axplusb.rb

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

end

def sub(s, x)
	return {'a' => s['a'] * x['a'], 'b' => s['a'] * x['b'] + s['b']}
end

def eb(s)
	if (s['a'].odd?) then
		xe = {'a' => 2, 'b' => s['b'].odd? ? - 1 : 0}
		return sub(s, xe), xe
	end
	return
end

def ob(s)
	if (s['a'].odd?) then
		xo = {'a' => 2, 'b' => s['b'].odd? ? 0 : -1 }
		return sub(s, xo), xo
	end
	return
end

def sbt(tr)
	if (tr[0, 1] == '0')
		k = {'a' => 2, 'b' => 0}
		t = {'a' => 1, 'b' => 0}
	else
		k = {'a' => 2, 'b' => -1}
		t = {'a' => 3, 'b' => -1}
	end
	
	tr.split('')[1..-1].each \
	{
		|s|
		if (s == '0') then
			t, p = eb(t)
		else
			t, p = ob(t)
			t['a'] *= 3
			t['b'] = 3 * t['b'] + 1
		end
		t['a'] /= 2
		t['b'] /= 2
		k = sub(k, p)
	}
	return k, t
end


			
tr = '110110110101101101011011011010110110101101101101011011010110110110101101101011011010110110110101101101'

k, t = sbt(tr)

puts(['Trajectory', tr, '  start =', k, '  end =', t, '  pick any r = 1,2,3,...'].join(' '))

n = k['a'] * 1 + k['b']
tr2 = ''
tr.length.times \
{
	tr2 << (n % 2).to_s
	n = f2(n)
}
puts("tr == s #{tr == tr2}")