This talk is a continuation of my talk given on February 23 (see
Abstract, slides, recording), but it can also be followed independently of that previous part. On February 23, I did not have much time to discuss the fact that there exists \(α_0<1\) such that the fractal percolation is almost surely purely α-unrectifiable for all \( α > α_0\). This result is from a joint paper with Esa Järvenpää, Maarit Järvenpää, Tamás Keleti and Tuomas Pöyhtäri. That paper is lengthy and contains many hard-to-follow technical details. In my talk, I try to explain some main ideas behind the complicated argument.