(a) Starting with an equilateral triangle (each side of length 1 unit) construct the inverted Koch snowflake up to stage 2 on graph paper.At each stage, each segment is 1 3 the length of the previous segment, and each segment is replaced by four segments. Determine the area bounded by the true fractal and the fractal dimension.

[14]

(b) Prove that D1 = lim l→0

N i=1 pi ln(pi )

−ln(l)

, by applying L’Hopital’s rule to the equation Dq = lim l→0 1

1 − q ln

N i=1 p q

i (l)

−ln l

.

[6]