Don’t miss #ComplexityThoughts: Issue #83 This week you will find latest research on AI, biology and population dynamics. open.substack.com/pub/manlius/...

A 5-fold quasicrystal as the orbit of the quasiaddition x ⊣ y = τ²x − τy on a regular pentagon (τ = Φ + δ). At δ = 0 you're exactly at the golden ratio. Sweep around it and the lattice breathes. Made with #python #numpy #matplotlib and #marimo.

A few days ago, I had the pleasure of giving a guided tour of my exhibition The Invention of Time to Sebastià Xambó, my high school mathematics teacher, who introduced me, back then, to some great books (lk Arbib’s here). Never forget to tell your teachers how important they have been in your life.

The last one?

It's taken way longer than I had originally anticipated (about 18 months), but I'm super excited to say that the project to translate Nils Aall Barricelli's groundbreaking 1954 paper on computational evolution and artificial life - "Esempi Numerici di Processi di Evoluzione" - is now complete! [1/2]

Sono uscite le nuove lezioni sul Corriere! 1) www.corriere.it/le-lezioni-d... 2) www.corriere.it/le-lezioni-d... 3) www.corriere.it/le-lezioni-d... #physics #philosophy #energy #entropy #information

Each cloud is one root of a 4th degree polynomial, smeared by Gaussian noise on the polynomial's coefficients. The cloud size at root r_k is controlled by κ_k = 1/∏_{j≠k}|r_k−r_j|, it diverges at near-collisions. Background: phase of p(z). Sound on 🔊 #MathArt #NumericalAnalysis

Pseudozeros of polynomials. Made with #python #numpy #matplotlib in a #marimo notebook

p(x) = x(x − r) One root pinned at 0, one orbiting Colors: arg(p(z)) White curves: ε-pseudospectrum, |p(z)| ≤ ε·√(1+ |z|² + |z|⁴) Black cloud: roots of 100k randomly perturbed copies of p. Made with #python #numpy #matplotlib inside a #marimo notebook. #math

No to summer!

In these dark days, when a few men—who believe themselves touched by God (often sexual harassers, empathy-less fanatics, and anti-science figures)—use religion to drag millions into hatred, I can’t help but be reminded of a quote by Steven Weinberg.

A stunning visualization born from a collaboration with @manlius.bsky.social : 55,486 galaxies and 29,555 streamlines tracing how matter flows across our local universe, built on data from the CosmicFlows-4 project. Article in the first reply 👇

Polynomial argument on the complex plane. Made with #python #numpy #matplotlib. @marimo.io notebook on molab👇👇👇👇👇👇👇

A degree-100 polynomial p. Color each point z of the plane by arg(p(z)). The zeros are the points where the full color cycle closes on itself. Let the roots drift, and the colors flow with them. Made with #python #numpy #matplotlib in a @marimo.io notebook.

The complex plane colored by the argument of a polynomial. Each root drifts along a tiny orbit and the color vortices follow: every swirl is a zero. Made with #python #numpy #matplotlib in a @marimo.io notebook.

Faticare in montagna è un privilegio, viva la libertà, viva il 25 Aprile. #skialp

Polynomial roots. Made with #Python #NumPy #Matplotlib in a #marimo notebook.

This paper claims you can define all elementary functions using just two primitive operations: the constant 1, and the binary function eml(x, y) := e^x - log(y). It's probably true but it may need work because it effectively defines i as √-1 ignoring the two choices here. arxiv.org/abs/2603.21852

Oggi su Specchio de La Stampa

Sembra un filmato generato con AI, invece è una breve clip che ho potuto realizzare grazie alle immagini reali ad alta risoluzione pubblicate dalla NASA. Sono foto vere, scattate da un essere umano con una Nikon tra le mani a oltre 400.000 km di distanza dal nostro pianeta. C'è solo da godere.

Polynomial roots. Made with #Python #NumPy #Matplotlib and @marimo.io

Polynomial roots. Made with #Python #NumPy #Matplotlib and @marimo.io

Enjoying the descent. Made with #pyt.... Made with a little bit of effort.

