construct100.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 = [n1]
	while (n != 1)
		n = f2(n)
		l << n
	end 
	
	return l
end

def outa(f1, l, a = {}, t = '')
	f = f1.nil? ? File.open('gnuplot.cmd', 'w') : f1
	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 key top right opaque; set title '#{t}'; ")
#	f.puts("set ytics nomirror; set y2tics;")
	f.puts("plot \\")
	(k - ['x']).each \
	{ 
		|x| 
		next if (a.member?(x) && a[x].nil?)
		f.puts("'$dat' using (column('x')):(column('#{x}')) with line #{a.fetch(x, '')} lw 2 title '#{x}',\\") 
	}
	f.puts
#	f.puts("reset; pause -1;")
	f.close if (f1.nil?)

end

l2 = []
(100..1000).each \
{
	|x|
	ns = '1' * x
	l1 = seq(ns.to_i(2))
	cg = l1.index { |x| x < l1[0] }
	cg = l1.size if (cg.nil?)
	cm = (0...cg).max_by { |x| l1[x] }
	
	p1 = l1[cm..cg].map { |x| x % 2 }.join
	p2 = l1[cg..-1].map { |x| x % 2 }.join
	d1 = d(p1)
	d2 = d(p2)
	e1 = e(p1)
	e2 = e(p2)
	
	l2 << {'x' => x, 'd1' => d1, 'd2' => d2, 'e1' => e1, 'e2' => e2}
	$stdout.puts(x)
}

outa(nil, l2)