construct188.rb

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

end

def seq(n)
	l = [n]
	
	while (n != 1)
		n = f2(n)
		
		l << n
		
	end
	return l
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 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 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, a = {}, fno = nil, t = '')
	fn = "gnuplot#{fno}.cmd"
	outa(f = File.open(fn, 'w'), l, a, t)
	f.close
	$stderr.puts([fn, t, l.size].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 d(s)
        c = s.split('').select { |x| x == '1' }.size
	d = c.to_f / s.length
        return d
        
end

def add(a, x)
	a[x] = a.fetch(x, 0) + 1
end

def val(a)
	return a.fetch(1, 0).to_f / a.fetch(2, 1)
end

def scan(l, a)
	l.each { |x| add(a, x % 3) }
end

def cg(l2)
	cg = l2.index { |x| x < l2[0] }
	return cg
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 sum(l)
	return l.inject { |t, x| t + x }
end

def avg(l)
	return sum(l).to_f / l.size
end

def corr(l, y1, yp = nil)
	
	yp, ye = ["#{y1}_y", "#{y1}_e"] if (yp.nil?)
	xa = avg(l.map { |x| x[y1] })
	ya = avg(l.map { |x| x[yp] })

	tx = ty = txy = e = 0.0
	m = nil
	l.each \
	{
		|z|
		
		x = z[y1]
		y = z[yp]

		z[ye] = (x - y).abs if (!ye.nil?)
		txy += (x - xa) * (y - ya)
		tx += (x - xa) ** 2
		ty += (y - ya) ** 2
	}
	d = Math.sqrt(tx) * Math.sqrt(ty)
	$z = 1e-4
	r = txy / (d.abs < $z ? $z : d)
	return r
	
end

def line(l)
	l1 = l.map { |x| x.to_s(2).length }
	mn = l1.min
	mx = l1.max
	t1 = t2 = 0
	l1.size.times \
	{
		|x|
		
		y1 = (l1[x].to_f - mn) / (mx - mn)
		y2 = x.to_f / (l1.size - 1)
		t1 += (y1 - y2)
		t2 += (y1 - y2).abs
	}

	return {
#		't1' => t1.to_f / l1.size, 
#		't2' => t2 / l1.size
	}
end

c1 = 500
w = 200
l1 = []
c1.times \
{
	|i|
	r = i.to_f / (c1 - 1)
	p = dense(w, r)
	n = terras121(p)
	
	scan((l = seq(n))[0...w], a = {})
	e = e(p)
	eq = (r)*(r - 1.0) * 2
	e1 = e + eq
	l1 << line(l[0...w]).merge({
		'e' => e,
		'a21' => 1.0 - val(a) - r, 
		'eq' => -eq,
		'e1' => e1,
	})
}

outafn(l1)

f = File.open('gnuplot.cmd', 'a')
f.puts('pause -1;')
f.puts("plot $dat using (column('e1')):(column('a21')) pt 5 title 'a21 vs e1'")
f.close

$stderr.puts(corr(l1, 'e1', 'a21'))