Governance by those who do the work.

Sunday, July 8, 2018

Fractal Scaling of Population Counts Over Time Spans

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

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