Penrose Snowflake Revisited

The 1st time I revisited this sketch was in response to some refactoring by Dan Myer see http://learning-ruby-processing.blogspot.co.uk/2010/01/refactoring-my-penrose-snowflake.html. Since the advent of OPENGL for two dimensional sketches, that is all old hat, since we no longer need to keep generating the geometry, we can create a shape and reuse it (multiple times in the same sketch if need be). So here we use a generic grammar library for simple lsystems:-

############################
# Simple lsystem grammar
############################
class Grammar

  attr_reader :axiom, :rules
  def initialize(axiom, rules)
    @axiom = axiom
    @rules = rules
  end

  def expand(production, iterations, &block)
    production.each_char do |token|
      if rules.has_key?(token) && iterations > 0
        expand(rules[token], iterations - 1, &block)
      else
        yield token
      end
    end
  end

  def each gen
    expand(axiom, gen) {|token| yield token }
  end

  def generate gen
    output = []
    each(gen){ |token| output << token }
    return output
  end

end

Here is the animation code adapted from a processing example:-

# A class to describe a Polygon (with a PShape)

class Polygon
  include Processing::Proxy
  # The PShape object
  attr_reader :s, :x, :y, :speed, :height

  def initialize(s_, width, height)
    @x = rand(width)
    @y = rand(height * -1.5 .. -height / 3)
    @s = s_
    @speed = rand(2 .. 6)
    @height = height
  end

  # Simple motion
  def move
    @y +=speed
    @y = -100 if (y > height + 100)
  end

  # Draw the object
  def display
    push_matrix
    translate(x, y)
    shape(s)
    pop_matrix
  end

  def run
    display
    move
  end
end

Here is the penrose snowflake

load_libraries :grammar, :polygon

class PenroseSnowflake
  include Processing::Proxy
  import 'grammar'

  attr_accessor :axiom, :grammar, :start_length, :theta, :production, :draw_length,
  :repeats, :xpos, :ypos
  DELTA = Math::PI / 10 # 18 degrees as radians

  def initialize width
    reset width
  end

  def reset width
    @axiom = "F3-F3-F3-F3-F"
    @grammar = Grammar.new( axiom,
      {"F" => "F3-F3-F45-F++F3-F"}
      )
    @start_length = width / 40
    @theta = 0
    @xpos = width / 80
    @ypos = 0
    @draw_length = start_length
  end

  ##############################################################################
  # Parses the production string, and draws a line when 'F' is found, uses
  # trignometry to calculate dx and dy rather than processing transforms
  ##############################################################################

  def create_flake production
    flake = create_shape
    fil = [200, 220, 255].sample
    flake.begin_shape
    flake.fill fil
    flake.stroke fil
    flake.vertex(xpos, ypos)
    repeats = 1
    production.each do |element|
      case element
      when 'F'
        flake.vertex(@xpos -= multiplier(repeats, :cos), @ypos += multiplier(repeats, :sin))
        repeats = 1
      when '+'
        @theta += DELTA * repeats
        repeats = 1
      when '-'
        @theta -= DELTA * repeats
        repeats = 1
      when '3', '4', '5'
        repeats += element.to_i
      else
        puts "Character '#{element}' is not in grammar"
      end
    end
    flake.end_shape CLOSE
    return flake
  end

  ##########################################
  # adjust draw length with number of repeats
  # uses grammar to set production string 
  # see 'grammar.rb'
  ##########################################

  def create_grammar(gen)
    @draw_length *= 0.4**gen
    @production = grammar.generate gen
  end

  ###########################################
  # a helper method that returns dx or dy with type & repeat
  # multiplier after Dan Mayer
  ###########################################

  def multiplier(repeats, type)
    value = draw_length * repeats
    # using equal? for identity comparison
    (type.equal? :cos)?  value * cos(theta) : value *  sin(theta)
  end
end

##
# Lindenmayer System in ruby-processing by Martin Prout
# Very loosely based on a processing Penrose L-System
# by Geraldine Sarmiento
###

attr_reader :polygons

def setup
  size displayWidth, displayHeight, P2D
  #stroke 255
  flakes = []
  @polygons = []
  penrose = PenroseSnowflake.new width
  (2 .. 4).each do |i|
    production = penrose.create_grammar(i)
    flakes << penrose.create_flake(production)
    penrose.reset width
  end
  40.times do
    polygons << Polygon.new(flakes.sample, width, height)
  end
end

def draw
  background 0
  # Display and move them all
  polygons.each do |poly|
    poly.run
  end
end