patterns – Quanta Magazine

With Fifth Busy Beaver, Researchers Approach Computation’s Limits

Ben Brubaker — Tue, 02 Jul 2024 14:00:00 +0000

Once upon a time, over 40 years ago, a horde of computer scientists descended on the West German city of Dortmund. They were competing to catch an elusive quarry — only four of its kind had ever been captured. Over 100 competitors dragged in the strangest creatures they could find, but they still fell short. The fifth busy beaver had escaped their clutches. Of course, that slippery beast and its...

Source

How to Build an Origami Computer

Jordana Cepelewicz — Tue, 30 Jan 2024 15:34:13 +0000

In 1936, the British mathematician Alan Turing came up with an idea for a universal computer. It was a simple device: an infinite strip of tape covered in zeros and ones, together with a machine that could move back and forth along the tape, changing zeros to ones and vice versa according to some set of rules. He showed that such a device could be used to perform any computation.

Source

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

Alex Stone — Thu, 18 Jan 2024 15:36:42 +0000

In 1969, the British mathematician John Conway devised a beguilingly simple set of rules for creating complex behavior. His Game of Life, often referred to simply as Life, unfolds on an infinite square grid of cells. Each cell can be either “alive” or “dead.” The grid evolves over a series of turns (or “generations”), with the fate of each cell determined by the eight cells surrounding it.

Source

New Proof Shows That ‘Expander’ Graphs Synchronize

Leila Sloman — Mon, 24 Jul 2023 14:36:23 +0000

Six years ago, Afonso Bandeira and Shuyang Ling were attempting to come up with a better way to discern clusters in enormous data sets when they stumbled into a surreal world. Ling realized that the equations they’d come up with were, unexpectedly, a perfect match for a mathematical model of spontaneous synchronization. Spontaneous synchronization is a phenomenon in which oscillators...

Source

Turing Patterns Turn Up in a Tiny Crystal

Elena Renken — Tue, 10 Aug 2021 13:28:19 +0000

The stripes looked like a mistake. Several years ago, a team of physicists at Stanford University led by Aharon Kapitulnik was trying to grow a thin layer of bismuth crystal on a metallic surface. But instead of forming a uniform sheet, the crystal became a patchwork of uneven growth. In some areas — those where the crystal layer was only one atom thick — a striking design emerged.

Source