#include "library.h"

/*
   after seeing that some starting points produce very long Collatz
   sequences while neighbouring ones produce very short ones, this
   presents the information graphically.

   The horizontal axis is N
   The vertical axis is the length of the Collatz sequence that starts with N

   horizontal axis compressed to allow N to go up to 5000
*/

int length_collatz_from(const int n)
{ if (n == 1)
    return 1;
  else if (n % 2 == 1)
  { const int rest = length_collatz_from(3*n+1);
    return 1 + rest; }
  else
  { const int rest = length_collatz_from(n/2);
    return 1 + rest; } }

void plot(const int a, const int b)
{ const int len = length_collatz_from(a);
  draw_point(a/10, 500 - len);
  if (a < b)
    plot(a+1, b); }

void main()
{ make_window(500, 500);
  set_pen_width(3);
  set_pen_color(color::red);
  plot(1, 5000); }