construct42.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 - 1)).map { a.delete_at(rand(a.size)) }.each { |x| s[x, 1] = '1' }
	return ('1' + s)
	
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 seq(n)

	n1 = n
	l = []
	begin
		l << n
		n = f2(n)
	end while (n != 1)
	
	return l
end

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

def dp(x)
	d(x.to_s(2)) >= 0.5
end

def avg(c)
	return [c['t'], c['c'].to_f / c['t']]
end

def inc(c, x, l, c1)
	c['c'] += x
	c['t'] += 1
	l << [avg(c), c1]
end

	
def seed(d, c1, l0, l1, l2)
	
	n = terras121(dense(50, d))

	l = seq(n)
	
	a0, a1, da = (0..2).map { {'c' => 0, 't' => 0 } }

	l.each_with_index \
	{
		|x, k|
		dpx, dpn = [dp(x), dp(n)]
		
		m = (dpx == dpn) ? 1 : 0
		
		inc(dpn ? a1 : a0, m, dpn ? l1 : l0, c1)
		
		inc(da, d(n.to_s(2)), l2, c1)
		
		n *= 3 if (x.odd?)
	}
	l0 << []
	l1 << []
	l2 << []
	
end

def graph(f, l, t)
	f.puts('$dat << eof')
	l.each { |x| f.puts(x.join("\t")) }
	f.puts('eof')
	f.puts("set title '#{t}'; plot $dat using 1:2:3 with line linecolor palette lw 2; unset title; pause -1;")
	
end


def data()
	
	l0 = []
	l1 = []
	l2 = [] 
	100.times { |x| seed(x.to_f / 99, x, l0, l1, l2) }

	f = File.open('gnuplot.cmd', 'w')
	graph(f, l1, 'dpn=1')
	graph(f, l0, 'dpn=0')

	graph(f, l2.select { |x| x.empty? || x[1] <= 50 }, 'da <= 50')
	graph(f, l2.select { |x| x.empty? || x[1] > 50 }, 'da > 50')
	f.close

end

data()