AKA Fine-Tuning The Chaos Machine
The above image is the perfect example of a moiré lattice and where it comes from. I noticed it while watching a lecture by a scientist cited below, for being the first to discover Hofstadter's Butterfly in real life. It's just the best image I've seen to explain what a moiré lattice is.
Credit: Graphene hBN Moire Lattices - taken from the presentation Bloch, Landau, and Dirac - Hofstadter's Butterfly in Graphene by Philip Kim - Kavli Inst 2018 [youtube link]
The perimeter of ignorance in science is also the front door of chaos theory. You could call it a lot of other things, most of which are listed in the tags for this post, but mostly, anything that's "too complicated" for us to understand right now, it's chaos-related. Discoveries in this field come from a bunch of different places, like interdimensional graphene, like topological operators, like epilepsy surgery.
Harnessing chaos: How the brain turns randomness into robust memory
Jan 2025, phys.org
Previous work on brain-imitating artificial intelligence systems known as neural networks suggested that injecting random fluctuations into their activity could actually improve their performance as they learned to perform a task.Noise appears to increase the amount of time it takes for inhibitory neuron connections with other neurons to weaken. This slowing effect in turn stabilizes neural patterns of activity related to memories, helping them persist over time.
(This whole thing makes me think very differently about background noise, and maybe even the idea of 'functional music')...
via Columbia Engineering Systems Intelligence Laboratory: Nuttida Rungratsameetaweemana et al, Random noise promotes slow heterogeneous synaptic dynamics important for robust working memory computation, Proceedings of the National Academy of Sciences (2025). DOI: 10.1073/pnas.2316745122
How topology drives complexity in brain, climate and AI
Feb 2025, phys.org
Yes it does
Transformative framework for understanding complex systems, using the new field of higher-order topological dynamics, and creating a connection between topological structures and emergent behavior. This comes from the field of information theory, and combines fusion of topology, higher-order networks, and non-linear dynamics.
via University of London: Ana P. Millán et al, Topology shapes dynamics of higher-order networks, Nature Physics (2025). DOI: 10.1038/s41567-024-02757-w
(Many body problem and higher order networks are the same thing - "interactions that extend beyond simple pairwise relationships".)
Most of us need to know: Hofstadter's butterfly (1976) was discovered before Mandelbrot coined the term "fractal" (1980), so he didn't know what to call it.
Hofstadter's butterfly: Quantum fractal patterns visualized
Feb 2025, phys.org
"Our discovery was basically an accident. We didn't set out to find this."This is the first time Hofstadter's butterfly has been directly observed experimentally in a real material.It was found using a moiré lattice - they were investigating superconductivity in twisted bilayer graphene, and when you hear twisted layers, you know we're also talking magic angle sandwiches. They used a scanning tunneling microscope to image moiré crystals at atomic resolution and examine their electron energy levels. The microscope works by bringing a sharp metallic tip less than a nanometer from the surface to allow quantum "tunneling" of electrons from the tip to the sample.
via Princeton University: Kevin P. Nuckolls et al, Spectroscopy of the fractal Hofstadter energy spectrum, Nature (2025). DOI: 10.1038/s41586-024-08550-2
Fitness centrality: New tool finds critical points in everything from cybersecurity to ecological conservation
Jan 2025, phys.org
The Vienna Complexity hub making waves
This approach is particularly good at finding nodes that, if removed, would isolate many other parts of the network—similar to a server failure interrupting the connection of many users in a communication network or a pump failure in a water supply network paralyzing the supply of water to districts.Species in ecological networks, nodes in cybersecurity, roads in transportation networks. That's great. But it's people where this really has impact. Imagine trying to disable a social movement that could disturb the social fabric of a nation. You find the people, the nodes, at the center of the social network, and ... remove them, let's say.
via Complexity Science Hub Vienna: Vito D P Servedio et al, Fitness centrality: a non-linear centrality measure for complex networks, Journal of Physics: Complexity (2025). DOI: 10.1088/2632-072X/ada845
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