262931.fig.003a
(a) 998 × 1152 pixel rendering of the boundary of a Koch snowflake
262931.fig.003b
(b) Scale dependence of entropy of (a)
262931.fig.003c
(c) Scale dependence of fractal dimension of (a)
262931.fig.003d
(d) 2000 × 2000 pixel rendering of the boundary of a Koch island
262931.fig.003e
(e) Scale dependence of entropy of (d)
262931.fig.003f
(f) Scale dependence of fractal dimension of (d)
262931.fig.003g
(g) 1460 × 1460 pixel rendering of Pascal’s triangle (mod 3)
262931.fig.003h
(h) Scale dependence of entropy of (g)
262931.fig.003i
(i) Scale dependence of fractal dimension of (g)
262931.fig.003j
(j) 2187 × 2187 pixel rendering of the Sierpinski carpet
262931.fig.003k
(k) Scale dependence of entropy of (j)
262931.fig.003l
(l) Scale dependence of fractal dimension of (j).
Figure 3: Results of applying our algorithms to four renderings of mathematical fractals. The entropies in (b), (e), (h), and (k) are in nats, which are the natural units for information and entropy, with base rather than : 1 nat 1.44 bits, and are plotted for . All the fractal dimension plots (c), (f), (i), and (l) use in (6), except for (i) where for the circles. Horizontal bar indicates Hausdorff dimension of each mathematical fractal.