construct12.rb

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

end

def adj(x, m, n, s2, p2, p, x3)
	s2.replace(p[0...x] + (x3 % 2).to_s)
	m = (s2[x, 1] == p[x, 1])
	n = p2.reverse.to_i(2)
	p2[x, 1] = m ? '11' : '01'
	return m, n, x3
end

def terras121(p)
	
	p2 = ['01', '11'][p[0, 1].to_i]
	n = 1
	n3 = 0
	m = p2 == '11'
	x3 = (p2.reverse.to_i(2)) >> 1

	(1...p.length).each \
	{
		|x|

		if (!m)
			ns = n.to_s(2)
			ns[0, 1] = ''
			m1 = x3 - 3**n3
			n1 = f2(m1)
		end

		n3 = p[0...x].split('').select { |z| z == '1' }.size
		
		s2 = ''
		m, n, x3 = adj(x, m, n, s2, p2, p, m ? (f2(x3) + 3**n3) : (n1 + 3**n3))
	}

	n = p2.reverse.to_i(2)

	return n
end

def dense(w, d)
	w2 = w - 1
	
	a = (0...w2).to_a
	s = '0' * w2
	(1..(d * w - 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 len(ns, p)
	l = ns.split(p)
	l = [] if (l.nil?)
	l.shift if (l[0] == '')
	return l.map { |x| x.length }
end

def len01(ns)
	return len(ns, /0+/), len(ns, /1+/)
end

def e(ns)
	return len01(ns).flatten.size.to_f / ns.length
end

def stat(l)
	t = l.inject { |a, x| a + x }
	t2 = l.inject { |a, x| a + x ** 2 }
	
        c = l.size
        a = t.to_f / c
        z = t2.to_f / c - a ** 2
        sd = Math.sqrt(z < 0 ? 0 : z)
        raise if (sd.nan?)
        return a, sd, l.max
end


def seq(n)
	n1 = n
	l = [n1]
	while (n != 1)
		n = f2(n)
		l << n
	end
	cg = l.index { |x| x < n1 }
	cg = 0 if (cg.nil?)
	cm = (0..cg).max_by { |x| l[x] }
	
	cm1 = (0...l.size).max_by { |x| l[x] }
	cg1 = l.rindex { |x| x >= n1 }
	return {'cm1' => cm1, 'cm' => cm, 'cg1' => cg1, 'cg' => cg, 'c' => l.size}
end

def gp(l)
        f = File.open('gnuplot.cmd', 'w')
        f.puts('$dat << eof')
        k = l[0].keys
        f.puts(k.join("\t"))
        l.each { |x| f.puts(x.values.join("\t")) }
        f.puts('eof')
	f.puts('set key top left; set colors classic; plot \\')
	(k - ['d1']).each \
	{
		|x|
		m = ''
		m = 'lw 2' if (x[-1, 1] == '1')
		m += ' dt 3' if (['cm', 'cg'].member?(x))
		f.puts("$dat using (column('d1')):(column('#{x}')) title '#{x}' with line #{m},\\")
	}
        f.close

end



l = []
c = 400
c.times \
{
	|x|
	n = terras121(dense(200, d1 = x.to_f / (c - 1)))
	l << seq(n).merge({'d1' => d1})
}

gp(l)