Fifth Homework Set Answers

7. The increments of both persistent and antipersistent fBm are normally distributed, hence mostly small. Consequently, for both, most driven IFS points lie on the backwards Z.

For persistent fBm changes tend to be in the same direction, so the driven IFS exhibits little oscillation between successive corners.

For antipersistent fBm changes tend to reverse sign, leading to oscillation between successive corners. This produces many points close to the 2-cycle between corners 1 and 2, between corners 2 and 3, and between corners 3 and 4.

That is, (b) corresponds to antipersistent fBm, while (a) corresponds to fBm.

(a)   (b)

Return to Homework 5 Practice.