Table 1.

The volume–size distribution obtained: (a) from several iterations of a fractal cube; and (b) from several iterations of a Menger Sponge

IterationNumberEdgeCumulative volumePercentage of total
(a) Fractal cube
 111.00000000001.0000100
 260.50000000001.750042.9
 3300.25000000002.218821.1
 41500.12500000002.511711.7
 57500.06250000002.69486.79
 637500.03125000002.80934.07
 718 7500.01562500002.88082.48
 893 7500.00781250002.92551.53
 9468 7500.00390625002.95340.95
102 343 7500.00195312502.97090.59
1111 718 7500.00097656252.98180.37
1258 593 7500.00048828132.98860.23
13292 968 7500.00024414062.99290.14
141 464 843 7500.00012207032.99560.09
157 324 218 7500.00006103522.99720.06
1636 621 093 7500.00003051762.99830.03
(b) Menger Sponge
 0
 170.33333333330.2593100
 21400.11111111110.451342.6
 328000.03703703700.593624.0
 456 0000.01234567900.698915.08
 51 120 0000.00411522630.777010.05
 622 400 0000.00137174210.83486.93
 7448 000 0000.00045724740.87764.88
 88 960 000 0000.00015241580.90943.49
 9179 200 000 0000.00005080530.93292.52
103 584 000 000 0000.00001693510.95031.83
1171 680 000 000 0000.00000564500.96321.34
121 433 600 000 000 0000.00000188170.97270.98
1328 672 000 000 000 0000.00000062720.97980.72
14573 440 000 000 000 0000.00000020910.98500.53
1511 468 800 000 000 000 0000.00000006970.98890.39
16229 376 000 000 000 000 0000.00000002320.99180.29
174 587 520 000 000 000 000 0000.00000000770.99390.21
1891 750 400 000 000 000 000 0000.00000000260.99550.16
191 835 008 000 000 000 000 000 0000.00000000090.99670.12