Fifth Homework Set Answers

2. Of the three f(α) curves, only (a) has maximum value 2. The maximum value of the f(α) curve is the dimension of the underlying attractor. Of the three IFS images, only (f) fills the whole square (not uniformly, to be sure), so (a) corresponds to (f).

The IFS (e) is a subset of a gasket, perhaps the whole gasket, if filled non-uniformly. Thus the dimension of (e) is at most log(3)/log(2), about 1.58. This matches the maximum value of the f(α) curve (b).

The IFS (d) consists of N = 4 pieces, each scaled by about r = 0.45,, hence has dimension log(4)/log(1/.45), about 1.74. This matches the maximum value of the f(α) curve (c).

(a)   (b)   (c)

(d)   (e)   (f)

Return to Homework 5 Practice.