It's been 7 months since my last post. The process of downsizing to a smaller home last winter put my projects on hold.
Although fractals have stubbornly refused to appear in my investigation of self-similar surface roughness, they have shown up at my day job as a data scientist at Digilant.
Investigating the possibility of combining weekly counts of unique user IDs, I discovered that the L^p-norm does so with surprisingly good accuracy on digital advertising datasets. The L^p-norm implies a scaling law. My son Martin (who also works at Digilant) noticed that the scaling law exponent is a fractal dimension. The L^p-norm and scaling law are implied by the Pareto distribution of lifetimes in a population. This link between the L^p-norm and fractal dimension should have application beyond counting populations.
We wrote a paper about these results at https://arxiv.org/abs/1806.06772
