Ocean waves are "emergent phenomena" that arise out of the complexity of forces active in a large body of water. Photo by Chris Potter.


Francis Galton
I know of scarcely anything so apt to impress the imagination as the wonderful form of cosmic order expressed by the ‘Law of Frequency of Error’.

Gerd Gigerenzer et al
Probability and statistics have transformed our ideas of nature, mind and society, changing the structure of power as well as of knowledge.


On the Algorithmic Nature of the World
by Hector Zenil and Jean-Paul Delahaye

A test based on the theory of algorithmic complexity and an experimental evaluation of Levin’s universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature.

Extending Galton's Binomial Quincunx to the Trinomial Septcunx
by Jennifer Harlow, Bry Ashman, and Raazesh Sainudiin

A project to create a visual cognitive tool for graphically illustrating the construction of the binomial and trinomial random vectors in two and three dimensions.

The truth wears off
by Jonah Lehrer

All sorts of well-established, multiply confirmed findings have started to look increasingly uncertain. It’s as if our facts were losing their truth: claims that have been enshrined in textbooks are suddenly unprovable.

Games of Chance
by D. Graham Burnett

The Random Mechanical Cascade mechanism and The Law of the Normal at the Princeton Engineering Anomalies Research laboratory.

Does god play dice? Randomness vs. deterministic explanations of
idea originality in crowdsourcing

by Nikolaus Franke et al

Which factors are responsible for the success of crowdsourcing tournaments? A huge experiment suggests that randomness outperforms deterministic explanations by over 500%. (pdf)

In Mysterious Pattern, Math and Nature Converge
by Natalie Wolchover

A precise balance of randomness and regularity known as “universality” has been observed in the spectra of many complex, correlated systems: a decentralized bus system in Mexico, the internet, the Earth’s climate, the nucleus of uranium atoms, and certain elements of number theory.

Statistics Done Wrong
by Alex Reinhart

Most scientists don’t know how to do statistics. Statistics Done Wrong is a guide to the most popular statistical errors and slip-ups committed by scientists every day, in the lab and in peer-reviewed journals.


Entropy and art,
by Rudolf Arnheim

Order is a necessary condition for anything the human mind is to understand. Arrangements such as the layout of a city or building, a set of tools, a display of merchandise, the verbal exposition of facts or ideas, or a painting or piece of music are called orderly when an observer or listener can grasp their overall structure and the ramification of the structure in some detail. Order makes it possible to focus on what is alike and what is different, what belongs together and what is segregated. When nothing superfluous is included and nothing indispensable left out, one can understand the interrelation of the whole and its parts, as well as the hierarchic scale of importance and power by which some structural features are dominant, others subordinate. (pdf)

by Albert-László Barabási

Randomness does not rule our lives, contrary to what scientists had previously assumed. (abridged version online)


Mozarts's Musical Dice Game
In 1787, Mozart wrote the measures and instructions for a musical composition dice game. This site is an implementation of such a game.

Computer Animation of Money Exchange Models
produced by Justin Chen under the guidance of Victor Yakovenko

Does an iron law of inequality exists in perfect games of chance where all the players play rationally?

Uncunx Java Applet
by Jeffrey S. Rosenthal

This applet simulates an "uncunx" (a modification of the standard "quincunx" device) for illustrating probability distributions.

Interactive Graph of the Standard Normal Curve
by Jeff Sauro

Graph displays areas under sections of the Normal Curve, with the option of specifying the mean and standard deviation.

Plinko Probability
Drops balls through a triangular grid of pegs and see the balls random walk through the lattice. Watch the histogram of final positions build up and approach the binomial distribution.

Chance in Life and the World
An applet illustrating Schrödinger's concept of order as nothing more than statistical regularities.

Pendulum Waves
Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion.


Exploring Emergence
on Serendip
Articles with interactive exhibits on order dependent on randomness.


What Is Random?: chance and order in mathematics and life,
by Edward Beltrami

Order and randomness are really two sides of the same mysterious coin.


Bean Machine
The quincunx or Galton Box.

Michael McIntyre's home page
The ideas of Cambridge atmospheric scientist Michael McIntyre, Emeritus Professor, Centre for Atmospheric Science at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, with reference to "the unimaginably large number of ways for complex systems to go wrong."

Random Walks
“Random Walks” underline math techniques for predicting how share prices vary or the movement of molecules in a liquid. They have the potential to prove useful in the implementation of quantum computers, possibly the next generation of computer.