#stern-brocot tree

[still-searching-for-et]

Using Stern-Brocot tree and fusc(n) recursive formula for the diatomic series.  Plotted the first 131,072 rational numbers.

Links to the Penn State paper “Recounting the Rationals” and a good read on the “Frequency of Rational Fractions on [0,1]”

https://www.math.upenn.edu/~wilf/website/recounting.pdf

https://arxiv.org/pdf/1802.00936.pdf

[right-fold]

Walking the Tree.

It’s just fun playing around with Stern-Brocot trees and a bit of Haskell…!

For any  fraction on the Stern-Brocot tree there is just one path to it from the root. That path can written as a sequence of left or right ‘turns’ at each node depending on whether the target node is smaller or larger than the current node. This leads to the

Stern Path

For example in this small tree

the path to, say,…

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