drag the resolution

r = 1 s = log(1/r) = 0.00 N(r) = 1 Φ = log N = 0.00 Φ/s = —

The boxes above are the ones that meet the set. Each time the width shrinks by a factor of 3, the number of survivors doubles — and the point below climbs one notch along a line whose slope is log 2 / log 3.