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# Patterns

## Latest Articles

### With Fifth Busy Beaver, Researchers Approach Computation’s Limits

After decades of uncertainty, a motley team of programmers has proved precisely how complicated simple computer programs can get.

### How to Build an Origami Computer

Two mathematicians have shown that origami can, in principle, be used to perform any possible computation.

### Math’s ‘Game of Life’ Reveals Long-Sought Repeating Patterns

John Conway’s Game of Life, a famous cellular automaton, has been found to have periodic patterns of every possible length.

### New Proof Shows That ‘Expander’ Graphs Synchronize

The proof establishes new conditions that cause connected oscillators to sway in sync.

### Turing Patterns Turn Up in a Tiny Crystal

The mechanism behind leopard spots and zebra stripes also appears to explain the patterned growth of a bismuth crystal, extending Alan Turing’s 1952 idea to the atomic scale.

### The Curious Strength of a Sea Sponge’s Glass Skeleton

A glass sponge found deep in the Pacific shows a remarkable ability to withstand compression and bending, on top of the sponge’s other unusual properties.

### Landmark Math Proof Clears Hurdle in Top Erdős Conjecture

Two mathematicians have proved the first leg of Paul Erdős’ all-time favorite problem about number patterns.

### How Randomness Can Make Math Easier

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

### Universal Pattern Explains Why Materials Conduct

Mathematicians have found that materials conduct electricity when electrons follow a universal mathematical pattern.