Chaos theory- on the oscilloscope

Projects Programming
1

Hi guys. Some days ago saw this code from the forum.

I simulated it on Proteus and I was able to graph some oscillators like Lorenz, Rossler and Chua but I couldn't graph systems with 4 state equiations. I'm new in Arduino so i will really appreciate your comments

Thank you in advance.

float x_pos;         
float y_pos; 
int x_out = 5;
int y_out = 6;
float x = 0.1;
float y = 0.1;
float z = 0.1;
float w = 0.1;

float a = 3;
float b = 22;
float c = 8.1;
float d = 4.1;
 
float xdot;
float ydot;
float zdot;
float wdot;
float dt = 0.01;

void setup()  { 

  pinMode(x_out, OUTPUT);
  pinMode(y_out, OUTPUT);
  // this next section changes the PWM frequency - don't mess with it!
    TCCR0A = (  1<<COM0A1 | 0<<COM0A0 |   // clear OC0A on compare match (hi-lo PWM)
    1<<COM0B1 | 0<<COM0B0 |   // clear OC0B on compare match (hi-lo PWM)
    1<<WGM01  | 1<<WGM00);    // set PWM lines at 0xFF

  TCCR0B = (  0<<FOC0A | 0<<FOC0B |   // no force compare match
    0<<WGM02 |      // set PWM lines at 0xFF
    0<<CS02  | 0<<CS01 |    // use system clock (no divider)
    1<<CS00 );

  TIMSK0 = (  0<<OCIE0B | 0<<TOIE0 |
    0<<OCIE0A ); 
} 

void loop()  {

xdot = a*x-y*z;
ydot = -b*y+x*z-z*w;
zdot  = -c*z+x*y;
wdot = d*(y-w);

x = x + (xdot * dt);
y = y + (ydot * dt);
z = z + (zdot * dt);
w = w + (wdot * dt);  

x_pos = 128+(50 * x);
y_pos = 128+(50 * y);

analogWrite(x_out, x_pos);
analogWrite(y_out, y_pos);
}
2

I wonder what the italics mean.

3

x_out and y_out are connected to an RC circuit ?

Avoid timer 0 if you can because it is used internally by the Arduino run time system.

4

Something must have been graphed even if wrong, so what were the values that got sent to anslogWrite?

a7

5

Yes, i used a kind of kalman filter to convert the PWM signal to analog.

Thank you, i´m gonna try it.

6

I sent x and y variables, but when i run the simulate nothing happen, there's no voltage at the pins. :frowning:

7

Sorry man, they are the equations of the system.

float x_pos;         
float y_pos; 
int x_out = 5;
int y_out = 6;
float x = 0.1;
float y = 0.1;
float z = 0.1;
float w = 0.1;

float a = 3;
float b = 22;
float c = 8.1;
float d = 4.1;
 
float xdot;
float ydot;
float zdot;
float wdot;
float dt = 0.01;

void setup()  { 

  pinMode(x_out, OUTPUT);
  pinMode(y_out, OUTPUT);
  // this next section changes the PWM frequency - don't mess with it!
    TCCR0A = (  1<<COM0A1 | 0<<COM0A0 |   // clear OC0A on compare match (hi-lo PWM)
    1<<COM0B1 | 0<<COM0B0 |   // clear OC0B on compare match (hi-lo PWM)
    1<<WGM01  | 1<<WGM00);    // set PWM lines at 0xFF

  TCCR0B = (  0<<FOC0A | 0<<FOC0B |   // no force compare match
    0<<WGM02 |      // set PWM lines at 0xFF
    0<<CS02  | 0<<CS01 |    // use system clock (no divider)
    1<<CS00 );

  TIMSK0 = (  0<<OCIE0B | 0<<TOIE0 |
    0<<OCIE0A ); 
} 

void loop()  {

xdot = a*x-y*z;
ydot = -b*y+x*z-z*w;
zdot  = -c*z+x*y;
wdot = d*(y-w);

x = x + (xdot * dt);
y = y + (ydot * dt);
z = z + (zdot * dt);
w = w + (wdot * dt);  

x_pos = 128+(50 * x);
y_pos = 128+(50 * y);

analogWrite(x_out, x_pos);
analogWrite(y_out, y_pos);
}
8

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