construct137.rb

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

end

def seqg(n)

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

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

end

def outafn(l, a = {}, fn = nil)
	outa(f = File.open(fn.nil? ? 'gnuplot.cmd' : fn, 'w'), l, a)
	f.close
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 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 lenx(ns, p)
	l = ns.split(p)
	return [0] if (l.empty?)
	l.shift if (l[0] == '')
	return l.map { |x| x.length }
end

def len1x(ns)
	return lenx(ns, /0+/)
end

def len0x(ns)
	return lenx(ns, /1+/)
end

def glides1(nw, t)
	
	l1 = []
	e = 0.64

	t.times \
	{
		|i|
		
		d = e + (i + 1).to_f / t * (1.0 - e)
		$stderr.puts(d)

		p = dense(nw + 1, d)
		n = terras121(p)

		l = seqg(n)

		redo if (l.size < n.to_s(2).length)
		l1 << n
	}

	return l1
end

def mx1(l1, fn)
	l1 = [''] if (l1.empty?)
	$t = 0 if ($t.nil?)
	l = l1.map \
	{ 
		|x| 
		mx = fn.call(x).max; 
		{'t' => $t += 1, 'mx' => mx, 'mxs' => x.length == 0 ? 0 : mx.to_f / x.length} 
	}
	$t += 100
	return l + [{}]
end

def graph(x)
	l = seqg(x)

	nw = l[0].to_s(2).length
	
	i = nw
#	i = 0
	l1 = l[i..-1].map { |x| x.to_s(2) }

	cm1 = (0...l1.size).max_by { |x| l1[x] }
	cm1 = 0 if (cm1.nil?)

#	$stderr.puts(cm1)
	
	fn = lambda { |x| len1x(x) }
	
	l = mx1(l1, fn)
	
	return l

end

l = glides1(400, 5).map { |x| graph(x) }.flatten

outafn(l, {'mxs' => 'axes x1y2', 't' => nil})