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# Fractals

## Latest Articles

### Number of Distances Separating Points Has a New Bound

Mathematicians have struggled to prove Falconer’s Conjecture, a simple, but far-reaching, hypothesis about the distances between points. They’re finally getting close.

### ‘Entropy Bagels’ and Other Complex Structures 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 Famed 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.

### Mathematicians Cross the Line to Get to the Point

A new paper establishes a long-conjectured bound about the size of the overlap between sets of lines and points.

### New Proof Threads the Needle on a Sticky Geometry Problem

A new proof marks major progress toward solving the Kakeya conjecture, a deceptively simple question that underpins a tower of conjectures.

### The Scientist Who Developed a New Way to Understand Communication

Mark Braverman has spent his career translating thorny problems into the language of information complexity.

### The Journey to Define Dimension

The concept of dimension seems simple enough, but mathematicians struggled for centuries to precisely define and understand it.

### Mathematicians Set Numbers in Motion to Unlock Their Secrets

A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.

### The Map of Mathematics

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.