#include "library.h"
#include <iomanip>

struct Complex
{ double re, im;

  Complex(double r, double i)
  { re = r;
    im = i; }

  Complex add(Complex b)
  { return Complex(re + b.re, im + b.im); }

  Complex sub(Complex b)
  { return Complex(re - b.re, im - b.im); }

  Complex mul(Complex b)
  { return Complex(re * b.re - im * b.im, re * b.im + im * b.re); }

  Complex div(Complex b)
  { return Complex((re * b.re + im * b.im) / (b.re * b.re + b.im * b.im), 
                   (im * b.re - re * b.im) / (b.re * b.re + b.im * b.im)); }

  double magnitude()
  { return sqrt(re * re + im * im); }

  void print()
  { cout << setprecision(15) << re;
    if (im >= 0)
      cout << "+";
    cout << setprecision(15) << im << "i\n"; } };



struct explorer
{ int screenw, screenh;
  double minre, maxre, minim, maxim;

  explorer(int screensize, double minr, double maxr, double mini, double maxi)
  { screenw = screenh = screensize;
    minre = minr;
    maxre = maxr;
    minim = mini;
    maxim = maxi;
    make_window(screenw, screenh);
    set_pen_width(2); }

  double screenx_to_real(double x)
  { return x / screenw * (maxre - minre) + minre; }

  double screeny_to_imag(double y)
  { return y / screenh * (maxim - minim) + minim; }

  double real_to_screenx(double r)
  { return (r - minre) / (maxre - minre) * screenw; }

  double imag_to_screeny(double i)
  { return (i - minim) / (maxim - minim) * screenh; }

  void clear()
  { fill_rectangle(0, 0, screenw, screenh, color::white); }

  void move_to(Complex c)
  { ::move_to(real_to_screenx(c.re), imag_to_screeny(c.im)); }

  void draw_to(Complex c)
  { ::draw_to(real_to_screenx(c.re), imag_to_screeny(c.im)); }

  void mark(Complex c)
  { double x = real_to_screenx(c.re), y = imag_to_screeny(c.im);
    ::move_to(x-5, y-5);
    ::draw_to(x+5, y+5);
    ::move_to(x-5, y+5);
    ::draw_to(x+5, y-5); }

  Complex complex_from_x_y(double x, double y)
  { return Complex(screenx_to_real(x),
                   screeny_to_imag(y)); } };



void main()
{ explorer E(600, -2, 2, -2, 2);
  // explorer E(600, -0.167, -0.067, -0.913, -0.827);
  // explorer E(600, -0.1445, -0.143, -0.8885, -0.8872);
  // explorer E(600, -0.14337, -0.14333, -0.887967, -0.887928);
  // explorer E(600, -0.143352733, -0.143352267, -0.88795955, -0.88796015);
  // explorer E(600, -0.1433525194, -0.1433525124, -0.887959812, -0.887959820);
  for (int x = 0; x < E.screenw; x += 1)
    for (int y = 0; y < E.screenh; y += 1)
    { bool gotbig = false;
      Complex c = E.complex_from_x_y(x, y);
      Complex z = c;
      for (int i = 0; i < 10000; i += 1)
      { if (z.magnitude() > 5)
        { gotbig = true;
          break; }
        z = z.mul(z).add(c); }
      if (gotbig)
        set_pixel_color(x, y, color::red);
      else
        set_pixel_color(x, y, color::yellow); }
    wait_for_mouse_click();
    E.complex_from_x_y(get_click_x(), get_click_y()).print();
    wait_for_mouse_click();
    E.complex_from_x_y(get_click_x(), get_click_y()).print(); }