construct120.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 \\")
	k.each \
	{ 
		|x| 
		next if (a.member?(x) && a[x].nil?)
		f.puts("'$dat' using (column('#{x}')) with line #{a.fetch(x, '')} lw 2,\\") 
	}
	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 triangle1(c)

	l = []
	c.times \
	{
		|nw|
		ns = '1' * (nw + 1)
		l << ns.to_i(2)
	}
	return l
end

def mx(l1, fn)
	l1 = [''] if (l1.empty?)
	l = l1.map { |x| mx = fn.call(x).max; {'mx' => mx, 'mxs' => mx == 0 ? 0 : mx.to_f / x.length} }

	return {'mx' => l.map { |x| x['mx'] }.max,
		'mxs' => l.map { |x| x['mxs'] }.max}
end

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

#	p(l1)
	
	mx1 = mx(l1, lambda { |x| len1x(x) })
	mx0 = mx(l1, lambda { |x| len0x(x) })

	return {'cg' => l.size, 'cgnw' => l.size - nw, 
		'mx0' => mx0['mx'],
		'mx1' => mx1['mx'],
		'mx01' => [mx0['mx'], mx1['mx']].max,
		'mx0s' => mx0['mxs'] * nw,
		'mx1s' => mx1['mxs'] * nw,
		'mx01s' => [mx0['mxs'], mx1['mxs']].max * nw
}
end

def graph(l)
	l2 = []
	l.each_with_index \
	{
		|x, j|
		l1 = seqg(x)
		l2 << data(l1)
		
		$stderr.puts(j) if (j % 10 == 0) 
	}

	outafn(l2, {'cg' => 'axes x1y2', 'cgnw' => 'axes x1y2'})

end

def glides(t)
	
	l1 = []
	e = 0.64

	t.times \
	{
		|nw|
		
		d = e + rand() * (1.0 - e)

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

		l = seqg(n)

		redo if (l.size < n.to_s(2).length)
		l1 << n
		$stderr.puts(nw) if (nw % 10 == 0) 
	}

	return l1
end


l = ARGV[0].nil? ? glides(1000) : triangle1(1000)

graph(l)