W2514 Emergence & Lindenmayer Systems (Part 4)

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Fractal Tree



  • Read Stacks
  • Review those Lindenmayer Systems that require use of a stack (pop/push). One example is a "Fractal Tree".


Getting Started[edit]

Modify the code from your previous experience.


Turtle objects are able to remember their current state and restore that state at a later point. The state is stored on a stack and is therefore in LIFO (Last In First Out) order. A turtle's state includes:

  • location
  • angle
  • pen color
  • pen width

Consider a Fractal Tree with the following translation mechanisms:

  • 0: draw a line segment (ending in a leaf)
  • 1: draw a line segment
  • [: push position and angle, turn left 45 degrees
  • ]: pop position and angle, turn right 45 degrees

When encountering a push or pop operation we can use the turtle's functionality as follows:

           case "[":
           case "]":

Regardless of what occurs between a push and a pop, the turtle will be in the same situation it was in immediately prior to the push. This enables us to build very complex systems, such as Kev's Wispy Tree.

Kev's Wispy Tree[1] (Adapted)[edit]

  • Alphabet: "F", "X", "[", "]", "+", "-", "0", "1", "2", "3"
  • Axiom: "FX"
  • Production Rules:
    • "F" -> "0FF-[1-F+F]+[2+F-F]"
    • "X" -> "0FF+[1+F]+[3-F]"
  • Geometric mechanism:
    • "F" -> Forward
    • "X" -> Forward
    • "-" -> Right 25 degrees
    • "+" -> Left 25 degrees
    • "[" -> Push
    • "]" -> Pop
    • "0" -> Pen color: red:140, green:80, blue:60
    • "1" -> Pen color: red:24, green:180, blue:24
    • "2" -> Pen color: red:48, green:220, blue:48
    • "3" -> Pen color: red:64, green:255, blue:64

👀 See Also[edit]

📺 Videos[edit]

Lindenmayer Systems and The Nature of Code
Procedural Plant Generation with L-Systems

📖 Texts[edit]

W2511 Emergence & Lindenmayer Systems (Part 1)
W2512 Emergence & Lindenmayer Systems (Part 2)
W2513 Emergence & Lindenmayer Systems (Part 3)
W2514 Emergence & Lindenmayer Systems (Part 4)

📚 References[edit]


  1. Add a Fractal Tree as one of the Lindenmayer Systems in your cycle
  2. Add a Fractal Plant as one of the Lindenmayer Systems in your cycle
  3. Add "Kevs Wispy Tree" as one of the Lindenmayer Systems in your cycle

Supplemental exercises:

  1. Add buttons to alter the angles used in drawing the L-Systems
  2. Construct your own Lindenmayer System and add it to your cycle
  3. Animate the entire production of the Lindenmayer System (not just from generation to generation, but the application of each production rule in sequence)

Key Concepts[edit]

Key Concepts
  • A Stack is an abstract data-type which is a collection of elements with two principal operations:
    • Push adds the specified element to the collection
    • Pop removes and returns the most recently added element
  • LIFO means Last in, first out

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