@hildabast

The drawbacks of https://instances.social are known, but my guess is that the s^{-0.5} power law distribution of the number N of instances per instance size s [1] is probably insensitive to the small number of instances that are effectively <s>defederated</s> off-network.

The N \propto s^{-0.5} distribution and the deviations from that [1] don't yet seem to be well-known. #SMinusHalfDistribution

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[1] https://codeberg.org/boud/fedistats_naive

5/7
(5) Distribution (total users): multiplying users by instances shows that above s = 10000, very roughly a bit less than a million users (more in one case) are in each of the eight bins from 10,000 to 1,000,000, making a bit less than 8 million users in total (in fact, about 6 million, also includes the smaller size instances).

#MastodonStatistics

3/7
(3) Distribution: a single power law of about

3600 s^{-0.55} instances,

for instances each with s user accounts, provides a reasonable looking fit (Theil-Sen) [1][2]. There are a lot more small instances and a lot less big instances. This is good, and consistent with an approximate self-similar scaling.

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2/7
(1) Growth: The third wave since 28 Oct 2022 has stabilised to around 50k new accounts/day. Constant extrapolation * 1yr => 18M new accounts by Dec 2023. Exponential extrapolation over 3 waves => 100k daily by 1 Jan 2023. [1][2]

(2) Growth: Increases in instances also go in waves, each exponentially decaying. Long term exponential extrapolation (robust = Theil-Sen) over all measured waves => 10k new instances/day by 1 Jan 2023.

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