Tool

Fibonacci word playground

Iterate the substitution 1 → 10, 0 → 1and walk the resulting string with a turtle that turns on every ‘0’.

Substitution steps: 20 (word length: 17,711)

Rules

Substitution (Fibonacci word):
  start: "1"
  iterate: 1 → 10,   0 → 1
  lengths follow Fibonacci numbers F_n
  current word length: 17,711

Drawing (turtle, on a square grid):
  for each symbol w[i] (i = 1, 2, …):
    step forward 1 unit
    if w[i] == '0':
      if i is odd  → turn left  90°
      if i is even → turn right 90°
    (no turn on '1')

Hausdorff dim: 3 log φ / log(1 + √2) ≈ 1.6379

Background at /fractals/fibonacci-word.

FAQ