Aggregate projected area exponent, α, versus fractal dimension, D_f, or equivalently the dimensionality, D. The data point at D_f = 1.82 (with the uncertainties in D_f and α indicated by the horizontal and vertical bars) is the best-fit value of α for soot aggregates, which have 1.7 ≤ D_f ≤ 1.9 (shaded range), taken from Köylü et al. (1995).