I74 Answer ― Gray Spiral

#include <stdlib.h>
#include <stdio.h>
#include <math.h>

int main(int argc, char *argv[])
{
  int r, nrows, c, ncols;
  int red, grn, blu;
  FILE *image;

  /* check the command line parameters */
  if ( argc != 4 )
  {
    printf("spiral fileName.ppm nrows ncols \n");
    return 0;
  }

  /* open the image file for writing in binary mode */
  if ( (image = fopen( argv[1], "wb") ) == NULL )
  {
    printf("file %s could not be created\n", argv[1]);
    return 0;
  }

  nrows = atoi( argv[2] );
  ncols = atoi( argv[3] );

  /* write out the PPM Header information */
  fprintf( image, "P6 ");
  fprintf( image, "%d %d %d ", ncols, nrows, 255 );

  /* find the maximum distance from the center of the image */
  double radius = sqrt( nrows*nrows + ncols*ncols )/2.0;
  double dist, thetaCC ;
  double cntR = nrows/2.0, cntC = ncols/2.0;

  /* write out the pixel data */
  for ( r=0; r<nrows; r++ )
    for ( c=0; c<ncols; c++ )
    {
      dist    = sqrt( (r-cntR)*(r-cntR) + (c-cntC)*(c-cntC)) ;
      thetaCC = atan2( (c-cntC), (r-cntR) );
      red     = 125 + 125*cos( 2*M_PI*(dist/radius) + thetaCC);
      grn     = 125 + 125*cos( 2*M_PI*(dist/radius) + thetaCC);
      blu     = 125 + 125*cos( 2*M_PI*(dist/radius) + thetaCC);
      fputc( red, image );  fputc( grn, image );  fputc( blu, image );
    }

  /* close the file */
  fclose ( image );

  return 1;
}

Comments: The hardest part of this program is calculating thetaCC. As usual, the programming is not hard, but the math may take some thought. This might be an opportunity for you to do that review of trigonometry you keep putting off.