pythagorean_tree.html

## pythagorean_tree.html
<html>
<head>
  <meta http-equiv="Content-Type" content="text/html; charset=utf-8">
</head>
<body>
  <canvas id="ptcanvas" width="400" height="400" style="border:1px dotted;float:left"></canvas>
  <script>
  function draw_square( ctx, x1, y1, x2, y2, x3, y3, x4, y4 )
  {
    ctx.beginPath( ) ;
    ctx.moveTo( x1, y1 ) ;
    ctx.lineTo( x2, y2 ) ;
    ctx.lineTo( x3, y3 ) ;
    ctx.lineTo( x4, y4 ) ;
    ctx.lineTo( x1, y1 ) ;
    ctx.fill( ) ;
    ctx.closePath( ) ;
  }

  // Squares should always have vertices 1 and 4 as the base, with 1 always being the left of the base.
  // The base of a child square is the one sitting on the isosceles right triangle formed with the parent.
  // For example, the left child's 1 and 4 vertices match up with the 2 vertex of the parent
  // and the top of the isosceles triangle. The right child's 1 and 4 are the top of the
  // triangle and vertex 3 of the parent.
  //    /\
  //   /  \ <-- bases of children, the rays (1-2 and 4-3) calculated below shoot up to form the diagonal of the child
  //  2 -- 3
  //  |    |
  //  1 -- 4
  function recurse_tree( ctx, x1, y1, x3, y3, swap, level, MAXLEVEL )
  {
    // TRUNK
    var xc, xd, x2, y2, x4, y4 ;
    xc = (x1 + x3)/2.0 ;  yc = (y1 + y3)/2.0 ;  // center point of square - credit to http://math.stackexchange.com/a/506853
    xd = (x1 - x3)/2.0 ;  yd = (y1 - y3)/2.0 ;  // rays representing the half-diagonals
    x2 = xc - yd ;        y2 = yc + xd ;        // corner 2
    x4 = xc + yd ;        y4 = yc - xd ;        // corner 4

    if( swap ) // this was the "rightward" child (base formed by top and vertex 3 above),
	           // meaning the 1 & 3 points passed should actually be 4 & 2 so the diagonal is the correct one:
			   // the "leftward" child's diagonal goes from its 1 to 3 vertex and is formed from the parent's 1->2 ray,
			   // so the "rightward" child must be adjusted so the diagonal runs 1->3 similarly instead of between 4->2
    {
      var tx = x4 ; var ty = y4 ;
      x4 = x1 ; y4 = y1 ;
      x1 = x2 ; y1 = y2 ;
      x2 = x3 ; y2 = y3 ;
      x3 = tx ; y3 = ty ;
    }
    draw_square( ctx, x1, y1, x2, y2, x3, y3, x4, y4 ) ;

    // only draw the leaves if we need to go another level deeper
    level++;
    if( level >= MAXLEVEL )
      return ;

    // LEAVES
    // draw these by shooting rays from the two base corners in the direction of the child to form their hypotenuses
    // the child hypotenuses are the same length as the sides of the parent
    var rayX = x2-x1 ; var rayY = y2-y1 ;
    recurse_tree( ctx, x2, y2, x2+rayX, y2+rayY, false, level, MAXLEVEL ) ;
    var rayX = x3-x4 ; var rayY = y3-y4 ;
    // this diagonal is the wrong diagonal based on the assumption of the function, set swap to true to switch them; see if comment above
    recurse_tree( ctx, x3, y3, x3+rayX, y3+rayY, true, level, MAXLEVEL) ;
  }


  // (x,y) is the base of the square, the BOTTOM side
  function draw_pythagoras_tree( canvas, x, y, slength, maxLevel )
  {
    var ctx = canvas.getContext( "2d" ) ;
    ctx.fillStyle = "#FF0000" ;
    recurse_tree( ctx, x, y, x+slength, y-slength, false, 0, maxLevel ) ;
  }

  draw_pythagoras_tree( document.getElementById( "ptcanvas" ), 175, 350, 50, 12 ) ;
  </script>
</body>
</html>