l_system

LSystem

home : https://hg.sr.ht/~ged/LSystem

code : https://hg.sr.ht/~ged/LSystem

github : https://github.com/ged/lsystem

docs : https://deveiate.org/code/lsystem

Description

A toolkit for creating and using Lindenmayer Systems (L-systems). It consists of a class that allows for declaration of the L-system's grammar, and another class that allows for the definition of how the symbols output by a grammar should be translated into work.

Examples

Most of these were stolen from the examples on Wikipedia, and can be found in the examples/ directory of the source.

Algae

Lindenmayer's original L-system for modelling the growth of algae.

• variables : A B
• constants : none
• axiom : A
• rules : (A → AB), (B → A)

Declare the rules:

algae = LSystem.declare do

	variables :A, :B
	axiom 'A'
	rules 'A -> AB',
	    'B -> A'

end

then iterate it 8 times and print out each generation:

iter = algae.each
8.times do |i|
    puts "n = %d : %s" % [ i, iter.next ]
end

This outputs:

n = 0 : A
n = 1 : AB
n = 2 : ABA
n = 3 : ABAAB
n = 4 : ABAABABA
n = 5 : ABAABABAABAAB
n = 6 : ABAABABAABAABABAABABA
n = 7 : ABAABABAABAABABAABABAABAABABAABAAB

You can also do more complex tasks with the symbols in each generation. For example, to generate pretty pictures.

Barnsley fern

• variables : X F
• constants : + − [ ]
• axiom : X
• rules : (X → F+[[X]-X]-F[-FX]+X), (F → FF)
• angle : 25°

Declare the rules:

fern = LSystem.declare do

  variables 'X', 'F'
  constants '+', '-', '[', ']'
  axiom 'X'
  rules \
    'X → F+[[X]-X]-F[-FX]+X',
    'F → FF'

end

Then hook them up to a Logo interpreter ([a monkeypatched version][tortoise-patch] of the [Tortoise gem][tortoise-gem]):

LSystem.run( fern, 8 ) do

  # The size of the canvas to draw on
  CANVAS_SIZE = 2000

  # F: draw forward
  # X : no-op
  # -: turn left 25°
  # +: turn right 25°
  # [: push position and angle
  # ]: pop position and angle
  production_map \
    'F' => :forward,
    '-' => :turn_left,
    '+' => :turn_right,
    '[' => :save_pos_and_angle,
    ']' => :restore_pos_and_angle

  ### Set up some instance variables
  def initialize( * )
    super
    @turtle = nil
    @positions = []
  end


  on_start do |i, _|
    @turtle = Tortoise::Interpreter.new( CANVAS_SIZE )
    @turtle.setpos( CANVAS_SIZE / 2, 0 )
    @turtle.direction = 90
    @turtle.pd
  end


  on_finish do |i, _|
    File.open( "fern_gn#{i}.png", File::WRONLY|File::TRUNC|File::CREAT, 0644, encoding: 'binary' ) do |fh|
      fh.write( @turtle.to_png )
    end
  end


  ### Draw a line forward
  def forward
    @turtle.fd( 5 )
  end


  ### Turn 25° to the left
  def turn_left
    @turtle.lt( 25 )
  end


  ### Turn 25° to the right
  def turn_right
    @turtle.rt( 25 )
  end


  ### Save the drawing position and angle
  def save_pos_and_angle
    @positions.push([ @turtle.position, @turtle.direction ])
  end


  ### Restore the next saved position and angle
  def restore_pos_and_angle
    to_restore = @positions.pop or raise IndexError, "Position stack underflow"

    @turtle.setpos( *to_restore.first )
    @turtle.direction = to_restore.last
  end

end

This generates a sequence of images, which for generation 8 yields:

Prerequisites

• Ruby

Installation

$ gem install lsystem

Contributing

You can check out the current development source with Mercurial via its project page. Or if you prefer Git, via its Github mirror.

After checking out the source, run:

$ rake setup

This task will install dependencies, and do any other necessary setup for development.

Authors

• Michael Granger [e-mail]

License

Copyright (c) 2020, Michael Granger All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

• Neither the name of the author/s, nor the names of the project's contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.