Oh I’d been looking for you. I’ve known it as the “degree of surprise” in Shannon entropy but it was the direct connection of Rényi entropy (generalization of the Shannon entropy) to fractal dimensions (which has held my interest for decades) that got me to here. I got to Rényi entropy via “Fractal Structure and Non-Extensive Statistics” which talked about Tsallis entropy which I got to from trying to figure out if intensive properties of matter were fractal (as the definition of “intensive properties” sounded a lot like self-similarity in fractals. “A diversity index (also called phylogenetic index) is a quantitative measure that reflects how many different types (such as species) there are in a dataset (a community), and that can simultaneously take into account the phylogenetic relations among the individuals distributed among those types, such as richness, divergence or evenness. These indices are statistical representations of biodiversity in different aspects (richness, evenness, and dominance).” https://en.wikipedia.org/wiki/Diversity_index

Oh I’d been looking for you. I’ve known it as the “degree of surprise” in Shannon entropy but it was the direct connection of
Rényi entropy (generalization of the Shannon entropy) to fractal dimensions (which has held my interest for decades) that got me to here. I got to Rényi entropy via “Fractal Structure and Non-Extensive Statistics” which talked about Tsallis entropy which I got to from trying to figure out if intensive properties of matter were fractal (as the definition of “intensive properties” sounded a lot like self-similarity in fractals.
 
“A diversity index (also called phylogenetic index) is a quantitative measure that reflects how many different types (such as species) there are in a dataset (a community), and that can simultaneously take into account the phylogenetic relations among the individuals distributed among those types, such as richness, divergence or evenness. These indices are statistical representations of biodiversity in different aspects (richness, evenness, and dominance).”
 
https://en.wikipedia.org/wiki/Diversity_index
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oh lookie lookie… it took some to get to this.
https://en.wikipedia.org/wiki/Intrinsic_dimension
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