Attribute VB_Name = "Module2"

'********************************************************************
'                 DEMO:  Lorenz and Roessler attractors             * 
'* ---------------------------------------------------------------- *
'* Until recently, the only known attractors were: the fixed point, *
'* the limit cycle and the torus. In 1963, Edwards Lorenz, a M.I.T. *
'* meteorologist, discovered a concrete example of a simple dynamic *
'* system presenting a complex behavior. To adapt them to the avail-*
'* able computers at that time, he began simplifying the equations  *
'* of meteorology to finally obtain a numerical model composed of 3 *
'* differential equations with 3 unknowns, x, y, z, with 3 parame-  *
'* ters, a, b and 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 computer, Lorenz had the idea,   *
'* to verify some results, to restart a calculation at mid course,  *
'* to spare time. For that purpose, he injected into the machine the*
'* intermediate results obtained before. He had the great surprise  *
'* that the new results were completely different! After suspecting *
'* some computer failure, Lorenz finally understood that the big    *
'* differences between both solutions came from very small differen-*
'* ces in numerical data. These small initial perturbations were    *
'* exponentially amplifying, by doubling every 4 days in simulated  *
'* time, so after two months the results were totally different!    *
'*                                                                  *
'* Lorenz then realized that it would be very hard to make meteo-   *
'* rological forecasts in the long range, the slightest change in   *
'* starting conditions will give an atmosphere evolution radically  *
'* different. That still occurs today even with much more sophisti- *
'* cated models of atmosphere.                                      * 
'*                                                                  * 
'* None of the three attractors known at that time could allow des- *
'* cribing the behaviour of such a dynamical system. Lorenz had just*
'* discovered a "strange and chaotic" attractor to which his name   *
'* was given.                                                       *
'*                                                                  *
'* The Roessler attractor is similar to the Lorenz one with another *
'* set of differential equations.                                   *
'*                                                                  *
'*                             Visual Basic Release By J-P Moreau.  *
'*                                     (www.jpmoreau.fr)            *
'********************************************************************
 'To be used with attract.frm and gr2d.bas


Public A, B, CC, x3, y3, z3 As Double
Public xx, yy, z As Double


Sub f()
    Const delta = 0.005
    Dim dx, dy, dz As Double
    dx = -(y3 + z3)
    dy = x3 + y3 * A
    dz = B + z3 * (x3 - CC)
    x3 = x3 + delta * dx
    y3 = y3 + delta * dy
    z3 = z3 + delta * dz
End Sub




Public Sub RunRoessler()
     
     Form1.Cls
     A = 0.2: B = 0.2: CC = 5.7
     x3 = -10: y3 = -1: z3 = -1
     flag = 0
     Fenetre -10, 12, -15, 55
     cloture 250, MaxX - 250, 250, MaxY - 250
     Bordure
     Display 500, 500, "ROESSLER  ATTRACTOR"
     Roessler (flag)
     flag = 1
     
End Sub


Sub Roessler(flag%)
Dim i As Double
    i = 0
    f
    If flag% = 0 Then
      Do
        f
        i = i + 1#
      Loop Until i > 1000
    End If
    MoveXY x3, y3 + z3 + z3
    i = 0
    Do
      f
      i = i + 1#
      LineXY x3, y3 + z3 + z3
    Loop Until i > 33000#
    Beep
End Sub

Sub Lorentz()
    f
    MoveXY xx, z
    n% = 0
    Do
      n% = n% + 1
      f1
      LineXY xx, z
    Loop Until n% >= 5000
End Sub

Sub f1()
Const delta = 0.01
Dim dx, dy, dz As Double
  dx = A * (yy - xx)
  dy = xx * (B - z) - yy
  dz = xx * yy - CC * z
  xx = xx + delta * dx
  yy = yy + delta * dy
  z = z + delta * dz
End Sub

Public Sub RunLorentz()
'DEMO  LORENTZ ATTRACTOR
'                               J-P Moreau

Form1.Cls
Display MaxX - 2500, MaxY - 750, "LORENTZ  ATTRACTOR"

A = 10: B = 30: CC = 2.6666
xx = 1: yy = 1: z = 1
Fenetre -22, 25, -8, 60
cloture 250, MaxX - 250, 250, MaxY - 250
Bordure
Lorentz
Beep

End Sub