- XLogo
This is a famous diagram showing a rectangle of golden ratio divided into an infinite series of squares. A logarithmic spiral can be drawn through the squares. Here, the spiral is approximated by a quater circle arc in each square.
To New
# set default screen, pen and turtle values
ResetAll SetScreenSize [400 400] HideTurtle
SetSC Black SetPC Green SetPS 1 PenUp
End
To Section :Side
If :Side < 2 [Stop] # stop when side too short
SetPC Green Square :Side # comment out for curve only
SetPC Red Curve :Side # comment out for squares only
Section :Side*0.618 # do again with smaller side
End
To Square :Side
Repeat 4 [Forward :Side Right 90]
End
To Curve :Side
Make "Step :Side*0.0524 # heading correction pi/60
Right 1.5
Repeat 30 [Forward :Step Right 3 Wait 4] # 90 degree arc in 30 steps
Left 1.5
End
To Lines
SetPC [0 0 128] # draw crossed lines in blue
PenUp SetPos [-185 88]
PenDown SetPos [184 -140]
PenUp SetPos [184 88]
PenDown SetPos [43 -140] Wait 30
End
To Go
New Lines SetPos [-185 -140]
Section 228 # begin with square of side 228
End
Also see Plastic Number.