Fractran (previously) is a Turing Complete language invented by John Conway (yes that John Conway) that uses only a simple list of fractions to form each program. Astonishingly it takes only a list of 14 fractions to form a program to generate all the primes. Here's the man himself explaining how it all works. [more inside]
Discovering Free Will (Part II, Part III) - a nice discussion of the Conway-Kochen "Free Will Theorem". [more inside]
Epic Conway's Game of Life. Sure, there's been lots of Conway's Life stuff on MeFi previously [1 2 3], but this squeezes a lot of awesome stuff into a short video.
Rational reductionist approaches to the neural basis for beauty run a similar risk of pushing the round block of beauty into the square hole of science and may well distill out the very thing one wants to understand.An essay by Bevil Conway and Alexander Rehding in PLoS Biology. (via)
The Angel Problem. The Angel and the Devil play a game on an infinite chess board...
A functional self-replicator has been designed for Conway's game of life. The deceptively simple automata 'Conway's game of life' is a model system that illustrates how simple 'physics' can give rise to incredibly complex phenomena. Although a menagerie of existing patterns have been discovered/engineered that display a variety of interesting behavior (eg here), there are also many unanswered questions about what is possible within the simulation. Recently, life-enthusiast mscibing succeeded in designing a universal constructor pattern that is capable of building a functional copy of itself. Its execution can be viewed directly (though it takes a while!) using Golly, a sweet, open-source app for viewing life simulations, as well as other cellular automata.
The Free Will Theorem - "If there exist experimenters with (some) free will, then elementary particles also have (some) free will." (previously)
Researchers discover gigantic "Caterpillar" spaceship that travels at (17/45)c. Just another exciting development in the Game of Life (previously).
Phutball (Rules, Java Applet), aka Philosophers' Football or ConwayGo is a deceptively simple 2-player game you can play on a Go board, or any rectangular grid. (It may be simple, but finding the right move is [PDF] NP Complete.)
President Bush pledged in 2003 that "A free Iraq will not be a training ground for terrorists... A free Iraq will not destabilize the Middle East." This past January, the CIA's National Intelligence Council observed that Iraq had become "a training ground, a recruitment ground" for jihadists. Now the senior Marine commander in Iraq, Lt. Gen. James Conway -- in a statement that has not yet been picked up by the media -- acknowledges that the war is furnishing a new "a training ground" for foreign fighters trained in urban warfare who will export terror all over the world, saying, "But there's not much we can do about it at this point in time."
The Geometry Center at the University of Minnesota, while now closed, maintains an awesome website with tons of math resources. I like sphere eversion, i.e. turning a sphere inside out. Link is to script of video, which explains things pretty well. Here is a clip [QT]. Also good: notes from a class on geometry and the imagination that John Conway and some friends gave awhile back. Old but good.
Beyond Life [Java]. Mirek's Cellebration is an beautiful applet for exploring all sorts of cellular automata. Source code and standalone version also available.
You may have heard of Conway's Game of Life, where pixels "live" or "die" based on a few simple rules about how many neighbors they have. But did you know that in the 30 years since the game was created, Life enthusiasts have (created? discovered?) an extensive catalog of (objects? creatures?) which interact to form some amazing, nifty, grinning, sometimes beautiful, rube-goldberg, occasionally even a little scary patterns often starting from the simplest of building blocks? (Including a Turing machine!) Or that a lone pixel can exert remarkable control over its environment? Now you can see in a few seconds in a java applet, on your desktop, or even on a PalmOS handheld the outcome of simple patterns that, when first discovered, no computer could handle. A mind blowing example of the power of emergent properties.
Eric's Treasure Trove of Life. The cellular automaton known as 'Conway's Game of Life', that is. Many things to see, from the Table to the B-Heptomino, and even an AK47 Reaction. There's a huge community out there devoted to discovering new 'still lifes', 'puffers' and 'induction coils'. Who would have guessed Life could be so interesting?