gap2.rb

def f2(n)
	return n.odd? ? (n * 3 + 1) / 2 : n / 2

end

def dense(w, d)
	w2 = w - 1
	
	a = (0...w2).to_a
	s = '0' * w2
	(1..((d * w).to_i - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' }
	return ('1' + s)
	
end

def d(s)
        c = s.split('').select { |x| x == '1' }.size
	d = c.to_f / s.length
        return d
        
end

def len01(ns)
	nl = ns.length
	l1 = ns.split(/0+/).map { |x| x.length }
	
	l2 = ns.split(/1+/)[1..-1]
	l2 = [''] if (l2.nil?)
	
	l0 = l2.map { |x| x.length }
	return l0, l1
end

def mx01(ns)
	len01(ns).flatten.max
end

def crossover(n)

	n1 = n
	l1 = [d(n1.to_s(2)) - 0.5]
	i = 0
	while (n != 1)
		n = f2(n)

		l1 << d(n.to_s(2)) - 0.5
		l1.shift if (l1.size == 3)
		break if (l1[0] * l1[1] < 0)
		i += 1
	end
	
	return i
end

def sample(c)
	
	$n = 0 if ($n.nil?)
	$stderr.puts($n += 1)

	l = []
	c.times \
	{
		|i|
		d = i.to_f / (c - 1)
		ns = dense(c, d)
		ns2 = f2(n = ns.to_i(2)).to_s(2)
		l << {'d' => d, 
			'd2' => d(ns2), 
			'mx1' => mx01(ns), 
			'mx2' => mx01(ns2),
			'co' => crossover(n)}
	}
	return l
end

def sum(l)

	t = 0.0
	l.each { |x| t += x }
	return t
end

def avg(l)
	return nil if (l.empty?)
	return sum(l) / l.size
end

def avgs(l)

	ks = l[0][0].keys
	l1 = []
	l[0].size.times \
	{
		|i|
		l1[i] = Hash[[ks, ks.map { |k| avg(l.map { |x| x[i][k] }) }].transpose]
	}
	return l1
	
end

l = avgs((1..10).map { sample(1000) })

f = File.open('gnuplot.cmd', 'w')
f.puts('$dat << eof')
f.puts(l[0].keys.join("\t"))
l.each { |x| f.puts(x.values.join("\t")) }
f.puts('eof')
f.puts('set key top center; set ytics nomirror; set y2tics; plot \\')
a = {'d2' => 'axes x1y2'}
(l[0].keys - ['d']).each { |x| f.puts("$dat using (column('d')):(column('#{x}')) title '#{x}' with line #{a.fetch(x, '')},\\") }
f.puts
f.puts('pause -1')
f.puts("plot $dat using (column('d')):(log(column('mx1'))) title 'log mx1' with line,$dat using (column('d')):(log(column('co'))) title 'log co' with line")
f.puts('pause -1')
f.puts("set key top left; unset y2tics; plot 0 lw 2,$dat using (column('d')):(column('mx2')-column('mx1')) title 'mx2 - mx1' with line")


f.close