = GREY(X,Y) within [0.0,+60.0],
                     0
where 'GREY' denotes a function of the grey level of the current point. This picture displays the 448500 integrations during 255 time steps; the initial conditions can be viewed as the lower left picture and are computed as a gaussian field. For each frame of this animation, the results are encoded as follows:
                    X = x  (unchanged),
                         0
                    Y = y  (unchanged),
                         0
                    GREY(X,Y) = z
a black and white scale is used -white points are the closest ones when black ones are the farthest-. Finally, this picture and this one exhibit a tridimensional rendering.

Instead of using regular initial conditions, any field can be tried. For example a fractal field was chosen and the results are bidimensionally and tridimensionally displayed respectively during 127 time steps (the lower left picture exhibits the initial conditions).


(CMAP28 WWW site: this page was created on 12/12/1996 and last updated on 04/26/2015 11:49:34 -CEST-)



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Copyright (c) Jean-François Colonna, 1996-2015.
Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 1996-2015.