Mathematical Modelling of Abiogenesis
16 June 2010 by Jacob Aron
IF YOU found a self-replicating organism living inside your computer, your first instinct might be to reach for the antivirus software. If, however, you are Andrew Wade, an avid player in the two-dimensional, mathematical universe known as the Game of Life, such a discovery is nothing short of an epiphany.
When Wade posted his self-replicating mathematical organism on a Life community website on 18 May, it sparked a wave of excitement. "This is truly ground-breaking work," wrote a fellow Life enthusiast, Adam Goucher, on the website Game of Life News. "In fact, this is arguably the single most impressive and important pattern ever devised."
A first for the game, the replicator demonstrates how astounding complexity can arise from simple beginnings and processes - an echo of life's origins, perhaps. It might help us understand how life on Earth began.
The Game of Life is the best-known example of a cellular automaton, in which patterns form and evolve on a grid according to a few simple rules. You play the game by choosing an initial pattern of "live" cells, and then watch as the configuration changes over many generations as the rules are applied over and over again (see "Take two simple rules".
The rules of the game were laid down by mathematician John Conway in 1970, but cellular automata first took off in the 1940s when the late mathematician John von Neumann suggested using them to demonstrate self-replication in nature. This lent philosophical undertones to Life, which ended up attracting a cult following.
Life enthusiasts have since catalogued an entire zoo of interesting patterns, such as "spaceships" that travel across the grid, or "guns", which constantly spawn other patterns. But a pattern that spawned an identical copy of itself proved elusive.
A programmer living in Toronto, Canada, Wade first dabbled with Life during the 1990s but eventually lost interest and moved on. It wasn't until 2009 that he began to experiment anew, spurred on by discoveries in the previous decade.
One such discovery was the universal constructor, a pattern of cells that can be programmed to spit out a variety of others in subsequent generations. In an effort to create a replicator, Life enthusiasts had tried connecting this constructor to a second pattern known as a "computer" because it is capable of arithmetic. But the result ran too slowly to be of any practical use.
Wade's breakthrough came after his real-life child was born. The duties of fatherhood limited the time he could spend playing the game, so he replaced the "computer" with a much simpler pattern called an "instruction tape", made up of smaller patterns known as "gliders". By placing these at precise intervals, he created a program that feeds into the constructor and dictates its actions, much like the punched rolls of tape once used to control the first computers.
This proved a smart move. "I wanted to see it working as soon as possible," he says. "I stripped out as much as I could, which cut out leads that could have taken me a long time to pursue."
Dubbed Gemini, his creature is made of two sets of identical structures, which sit at either end of the instruction tape. Each is a fraction of the size of the tape's length but, made up of two constructor arms and one "destructor", plays a key role. Gemini's initial state contains three of these structures, plus a fourth that is incomplete.
As the simulation progresses the incomplete structure begins to grow, while the structure at the start of the tape is demolished. The original Gemini continues to disassemble as the new one emerges until after nearly 34 million generations, new life is born (see diagram).
The "offspring" is identical to its parent, but it has shifted up and slightly to the left - another first for Life: every other known pattern moves along one of the eight compass points, but Gemini travels across the grid in a north by north-west direction.
As a result of this, and the ability to program universal constructors using simple tape, Gemini has reinvigorated Life. Players are now looking forward to creating ever more novel and complex patterns. "Another milestone might be a self-replicating pattern that creates increasing copies of itself, or a space-filling replicator that can make multiple copies to eventually fill an arbitrarily large area of the Life plane," says Dave Greene, who helped create the universal constructor Wade used.
Gemini's implications extend to the real world. "There's a fascination with the complexity that is coming out of these incredibly simple rules," says Susan Stepney, a computer scientist at the University of York, UK, who ran Gemini inside Life, at New Scientist's behest. "Eventually that leads on to biology, putting simple atoms together to make complex life."
Because Wade's replicator copies itself piece by piece, it is analogous to a photocopier rather than a living cell, she says. But it still has implications for understanding life. "The fact that it's doing it differently from biology is in itself interesting, because it shows there are multiple ways of solving the same problem. It's a very impressive technical achievement."
It's doing it differently from biology, showing there are multiple ways of solving the same problem
Stephen Wolfram, famous for championing cellular automata as a replacement for scientific equations, disputes Gemini's relevance to living cells. He says that feeding a program to a universal constructor merely to create a self-replicating creature - Wade's approach, and Von Neumann's original suggestion - is overkill. He points to a much simpler example, a one-dimensional cellular automaton known as "rule 90" that will duplicate any starting line of cells after a certain number of steps.
Rather than contributing to our understanding of life, Wolfram says Wade's discovery could help devise ways to build a molecular-scale computer, starting from tiny components like the cells in Life. "This discovery is helping us understand the world of constructing things from dumb components," he says.
Edit: Subject name change to be more specific...
"Experiments are the only means of knowledge at our disposal. The rest is poetry, imagination." Max Planck