The logistic map is a good starting point if you want to understand chaos and complexity in a simple setting. As we vary the free parameter "r" limit cycles appear on the left plot. At first there is only one, then 2, then 4, then more and more, shown in the right. (1/2)

8 new Near-Earth Asteroids have been discovered by the Vera Rubin Observatory from just 10 hours of sky scanning over the course of a few nights. Imagine what Rubin will do when it's fully operational. #LSST #RubinObservatory #NEO

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Just another weekend playing board games in the backyard #MindclashGames has some amazing game designers. In #Anachrony you receive boons from your future self, but, if you don't remember to send those boons back to your past self, time paradoxes ensue!

Happy Summer Solstice!

I'm great at hide and seek.

The world gently asked, "where are you, little one?"
I tried to hide, and it flickered, fading at my silence.
"Here! I'm here!" I yelled, and felt the grass under my toes.

I'm terrible at hide and seek.

Inspired largely by @ricardsole.bsky.social's 2004 paper, we looked at the topologies of more modern photochemical chemical networks in 2023 ➡️ agupubs.onlinelibrary.wiley.com/doi/10.1029/...

See other great work on this topic by @tessafisher.bsky.social et al.!

This is Ursy's "Um, back scratches haven't started yet, should I go chase the cat instead?" look.

Chaos is unpredictability, a property even deterministic systems display. In the Lorenz system, two trajectories, infinitesimally close to each other, will begin to diverge. Can you predict when? #chaos #dynamicalsystems #LorenzAttractor #Mathematics

The Lorenz system is a simple set of ordinary differential equations, yet exhibits complex and chaotic behavior. Simple rules can lead to incredibly rich, unpredictable behavior. The loops you see below are called an attractor: they attract far off points into their chaotic orbit.

It was warm enough today to sit on the Adirondack chairs while math-ing. These two boopers decided to join. It was a good day.

What is agency?

This is a model of a protocell based on a model studied by Matthew Egbert, a brilliant collaborator at the University of Aukland whose research interests space the gamut of artificial life.

(Continued...)

From fireflies to seizures, synchronization is a critical phenomenon in many biological systems. We construct the Langevin equation for localized interventions on the Kuramoto model to describe how to induce or prevent synchronization. Check out our new paper: journals.aps.org/prresearch/a...