construct39.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 len(ns, p)
	l = ns.split(p)
	l = [] if (l.nil?)
	l.shift if (l[0] == '')
	return l.map { |x| x.length }
end

def len01(ns)
	return len(ns, /0+/), len(ns, /1+/)
end

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

def sample(l, c)
	return l if (l.size < c)
	r = l.size / c
	l2 = *(0...l.size).select { |x| x % r == 0 }
	l2[c..-1] = []
	return l.values_at(*l2)
	
end

def graph(f, l, t = '')
	f.puts("$dat << eof")
	l.each \
	{
		|l1, c|
		
		l1.each { |x| f.puts([x, c].join("\t")) }
		f.puts
	}
	f.puts("eof")

	t2 = t.gsub(' ', '')
	w1 = "set terminal gif; set output 'out_#{t2}.gif';"; 
	w2 = "unset terminal; unset output;";
#	w2 = "pause -1;"
	f.puts("print '#{t}'; set title '#{t}'; #{w1} plot [][0:1] $dat using 1:2:3 with line linecolor palette lw 2; #{w2}")
	$i = 0 if ($i.nil?)
	$i += 1
	$stderr.puts(t)
end

def line(l, f, w = false)
	a = {}

	l.each \
	{
		|i, ns|

		next if (w && a.member?(ns.length))
		a[ns.length] = f.call(ns)
	}

	return a.keys.sort.map { |x| [x, a[x]] }

end


l = (1..100).map {  count(dense(50, 0.5))['l'] }
	.sort_by { |x| x.size }
	.map { |l1| [(0...l1.size).to_a, l1.map { |x| x.to_s(2) }].transpose }

f = File.open('gnuplot.cmd', 'w')


graph(f, l.map { |l1| [l1.map { |x| [x[0], d(x[1])] }, l1.size] }, 'd')
graph(f, l.map { |l1| [l1.map { |x| [x[0], e(x[1])] }, l1.size] }, 'e')

graph(f, l.map { |l1| [l1.map { |x| [-(l1.size - x[0]), d(x[1])] }, l1.size] }, 'd2')
graph(f, l.map { |l1| [l1.map { |x| [-(l1.size - x[0]), e(x[1])] }, l1.size] }, 'e2')

graph(f, l.map { |l1| [line(l1, lambda { |x| d(x) }), l1.size] }, 'd by w')
graph(f, l.map { |l1| [line(l1, lambda { |x| d(x) }, true), l1.size] }, 'd by w 2')

graph(f, l.map { |l1| [line(l1, lambda { |x| e(x) }), l1.size] }, 'e by w')
graph(f, l.map { |l1| [line(l1, lambda { |x| e(x) }, true), l1.size] }, 'e by w 2')

f.close