unsigned int secant_fractal(double x, double y, unsigned int escape, unsigned int iterations) {
  for(unsigned int iter = 0; iter < iterations; iter++) { 
    double next_x;
    next_x = x / cos(y);
    y = y / cos(x);
    x = next_x;
    if((pow(x, 2) + pow(y, 2)) >= escape) return iter;
  }
}
unsigned int cosecant_fractal(double x, double y, unsigned int escape, unsigned int iterations) {
  for(unsigned int iter = 0; iter < iterations; iter++) { 
    double next_x;
    next_x = x / sin(y);
    y = y / sin(x);
    x = next_x;
    if((pow(x, 2) + pow(y, 2)) >= escape) return iter;
  }
}

double cosecant_single(double a, double b) { return a / sin(b); }
double secant_single(double a, double b) { return a / tan(b); }


__kernel void render_frame(__global unsigned int *frame_output, __global double *mask, 
    double x_step, double y_step,
    double x_start, double y_start,
    unsigned int iterations, unsigned int escape, double ratio) {  
  unsigned int result;
  double x = (get_global_id(0) * x_step) + x_start;
  double y = (get_global_id(1) * y_step) + y_start;
  size_t img_index = (get_global_id(1) * get_global_size(1)) + get_global_id(0);

  unsigned int iter;
    
  
  for(iter = 0; iter < iterations; iter++) { 
    double next_x;
    double r = mask[img_index];
    next_x = (r * cosecant_single(x, y)) + ((1 - r) * secant_single(x, y));
    y = (r * cosecant_single(y, x)) + ((1 - r) * secant_single(y, x));
    x = next_x;
    if((pow(x, 2) + pow(y, 2)) >= escape) break;
  }
  

  
  frame_output[img_index] = iter;
  //frame_output[img_index] = mask[img_index] * 255;
}