I have found this gem in the web, and I couldn't agree more. Maybe, the only change I'd consider is Bees → BeeRs but 🐝 are way more important for the 🌍

IFS Fractals with Memory and a Little Bit of Non-Linearity. Made with #Python #NumPy #Matplotlib and @marimo.io

#mybackyard #nopython

Holy moly! There are 40 old Soviet uranium-fueled nuclear reactor cores in orbit! I didn't know that: mastodon.social/@sundogplane... A while back, one exploded over northern Canada and spewed out radioactive material: www.cbc.ca/arts/operati...

Algebraic creatures Made with #Python #NumPy #Matplotlib and @marimo.io

Algebraic creatures Made with #Python #NumPy #Matplotlib and @marimo.io

Algebraic creatures Made with #Python #NumPy #Matplotlib and @marimo.io

A fair coin "knows" π. Stop flipping when heads first outnumber tails. The expected fraction of heads is π/4. Average many trials → estimate π. Result by J. Propp, animated for #PiDay. Made with #Python #NumPy #Matplotlib and @marimo.io #Mathematics #MathArt #CreativeCoding

An eigen-starfish! Made with #python #numpy #matplotlib and @marimo.io

El Nino in arrivo e potrebbe essere forte. I modelli a medio-lungo termine stanno convergendo verso il ritorno della fase ENSO positiva, nota come EL NINO. Dopo un anno e mezzo dominato da una debole NINA e da fasi neutre, sembra sempre più probabile il ritorno del NINO a partire da maggio. 1/7

Inverno 2025/2026 Secondo i dati forniti da Copernicus, l’inverno appena trascorso (quello meteorologico) è stato, a livello globale, il quinto più caldo della serie storica. Lo scarto rispetto alla media 1991-2020 è stato pari a +0,51 gradi. 1/4

No, it's not a pipe dream! For more details on how category theory helps us model complex systems, try the talk, slides and papers here: math.ucr.edu/home/baez/co...

Piogge tossiche, aria irrespirabile. Teheran è avvolta e sovrastata dai fumi tossici prodotti dagli incendi dei deposti di petrolio della città. Le riserve sono state bombardate dalle forze israeliane (come ufficialmente dichiarato). 1/6

The argument principle, made visual. Drag the zeros of a cubic and watch the image curve wind around the origin, each zero inside Γ contributes exactly one winding. Inspired by Needham's Visual Complex Analysis. Built with #python and @marimo.io + #wigglystuff. Code 👇👇👇👇

Created using pure vibe coding with Claude Code: a minimal, distraction-free writing app with local LLM assistance (LMStudio/Ollama), Markdown & Mathtext support. Creative writing with AI help, no privacy or copyright worries. Repo in the first comment 👇👇👇, contributors welcome!

New in the @marimo.io gallery! How do you invert a matrix? Let a system reach thermal equilibrium and read the answer from its fluctuations. Interactive notebook on thermodynamic linear algebra, based on Aifer et al. (2024).👇👇👇👇

📊 This paper by Crameri et al. (2020) shows why #color choice in figures matters. Rainbow 🌈 & red–green 🛑❇️ colormaps distort gradients, create artificial boundaries, & exclude readers with #ColorVision deficiency. They quantify visual error & argue for perceptually uniform, #CVD friendly colormaps👍

The Bak-Sneppen model is now in the official @marimo.io gallery, my first notebook there 🍃 A 3D interactive simulation of self-organized criticality: complexity emerging from the simplest rule. Link below 👇👇

A matter of convergence. Made with #Python #NumPy #Matplotlib inside a #marimo notebook.

Partial sums of geometric series. Made with #Python #NumPy #Matplotlib inside a @marimo.io notebook.

Partial sums of the Taylor series of the exponential function. Made with #Python #NumPy #Matplotlib inside a @marimo.io notebook.

From github.com/cduck/hyperb... Cc @sconradi.bsky.social Poincaré disk FTW