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Koch curve

This is a fractal curve. You can find more information about this at Wikipedia.

Logo script:

# Koch curve

reset
canvassize 850, 550
go 125, 350
turnright 90

learn koch $x, $t {
  if($t>0) {
    $t=$t-1
    $x=$x/3
    koch $x, $t
    turnleft 60
    koch $x, $t
    turnright 120
    koch $x, $t
    turnleft 60
    koch $x, $t
  } else {
  forward 3*$x 
  }
}
koch 200, 6

Result:

Sierpinski Triangle

Another famous fractal is the Sierpinski triangle.

Logo script:

# Sierpinski triangle

learn sierp $l {
  if $l > 2 {
    repeat 3 {
      sierp $l/2
      forward $l
      turnleft 120
    }
  }
}

reset
canvassize 600, 533
go 50, 483
turnright 90
sierp 500

Result: