Hi

Here is binary decomposition of target set  for both interior ( attraction time) and exterior ( escaping time ).

Second file is computed without modification :

unsigned char ComputeColorOfBD (complex double z)
{





  double cabs2z;


  int i; // number of iteration
  for (i = 0; i < IterMax_LSM; ++i)
    {


cabs2z = cabs2(z); // cabs2(zp-z) = cabs2(z) because zp = zcr = 0

      //
       if ( cabs2z > ER2  ||  cabs2z < AR2 )
        {
        if (creal(z) > 0)
        {  return 0;}
        else {return 255; }
     
     
      }

     

      z = f(z);

    }

  return iColorOfUnknown;


}

first  with modification :

// Modified BD
unsigned char ComputeColorOfMBD (complex double z)
{





  double cabs2z;
  double turn;

  int i; // number of iteration
  for (i = 0; i < IterMax_LSM; ++i)
    {


cabs2z = cabs2(z); // cabs2(zp-z) = cabs2(z) because zp = zcr = 0

      //
       if ( cabs2z > ER2  ) // exterior
        {
        if (creal(z) > 0)
        {  return 0;}
        else {return 255; }
     
     
      }
     
      if ( cabs2z  < AR2 ) // interior is tuned
      {
      turn = c_turn(z);
      if (turn < t0 || turn > t0+0.5)
      {  return 0;}
        else {return 255; }
     
     
      }

     

      z = f(z);

    }

  return iColorOfUnknown;


}



Compare the interior of both files :
The idea is from video: Adrien Douady _ La dynamique du lapin (1996)

Automatic translation : we  take a small sector from origins and its reciprocal images. If we rotate this small sector something special happens at some point : it aligns with the it's images and forms what are called carrots.

What do you think ?


Linkback: https://fractalforums.org/index.php?topic=4743.0

only boundaries

// for MBD
  t0 = ((double) numerator) / period; // Is it iternal angle from inetrnal adress  ???

so for 3/7