Chaos in Fibonacci sequence bit representation

fib.png

fib.rb

require 'chunky_png'

def bit_triangle(ints)
  # colors taken from Espresso Libre theme for TextMate
  brown        = ChunkyPNG::Color.rgb(0x38, 0x2c, 0x25)
  blue         = ChunkyPNG::Color.rgb(0x00, 0x66, 0xff)
  green        = ChunkyPNG::Color.rgb(0x43, 0xaa, 0x43)
  bg_color     = brown
  bit_color    = green
  width        = ints.length
  height       = ints.max.bit_length

  png = ChunkyPNG::Image.new width, height, bg_color
  ints.each_with_index do |int, x|
    int.bit_length.times do |bit_index|
      y = height - bit_index - 1 # 0,0 is topleft, this inverts it to botleft
      png[x, y] = bit_color if int[bit_index].zero?
    end
  end

  png
end

# Fibonacci numbers
#
# Got the idea from
#   http://mathworld.wolfram.com/FibonacciNumber.html
# Definition of the golden ratio from Euclid's Elements:
#   A straight line is said to have been cut in extreme and mean ratio when,
#   as the whole line is to the greater segment, so is the greater to the less.
#   http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/defVI3.html
fibs = [0, 1]
fib  = -> n { fibs[n] ||= fib[n-1] + fib[n-2] }
png  = bit_triangle (0..590).map(&fib)
file = 'fib.png'
png.save(file)
exec 'open', file