The Dragon Curve or Dragon Fractal is a nifty little shape!

Here are the first 12 iterations. You see the dragon shape begin to emerge. I've put a red dot before each one, so you can see how it doesn't always go forward right away.

;export dragon
to dragon :count :length :angle
ifelse :count = 0
[ fw :length  ]
[
  ifelse (:angle = 1)
  [
    rt (45 * :angle)
    dragon (:count -1) :length / sqrt(2)  :angle
    lt 90 * :angle
    dragon (:count -1) :length / sqrt(2) (:angle * (0-1))
    rt (45 * :angle)
  ]
  [
    rt (45 * :angle)
    dragon (:count -1) :length / sqrt(2)  (:angle * (0-1))
    lt 90 * :angle
    dragon (:count -1) :length / sqrt(2) (:angle)
    rt (45 * :angle)
  ]
]
end

;import dragon
to dot
  color [250 0 0]
  circle 1
  color [0 0 0]
end
setxy 40 40
dot
dragon 0 70 1
setxy 150 40
dot
dragon 1 70 1
setxy 260 40
dot
dragon 2 70 1
setxy 40 140
dot
dragon 3 70 1
setxy 150 140
dot
dragon 4 70 1
setxy 260 140
dot
dragon 5 70 1
setxy 40 240
dot
dragon 6 70 1
setxy 150 240
dot
dragon 7 70 1
setxy 260 240
dot
dragon 8 70 1
setxy 40 340
dot
dragon 9 70 1
setxy 150 340
dot
dragon 10 70 1
setxy 260 340
dot
dragon 11 70 1

The "TwinDragon" is achievable by drawing two dragons, one after the other, with a 180 degree turn in the middle. They fit snugly together, or as Mathematicians says, they 'tile the plane'.

;import dragon
to twin_dragon :count :length :color1 :color2
    color :color1 ;(000 000 200)
    dragon :count :length 1
    rt 180
    color :color2 ;(200 000 200)
    dragon :count :length 1
    rt 180
    pu
    dragon 1 :length 1
    pd
end
repeat 5 [
 twin_dragon 10 70 (000 000 200) (200 000 200)
 twin_dragon 10 70 (000 200 000) (200 000 000)
]

See Also

• NumberPhile: DragonCurve Video