- XLogo recursion
This program produces a fractal of nested squares. Squares are drawn from their centre, so each of the squares four corners is centred on a smaller square.
The reduction factor is a half. This means that each square is half the size. The ever smaller squares never quite touch.
For less reduction, the squares will overlap, which looks messy. However, with a reduction factor equal to 1.618 (the Golden Ratio), squares will exactly overlap. They are actually drawn precisely on top, giving a more tidy effect.
For a Golden ratio pattern, change the 2 to 1.62 and reduce the side to 160.
# set default screen, pen and turtle values
ResetAll SetScreenSize [400 400] HideTurtle
SetSC Black SetPC Green SetPS 1 PenUp
To RSquare :Order :Side
If :Order < 0 [Stop]
Back :Side/2 Right 90 Back :Side/2
Repeat 4 [
SetPW :Order+1 # comment out for no line widths
PenDown Forward :Side PenUp Left 90 Wait 1
RSquare :Order-1 :Side/2] # Golden Ratio replace 2 with 1.62
Forward :Side/2 Left 90 Forward :Side/2
FillSquare # comment out for no fills
SetPC DarkGreen Left 45 Forward 5 Fill
Back 10 Fill Forward 5 Right 45 SetPC Cyan
To Go :Order
New SetPC Cyan
Make "Side 192 # Replace 192 with 160 for Golden Ratio
RSquare :Order :Side
Type go + order to run.
Also see Squares Corner