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].
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].
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.
and
tridimensionally 
displayed respectively during 127 time steps (the lower
left picture exhibits the initial conditions).