A fractal surface defined by means of three bidimensional fields [Une surface fractale 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 = Fx(u,v)
```
```                    Y = Fy(u,v)
```
```                    Z = Fz(u,v)
```
with:
```                    u ∈ [Umin,Umax]
```
```                    v ∈ [Vmin,Vmax]
```
[Umin,Umax]*[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 = Mx(i,j)
```
```                    Y = My(i,j)
```
```                    Z = Mz(i,j)
```
with:
```                    i = f(u,Umin,Umax,Nu)
```
```                    j = g(v,Vmin,Vmax,Nv)
```
where 'f' and 'g' denote two obvious linear functions...

[Plus d'informations sur ce processus]

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

• Fx
• Fy
• Fz

See the eight first iterations of the fractal process:

• one iteration,
• two iterations,
• three iterations,
• four iterations,
• five iterations,
• six iterations,
• seven iterations,
• eight iterations.

See its normal field.

(CMAP28 WWW site: this page was created on 11/21/2004 and last updated on 04/16/2023 20:51:31 -CEST-)

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