Indeed, the reason for the exact relation sigma (1/4^n) == 1/3 becomes more obvious. Split an area into fourths, use up one fourth, and another fourth of that

Indeed, the reason for the exact relation sigma (1/4^n) == 1/3 becomes more obvious. Split an area into fourths, use up one fourth, and another fourth of that fourth, and the whole set becomes an infinite series of triples, with the middle (shaded) one filled in.