Percolation test

Credit: Kotryna Zukauskaite

Connections, relationships, or the ability to see how deep connections among said relationships occur  describes genius to yours truly without question. Seems the connection meme is a big deal with SA as well.

A branch of mathematics called percolation theory offers a surprising answer: just a few people can make all the difference. As users join a new network, isolated pockets of connected phones slowly emerge. But full east-to-west or north-to-south communication appears all of a sudden as the density of users passes a critical and sharp threshold. Scientists describe such a rapid change in a network's connectivity as a phase transition—the same concept used to explain abrupt changes in the state of a material such as the melting of ice or the boiling of water.

AKA phase transitions from water to ice is percolation theory writ large from this writer's perspective.

Credit: Jen Christiansen (graphic); Wee People font, ProPublica and Alberto Cairo (figure drawings)

It gets better.

Percolation theory examines the consequences of randomly creating or removing links in such networks, which mathematicians conceive of as a collection of nodes (represented by points) linked by “edges” (lines). Each node represents an object such as a phone or a person, and the edges represent a specific relation between two of them. The fundamental insight of percolation theory, which dates back to the 1950s, is that as the number of links in a network gradually increases, a global cluster of connected nodes will suddenly emerge.

Credit: Jen Christiansen (graphic); Wee People font, ProPublica and Alberto Cairo (figure drawings)

Awesome article to the max. Read SA's detailed piece The Mathematics of How Connections Become Global in its entiredty to learn why chaos and phase transitions rule. 

Had to add another :)

Credit: Jen Christiansen (graphic); Wee People font, ProPublica and Alberto Cairo (figure drawings)