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# complex systems

## Latest Articles

### The New Math of How Large-Scale Order Emerges

The puzzle of emergence asks how regularities emerge on macro scales out of uncountable constituent parts. A new framework has researchers hopeful that a solution is near.

### Complex Structures Like ‘Entropy Bagels’ Emerge From Simple Rules

Simple rules in simple settings continue to puzzle mathematicians, even as they devise intricate tools to analyze them.

### The Quest to Decode the Mandelbrot Set, Math’s Most Famous Fractal

For decades, a small group of mathematicians has patiently unraveled the mystery of what was once math’s most popular picture. Their story shows how technology transforms even the most abstract mathematical landscapes.

### New Proof Finds the ‘Ultimate Instability’ in a Solar System Model

For the first time, mathematicians have proved that planetary orbits in a solar system will always be unstable.

### A New Idea for How to Assemble Life

If we want to understand complex constructions, such as ourselves, assembly theory says we must account for the entire history of how such entities came to be.

### Simpler Math Predicts How Close Ecosystems Are to Collapse

By replacing thousands of equations with just one, ecology modelers can more accurately assess how close fragile environments are to a disastrous “tipping point.”

### Starfish Whisperer Develops a Physical Language of Life

Nikta Fakhri is adapting and extending concepts from physics to describe how tiny biological components give rise to living organisms.

### The Year in Math

Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.

### Chaos Researchers Can Now Predict Perilous Points of No Return

A custom-built machine learning algorithm can predict when a complex system is about to switch to a wildly different mode of behavior.