Welcome to Quantum Magazine's podcast.

Each episode we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

In Raiders of the Lost Ark, Indiana Jones is on a quest to find a secret chamber that holds the legendary

arc of the covenant. There's a trick to finding its exact location. The sun must shine through

a special crystal in a certain room at a certain time of day, revealing a secret map.

This is the stuff movies and myths are made of.

The idea that essential information can be revealed when circumstances are just right.

This idea also appears in mathematics, sometimes in unlikely settings.

Three mathematicians have proven that when a certain type of randomness is tuned perfectly,

intricate geometric shapes emerge in plain sight.

It's similar to the map revealed on the floor in Indiana Jones.

The shapes that emerge are checkerboard-like designs arranged at random across grids that are themselves

constructed by a random process. You'd think this piling of randomness atop randomness would

produce a mess. But as it turns out, in the same way that every snowflake is unique,

but all snowflakes are snowflakes, the disorder converges to a universal form, provided that the

conditions are just right. Everyone knows that mathematicians study shapes. Most of those shapes

follow deterministic rules. If I give you instructions for constructing

a sphere, you'll construct the exact same sphere every time. But mathematicians also study shapes

constructed by random processes. Think about the shape created when you take a random walk if you trace your meandering path.

Besides the random walk, there are other kinds of random geometric objects. These include random

two-dimensional surfaces like a landscape filled with randomly pitched hills and valleys and

...