W2514 Emergence & Lindenmayer Systems (Part 4)

From Coder Merlin
Fractal Tree

Prerequisites[edit]

Research[edit]

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

Experiment[edit]

Getting Started[edit]

Continue with the previous project.

Enter into the Sources directory of the project.

cd ~/projects/IgisShell-LSystems/Sources/IgisShell/

First Steps[edit]

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)

Exercises[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

Kevs Wispy Tree (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

Note: Adapted from http://www.kevs3d.co.uk

Supplemental Exercises[edit]

  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

Bonus Exercises[edit]

  1. 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]

  • 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