construct40.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 seq(n)

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

def count(ns)
	l = seq(ns.to_i(2))
	
	cm1 = (0...l.size).max_by { |x| l[x] }
	cg = l.index { |x| x < l[0] }
	
	cm = (0...cg).max_by { |x| l[x] }
	cg1 = l.rindex { |x| x > l[0] }
	
	
	return {'ns' => ns, 
	'cm' => cm, 
	'cm1' => cm1, 
	'cg' => cg, 
	'cg1' => cg1, 
	'l' => l
	}

end

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

def avg(l)
	l.inject { |t, x| t + x }.to_f / l.size
end

def out(f, l, a = {}, t = '')
	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 colors classic; set ytics nomirror; set y2tics; set title '#{t}'; plot \\")
	k.each { |x| f.puts("'$dat' using (column('#{x}')) with line #{a.fetch(x, '')},\\") }
	f.puts
	f.puts("reset; pause -1;")

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 dataset()
	l = (1..100).map {  count(dense(50, 0.5))['l'] }.sort_by { |x| x.size }


	l2 = l.map \
	{
		|l1|
		l2 = l1.map { |x| d(x.to_s(2)) }
		l3 = []
		n = l1[0]
		l1.size.times { l3 << d(n.to_s(2)); n *= 3; }
		{'c' => l1.size, 
		'da' => avg(l2), 
		'dp' => l2.select { |x| x > 0.5}.size,
		'd3a' => avg(l3), 
		'd3p' => l3.select { |x| x > 0.5}.size 
		}
	}
	$i = 0 if ($i.nil?)
	$i += 1
	$stderr.puts($i)
	return l2
end

f = File.open('gnuplot.cmd', 'w')
out(f, avgs((1..100).map { dataset() }), {'da' => 'axes x1y2', 'd3a' => 'axes x1y2'})
f.close