Estimate pi from an image of a circle

estimate_pi.rb

# solution for http://www.reddit.com/r/dailyprogrammer/comments/3f0hzk/20150729_challenge_225_intermediate_estimating_pi/
require 'set'
require 'chunky_png'

# load the image from the data segment
raw_png = DATA.read.delete("\n").unpack('m0').first
image   = ChunkyPNG::Image.from_blob(raw_png)

# extract the colours
colours = image.pixels.uniq
raise "Expected 2 colours, got #{colours.inspect}" unless colours.length == 2
black, white = colours.sort

# for each black pixel, record it's x value
xs = image.height.times.flat_map do |y|
  image.width.times.select { |x| image[x, y] == black }
end

# calculate pi
area     = xs.length
diameter = xs.max - xs.min
radius   = diameter / 2.0
pi       = area / (radius**2) # a = πr², solved for π
puts pi

# >> 3.148117086055024

__END__
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