#include "library.h"

double f(const double x, const double y)
{ const double a = sqrt(x*x+y*y)-10.0;
  return 1.0/sqrt(sqrt(a*a+1.0)); } 

double maximum(const double a, const double b)
{ if (a>b)
    return a;
  else
    return b; }

double maximum(const double minx,
               const double maxx,
               const double miny,
               const double maxy)
{ const double midx=(minx+maxx)/2.0, midy=(miny+maxy)/2.0;
  if (maxx-minx<0.1 && maxy-miny<0.1)
    return f(midx, midy);
  const double m1 = maximum(minx, midx, miny, midy);
  const double m2 = maximum(midx, maxx, miny, midy);
  const double m3 = maximum(minx, midx, midy, maxy);
  const double m4 = maximum(midx, maxx, midy, maxy);
  const double answer = maximum(maximum(m1, m2), maximum(m3, m4));
  return answer; }

void plot(const double minx,
          const double maxx,
          const double miny,
          const double maxy)
{ const double midx=(minx+maxx)/2.0, midy=(miny+maxy)/2.0;
  if (maxx-minx<0.1 && maxy-miny<0.1)
  { const double value = f(midx, midy);
    set_pen_color(value, 0.0, 1.0-value);
    draw_point(10*midx+305, 10*midy+305); }
  else
  { plot(minx, midx, miny, midy);
    plot(midx, maxx, miny, midy);
    plot(minx, midx, midy, maxy);
    plot(midx, maxx, midy, maxy); } }

void main()
{ const double m = maximum(-30, 30, -30, 30);
  make_window(610, 610);
  plot(-30, 30, -30, 30); }