construct164.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 len(ns, p)
	l = ns.split(p)
	l = [] if (l.nil?)
	l.shift if (l[0] == '')
	return l.map { |x| x.length }
end

def len1(ns)
	return len(ns, /0+/)
end

def len0(ns)
	return len(ns, /1+/)
end

def len01(ns)
	return len1(ns), len0(ns)
end

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

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

def outd(f, l)
	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')
	return k
end

def outa(f, l, a = {}, t = '')
	
	k = outd(f, l)
	f.puts("set colors classic; set key top left opaque; set title '#{t}'; ")
	f.puts("set ytics nomirror; set y2tics;")
	f.puts("plot \\")
	k, ct = [k - ['t'], "(column('t')):"] if (k.member?('t'))
	k.each \
	{ 
		|x| 
		next if (a.member?(x) && a[x].nil?)
		opt = a.fetch(x, '')
		opt += ' lw 2 ' if (!opt.include?('lw'))
		opt += ' with line ' if (!opt.include?('with') && !opt.include?('pt'))
		f.puts("'$dat' using #{ct}(column('#{x}')) #{opt} title '#{x}',\\") 
	}
	f.puts
#	f.puts("reset; pause -1;")

end

def outafn(l, fn = nil, t = '', a = {})
	outa(f = File.open(fn.nil? ? 'gnuplot.cmd' : fn, 'w'), l, a, t)
	f.close
	$stderr.puts([t, fn].inspect)
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 sum(l)
	return l.inject { |t, x| t + x }
end

def avg(l)
	return l.empty? ? 0 : sum(l).to_f / 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

def midpt(ns)
	w2 = ns.length / 4
	l = ns.split('')
	i = j = 0
	while (i < w2 && j < l.size)
		i += l[j].to_i
		j += 1
	end
	return j.to_f / ns.length
end


def dataset(d1)
	p = dense(100, d1)
	n = n3 = terras121(p)

	l = []
	100.times \
	{
		|j|
		ns3 = n3.to_s(2)
		ns = n.to_s(2)
		
		l << {'m' => midpt(ns), 
			'mr' => midpt(ns.reverse),
			'm3' => midpt(ns3), 
			'm3r' => midpt(ns3.reverse)
			}
		n3 *= 3 if (n.odd?)
		n = f2(n)
	}
	return l
end

[0.65, 0.75, 0.85, 0.95].each_with_index \
{
	|d, i|
	outafn(avgs((1..400).map { dataset(d) }), "gnuplot#{i + 1}.cmd", "d=#{d}", {'r' => 'axes x1y2', 'r3' => 'axes x1y2 lt 7'})
}