INFORMATIONAL COMPLEXITY: Applications to architecture, arts and music.
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Maybe it may appears surprising to explain and analyse the contrast between moerne architecture, art, music, and our occidental patrimonial reachess. Why so many people are visiting ancient churches, castles ?
More than our recent buildings, paintings or modern music ?

Anyway, recent advances in mathematics may explain logically this phenomenon : Mathelatically speaking, informative complexity of anything : say castle, painting or music can be computed scientifically. Mybe this can look surprising, but it's matematically proven.

The Kolmogorov-Chaïtin (see below) theorem allows it.
Other algorithms such as the luminance  derivative  in a picture, allows it equally.
What response these algorithms are giving to us :
When they analyse an architectural scene, or a contemporary modern art sculpture or music (for example buildings or tge recent "moder art" pieces (see in place Vendôme and Versailles park) they measure only a very weak informative complexity.
But when the same algorithms analyse high culturel level scenes or music  (say also an advertsement, or ancient building) they reveal  a strong informative complexity .
One could deduce than inhabitants of poor cities are living in an informative empty. I think one must highlight this discovery
Watch for example the "plug anal" of McCarthy in Vendôme place in Paris, or Château de Versailles with the "vagin de la Reine" by Anish Kapoor.

The real goal of this pseudo "art" consists in showing what is the informative empty. In order to suppress the remembrence of all the  masterpieces of our civilisation. This allow building a new civilisation with people without any roots.

A similar computation of the  informative complexity  can also be applied to music.
(Compare for exemple Bach scores to contemporary music scores)

This is now the informational complexity  défined for a simple bit array :

Informationnal complexity of a bit array has been defined for the first time by Kolmogorov and Chaitin by this surprising formula :
DEFINITION :
Informative complexity  of a bit array of size n is equal to the neperian logarithm of n, added with the lenght of the shortest program able to generate this bit array.

The following example is showing astonishing examples of seeming complexity.
It is very surprizing to discover that a so short program could generate such a picture of a so complex vegetal shape as a fern.
Our eyes and brain are in fact fantastic detectors of spatio-temporal complexity.
One can watch similar phenomenons in arts, architecture and music.

Picture size in pixels : 1 553 000 bytes
 PROGRAM SIZE : 820 bytes
void    fougere0(void)
{
    A1.init(2,2);A1.m[0][0] = 0;A1.m[0][1] = 0; A1.m[1][0] = 0.16; A1.m[1][1] = 0;
    A2.init(2,2);A2.m[0][0] = 0.2;A2.m[0][1] = -0.26; A2.m[1][0] = 0.23;A2.m[1][1] = 0.22;
    A3.init(2,2);A3.m[0][0] = -0.15,A3.m[0][1] = 0.28; A3.m[1][0] = 0.26;A3.m[1][1] = 0.24;
    A4.init(2,2);A4.m[0][0] = 0.85;A4.m[0][1] = 0.04; A4.m[1][0] = -0.04; A4.m[1][1] = 0.85;
    B1.init(2,1);B1.m[0][0] = 0;B1.m[1][0] = 0;
    B2.init(2,1);B2.m[0][0] = 0;B2.m[1][0] = 1.6;
    B3.init(2,1);B3.m[0][0] = 0;B3.m[1][0] = 0.44;
    B4.init(2,1);B4.m[0][0] = 0;B4.m[1][0] = 1.6;
    P.init(1,4);P.m[0][0] = 0.01;P.m[0][1] = 0.08;P.m[0][2] = 0.15;P.m[0][3] = 0.1;
    Z.init(2,1);
    TEMP.init(2,1);
    XY.init(2,1);
    niter = NITER;
    ifs();
}
//
void    ifs(void)
{
    long    i;

    //BOUCLE
    L_Bar(300,320,400,450);
    L_setpencolor(2);
    for(i=0;i<niter;i++)
    {
        kf=(double)rand();
        kf = kf/0x7FFF;
        w(kf);
        xy[i][0] = 500 + (int)(XY.m[0][0]*ech);
        xy[i][1] = 700 - (int)(XY.m[1][0]*ech);
    }
    return;
}
Picture of the TGB (très grande bibliothèque (Library) in Paris ) : When analyzed by a complexity detector software, one get a very low complexity level. One get similar results with  the immense majority of cotemporary architecture.
http://www.idsia.ch/~juergen/femmefractale.html
At the contrairy, ancient buildings which have been built during past centuries  are containing a high level of informative complexity. This phenomenon reflects all the informative messages they are holding. At the opposite side, modern architecture and furniture have very low informative complexity levels.
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