
84 Pedodiversity
at step k and 4
k
reduced copies are needed to recover it. Then the self-
similarity dimension is 1.261.
261.1)3log(/)4log()3/1log(/)4log( ==−=
kk
D
ss
The Sierpinski carpet is another example of a self-similar fractal
(Fig. 4.2). The square is the initiator in this case. The generator is obtained
by dividing the square into nine smaller equal squares and extracting the
one from the center. If the Sierpinski carpet is reduced by a factor of one
third and eight copies are made, then these copies can be pasted together
to give back the Sierpinski carpet; one ninth reduction requires 64 copies,
one twenty seventh reduction requires 512 ...