
The Pythagoras tree is a fractal tree constructed from squares. It is named after Pythagoras because each triple of touching squares encloses a right triangle, in a configuration traditionally used to represent the Pythagorean theorem.




Task
Construct a Pythagoras tree of order 7 using only vectors (no rotation or trigonometric functions).




Related tasks
 Fractal tree


 
Subroutine pythagoras_tree(x1, y1, x2, y2, depth)
	If depth > 10 Then Return
 
	dx = x2 - x1 : dy = y1 - y2
	x3 = x2 - dy : y3 = y2 - dx
	x4 = x1 - dy : y4 = y1 - dx
	x5 = x4 + (dx - dy) / 2
	y5 = y4 - (dx + dy) / 2
	#draw the box
	Line x1, y1, x2, y2 : Line x2, y2, x3, y3
	Line x3, y3, x4, y4 : Line x4, y4, x1, y1
 
	Call pythagoras_tree(x4, y4, x5, y5, depth +1)
	Call pythagoras_tree(x5, y5, x3, y3, depth +1)
End Subroutine
 
w = 800 : h = w * 11 \ 16
w2 = w \ 2 : diff = w \ 12
 
Clg
FastGraphics
Graphsize w, h
Color green
Call pythagoras_tree(w2 - diff, h - 10, w2 + diff, h - 10, 0)
Refresh
ImgSave "pythagoras_tree.jpg", "jpg"
End
 