W2514 Emergence & Lindenmayer Systems (Part 4)

Within these castle walls be forged Mavens of Computer Science ...

— Merlin, The Coder

Fractal Tree

Prerequisites

• W2513 Emergence & Lindenmayer Systems (Part 3)

Research

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

Experiment

Getting Started

Modify the code from your previous experience.

Stack

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 "[":
                turtle.push()
                turtle.left(degrees:45)
           case "]":
                turtle.pop()
                turtle.right(degrees:45)

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 (Adapted)

• 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

📺 Videos

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

📖 Texts

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

Exercises

Exercises

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

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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

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