traverse9.rb

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

end

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

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

def len01x(ns)
	return lenx(ns, /0+/), lenx(ns, /1+/)
end

def e(ns)
	return len01x(ns).flatten.size.to_f / ns.length
end

def seq(n)

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

def mx01x(ns)
	l1, l0 = len01x(ns)
	return (l1 + l0).max.to_f
end

def measure(l)
	cm1 = (0...l.size).max_by { |x| l[x] }
	cg = l.index { |x| x < l[0] }
	cg = l.size - 1 if (cg.nil?)
	
	cg1 = l.rindex { |x| x >= l[0] }
	cm = (0..cg).max_by { |x| l[x] }
	c = l.size

	n = l[0]
	ns = n.to_s(2)
	mx01 = mx01x(ns)
	mx01s = mx01.to_f / ns.length

	{'n' => n,
	'cg' => cg, 
	'cg1' => cg1,
	'c' => c, 
	'cm1' => cm1, 
	'cm' => cm, 
	'mx01' => mx01,
	'mx01s' => mx01s,
	'd' => d(ns),
	'e' => e(ns)}
end

def stat(l)
	return 0, 0, 0 if (l.empty?)
	
	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 stats(a)
	s = {}
	ks = a.first[1].keys - ['z', 'f']
	ks.each \
	{
		|k|
		av, sd = stat(a.values.map { |x| x[k] })
		s["#{k}_a"] = av
		s["#{k}_sd"] = sd
	}

	a.each \
	{
		|k, x|
		z = 0
		ks.each { |k| z += ((x[k] - s["#{k}_a"]) / s["#{k}_sd"]) ** 2 }
		x['z'] = z
	}
end

def count(a, n, x = 'a')
	m = a.member?(n)
	a[n] = measure(seq(n)) if (!m)
	a[n]['f'] = x
	
end

def node(a, n)

	count(a, n)
	count(a, n * 2, 'b')
	count(a, (n - 1) / 3, 'b') if (n % 3 == 1 && ((n - 1) / 3).odd?)
end

def adv(a, x, s, f)
	n = x['n']
	f.puts([s, n, x['z']].join("\t"))
	node(a, n)
end

a = {}
n = 1
c = 100

c.times { node(a, n += 1) }

f = File.open('gnuplot.cmd', 'w')
f.puts('$dat << eof')
f.puts(['s', 'n', 'x_z'].join("\t"))

200.times \
{
	|i|
	stats(a)

	l2 = a.values.select { |x| x['f'] == 'b' }
	l = l2.sort_by { |x| x['z'] }.reverse
	
	x1 = l2.min_by { |x| x['n'] }
	
	adv(a, x1, 1, f)
	(c / 2).times \
	{
		raise if (l.empty?)
		x = l.shift
		adv(a, x, 2, f)
	}
}
f.puts('eof')
f.puts("plot $dat using x:(log(column('n'))):(column('s')) with point linecolor variable pt 5 ps 0.5; pause -1;")
f.puts("plot $dat using x:(log(column('x_z'))):(column('s')) with point linecolor variable pt 5 ps 0.5; pause -1;")