[sdiy] Logistic Equation chaos engine?

[s.thomas]

Hi ..still on the topic of Lorenz attarctors and chaos..it might be fun to see if one could  design an anlogue circuit that solves the so called' logistic equation'
(for those who like maths see http://mathworld.wolfram.com/LogisticEquation.html for a nice review and pretty pictures) . The solutions to this equation (or at least the recurrence relation thats based on this equation) can approach chaos ..and show period doubling and bifurcation etc. I would guess  it must be possible to solve simple recurrence relations using analogue computer type circuits?

cheers
steve thomas

  ----- Original Message ----- 
  From: Jaroslaw Ziembicki 
  To: SDIY 
  Sent: Friday, July 04, 2003 11:07 AM
  Subject: [sdiy] Digital simulation of the Lorenz attractor


  Hi,
  I wrote a C program that simulates the Lorenz attractor
  and plots the results. The graphic mode should be set.
  Here is the basic subroutine. Maybe somebody will find
  it useful.
  Regards
  Jarek


  void Lorenz(void)
  {
  /* simulation variables/parameters: */
    float x = 0.1;
    float y = 0.0;
    float z = 0.0;
    float s = 10.00;
    float r = 28.00;
    float b =  2.67;
    float dt = 100E-6;
  /* graphics' variables/parameters: */
    float xxscale = 0.02*(float)(getmaxx()+1); /* for plot scaling */
    float yyscale = 0.01*(float)(getmaxy()+1); /* for plot scaling */
    WORD xx0 = (getmaxx()+1)/2;     /* plot center x */
    WORD yy0 = (getmaxy()+1)/2;     /* plot center y */
    WORD color = 15;

  /* border, x and y axes: */
    setcolor(DARKGRAY);
    rectangle(0,0,getmaxx(),getmaxy());
    line(0,yy0,getmaxx(),yy0); line(xx0,0,xx0,getmaxx());
  /* loop: */
    while ( kbhit() ) getch();
    do
    {
      float dx,dy,dz;
      WORD    xx,yy;

      /* put a pixel: */
      xx = xx0+(int)(xxscale*x); yy = yy0-(int)(yyscale*z);
      putpixel(xx,yy,color);
      /* new x,y,z values: */
      dx = dt * (s*(y-x));
      dy = dt * (r*x - y - x*z);
      dz = dt * (x*y - b*z);
      x += dx; y += dy; z += dz;
      /* next color: */
      color++; if ( color > 15 ) color = 0;
    }
    while ( !kbhit() );
  }

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