A Hamiltonian path is a route that passes through every node in a graph exactly once. Finding Hamiltonian paths can overload even the best-known algorithm for the job. Finding Eulerian paths that pass through every edge is computationally simpler. https://buff.ly/45bxIIo

This is the Weierstrauss function, a “monster” that is continuous everywhere but differentiable nowhere. First published in 1872, it prompted scrutiny of assumptions in calculus. Similar functions are used to study random motion and analyze risk. www.quantamagazine.org/the-jagged-m...

It was a fun challenge animating a deep zoom into a Weierstrass function—continuous everywhere, differentiable nowhere—for today's article by Solomon Adams in @quantamagazine.bsky.social

I wrote a spatial indexing algorithm that follows the path of a recursive space-filling curve (akin to a Hilbert curve but designed to proceed diagonalwise in 3D). Good for sorting the 148 named CSS colors into a black-to-white spectrum:

observablehq.com/@pamacha/sor...

Another experiment with UMAP – nested embeddings! A spherical embedding of the scikit-learn digit dataset, along with independent embeddings for each digit. Preprocessed in Python, visualized with D3.js:

observablehq.com/@pamacha/nes...

A first pass at UMAP on a sphere! The scikit-learn digit dataset, embedded with Python, visualized with JS, packaged & deployed with Observable Framework:

pamacha.observablehq.cloud/spherical-um...