From: Andreas Launila <ruby-talk@...>
Date: 2007-06-11T01:53:21+09:00
Subject: Re: [QUIZ] Mexican Blanket (#127)

Ruby Quiz wrote:
> So the challenge is to make a pattern generator to generate the patterns as seen
> in the ASCI and picture. 
> 

Idea: Each line constains a repeating pattern, and the lines themselves
are also repeating patterns. Therefore compute the supersequence of the
lines, then extract subsequences from that to retrieve the complete pattern.



INTERVAL_LENGTH = 5 # The interval at which the color-pattern changes.
LINE_LENGTH = 100
ROW_COUNT = 200

# Mexican flag.
colors = %w{G W R}

# Cycle the colors if we need more. The relationship between
# supersequence length l, interval_length w, and number of colors c is
# l = (1 + (c-1) * w) * w <=> c = ceil((l - w) / w^2) + 1
length_needed = ROW_COUNT + LINE_LENGTH - 1
colors_needed = ((length_needed - INTERVAL_LENGTH).to_f /
  INTERVAL_LENGTH**2).ceil + 1
colors *= (colors_needed.to_f / colors.size).ceil

# Create a supersequence for the lines. Reverse the colors and slice
# from the end of the pattern to get the correct order.
color_pattern = colors.reverse.map{ |c| c * INTERVAL_LENGTH }.join
line_superseq = ''
INTERVAL_LENGTH.upto(color_pattern.size) do |i|
  line_superseq << color_pattern.slice(-i, INTERVAL_LENGTH)
end

# Sample the line-sequence a few times to produce the complete pattern.
ROW_COUNT.times do |i|
  puts line_superseq[i, LINE_LENGTH]
end


I didn't really understand what kind of symmetry was requested, but
replacing the colors with the following can be used to create the
pattern posted by Harry, the need for repetition of colors probably
means I misunderstod something though.


# Recreates the pattern posted by Harry.
colors = %w{G W R B Y R G R}
colors += colors.reverse


-- 
Andreas Launila