Forty years ago, a British mathematician named John Conway invented something he called the "Game of Life." It's not the silly board game you probably played in your youth. It is, rather, a type of cellular automaton or "CA" which is really a very simple type of computer program. The display is a grid of squares. In the grid, any kind of pattern may be placed by filling in squares. The rules of the game--the code of the program in essence--describe how a square will change with each run of the program. For instance, a square remains filled if it has either two or three neighbors. You can see some animated examples on the wikipedia Life page or at this interactive online version. From a set of very simple rules, the behavior is quite unpredictable, even life-like (hence the name) in a crude way.
But just recently, something totally new came about. A student, Andrew Wade, invented a pattern that produces a new version of itself. I.e. it reproduces. This had never been accomplished in the Conway Life CA, though many had tried. It's called a "spaceship" or "glider" because, as each new generation appears, it glides across the grid. It was given the name "Gemini" because of it's dual-lobed structure. You can see a picture of it, though in actuality, it is some 4 million squares in either direction. It takes over 30 million iterations to create the child copy, cannibalizing itself in the process. The scale of these numbers, if it is the smallest self-replicating entity in Conway's Life, give you an idea of why it was only just now invented after 40 years. I say "invented" because it was the product of an intense, concerted effort, using software to build and refine until the goal of self-replication was achieved. Now that's what I call intelligent design.
But could have such a pattern arisen by accident? After all, Conway's Life has been incorporated into screensavers, so it's probably had millions of cpu-hours testing randomly-generated patterns. On Sun's OpenLook desktop, it was the default screensaver, where filled cells used the Sun logo, color-coded with the number of steps that they'd been "alive." However, the grid was only a few hundred cells, and on the hardware it ran on, 30 million iterations would take about a year!
But I'd have to guesstimate that even on a grid with many billions of cells running for many trillions of iterations, Gemini or something like it would be very, very unlikely to occur by pure chance. The rules of Conway Life are extremely harsh, necessitating a very complex pattern to reproduce, as you can see in Gemini with all of it's structure.
The fascinating thing about that is, kinda like a real organism, it has all this defensive structure, which basically allows it to live just long enough to create the copy. As the defensive structure is being broken down, there's a tape structure in the middle, containing patterns that are used to build up the new structure.
Now of course the interesting question is, can we draw any conclusions about the evolution of life on Earth? It's too different I think, the rules are much more complex. Further, by contrast, those rules drive many processes that would tend to build things up: think about tides pushing sediments into pools, being filtered by buoyancy, and pumped with energy. A closer analog may be interstellar space, which you might even model using a CA, to see what it takes to build up, say, amino acids. In his book A New Kind of Science, Stephen Wolfram (creator of Mathematica) tries to make the case that modeling physical processes in terms of simple computational steps (in other words, a CA) can be a good alternative to equations, which is the traditional way, but become unwieldy as the complexity of a simulation grows. This is becoming more common; for example, at our summer team meeting last year, one of the geologists showed the results of a CA simulating the growth of stromatolites.