A fractal surface (one iteration) defined by means of three bidimensional fields [Une surface fractale (une itération) définie à l'aide de trois champs bidimensionnels].




Many surfaces -bidimensional manifolds- in a tridimensional space can be defined using a set of three equations:
                    X = F (u,v)
                         x
                    Y = F (u,v)
                         y
                    Z = F (u,v)
                         z
with:
                    u E [U   ,U   ]
                          min  max
                    v E [V   ,V   ]
                          min  max
[Umin,Umax]x[Vmin,Vmax] then defined a bidimensional rectangular domain D.
                       v ^
                         |
                    V    |...... ---------------------------
                     max |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                         |      |+++++++++++++++++++++++++++|
                    V    |...... ---------------------------
                     min |      :                           :
                         |      :                           :
                         O------------------------------------------------->
                                U                           U              u
                                 min                         max

If D is sampled by means of a bidimensional rectangular grid (made of Nu.Nv points), the three {X,Y,Z} coordinates can be defined by means of three rectangular matrices:
                    X = M (i,j)
                         x
                    Y = M (i,j)
                         y
                    Z = M (i,j)
                         z
with:
                    i = f(u,U   ,U   ,N )
                             min  max  u
                    j = g(v,V   ,V   ,N )
                             min  max  v
where 'f' and 'g' denote two obvious linear functions...


[for more information about this process]
[pour plus d'informations sur ce processus]


For the fractal surface, the three {X,Y,Z} fields/matrices are as follows:




(CMAP28 WWW site: this page was created on 11/23/2004 and last updated on 01/28/2014 16:17:13 -CET-)



[for more information about that kind of picture and/or process [pour plus d'informations sur ce type d'image et/ou de processus]]


[Please visit the related GeneralitiesVisualization picture gallery [Visitez la galerie d'images GeneralitiesVisualization associée]]
[Go back to AVirtualSpaceTimeTravelMachine [Retour à AVirtualSpaceTimeTravelMachine]]
[The Y2K bug [Le bug de l'an 2000]]

[Site Map, Help and Search [Plan du Site, Aide et Recherche]]
[Mail [Courrier]]
[About Pictures and Animations [A Propos des Images et des Animations]]


Copyright (c) Jean-François Colonna, 2004-2014.
Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / Ecole Polytechnique, 2004-2014.