Menger_sponge_(IFS).jpg

After 4 iterations:

Iteration Rule:

Dimensions after 4 iterations:

Limiting Properties, Hausdorff Dimension:
Linkto>Wolfram Alpha Widget

After 30 iterations
{"surface area = 5.06588x10^10 (times initial face area)
volume = 0.0123023% (of initial Cubic volume)"}
That's right ... over 50,658,800,000 times more surface area
which is approx.
~~ 0.17 x the number of stars in our galaxy
~~ 0.48 x the number of people who have ever lived (~~ 1.1 x10^11)
~~ 7.8 x the number of people alive today (~~ 6.5 x 10^9)
for, basically the same starting volume as ZERO iterations !