/***************************************************************************
* L O R E N T Z A T T R A C T O R *
* ------------------------------------------------------------------------ *
* TUTORIAL: *
* *
* Until recently, the only known attractors were the fixed point, the *
* limit cycle and the torus. In 1963, Edwards Lorentz,meteorologist at the *
* M.I.T.,discovered a practical example of a simple dynamic system presen- *
* ting a complex behaviour. To adapt them to computers available at that *
* time, he began with simplifying the equations of meteorology to obtain *
* finally a model composed of three differential equations with three *
* unknown variables x, y, z and three parameters a, b, c: *
* *
* dx / dt = - a x + a y *
* dy / dt = b x - y - x z *
* dz / dt = -c z + x y *
* *
* During very long simulations on a computer, Lorentz decided, to check a *
* result, to restart the same calculation halfway in order to spare time. *
* For that, he reinjected into the computer the intermediate date obtained *
* earlier. He was very surprised to see that the new results were comple- *
* tely different from the first ones. After he suspected some computer *
* failure, Lorenz understood at last that the big difference between both *
* solutions came from very small differences in data. These small pertur- *
* bations exponentially amplified themselves, being doubled every four *
* days in simulated time, so after two months the results became entirely *
* different ! *
* *
* Lorentz then realized that it would be very difficult to make meteorolo- *
* gical foresights in the long term, the slightest change in initial con- *
* ditions leading to a radically different evolution of atmosphere. *
* *
* This is still the case today with atmospheric models much more sophis- *
* ticated. *
* *
* None of the three attractors known at the time could predict the beha- *
* viour of such a dynamic system. Lorentz had just discovered a strange or *
* "chaotic" attractor to which his name was given. *
* ------------------------------------------------------------------------ *
* REFERENCE: *
* "Graphisme dans le plan et dans l'espace avec Turbo Pascal 4.0 *
* By R. Dony - MASSON, Paris 1990" [BIBLI 12]. *
* *
* Visual C++ version by J-P Moreau *
* (to be used with Lorenz.mak and Gr2d.cpp) *
* (www.jpmoreau.fr) *
***************************************************************************/
#include
#include
#include
#include
HDC hdc;
RECT rect;
//Functions used here of module Gr2D.cpp
void Fenetre(double,double,double,double);
void Cloture(int,int,int,int);
void Bordure();
void MoveXY(double,double);
void LineXY(double,double);
//"home made" graphic commands for hdc environment used by above functions
void DrawPixel(int ix,int iy) {
//sorry, no other available command found
Rectangle(hdc,rect.left+ix,rect.top+iy,
rect.left+ix+2,rect.top+iy+1);
}
void Swap(int *i1,int *i2) {
int it;
it=*i1; *i1=*i2; *i2=it;
}
void DrawLine(int ix1,int iy1,int ix2,int iy2) {
int i,il,ix,iy;
float dx,dy;
if (ix2