These algorithms are known as L-systems, and the computer-generated L-plants are now used in movie special effects as realistic looking vegetation.

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1 Imagine a grid of squares that stretch away in all directions. Imagine the grid is infinite--or at least, so large that you'll never find the edge of it. Let's pretend that each square can either contain life--be "alive"--or contain nothing and be "dead". We'll show the "dead" squares as empty white squares, and the "alive" squares in black. Now let's try and make our simple universe resemble the real world of cell biology. We know that in the real world, life tends to spread into adjoining areas. So let's say that in our grid world, if an empty square has three living neighbors, it will become inhabited by life too. Similarly, we know that lone cells tend to die out, so let's say that if a live square has fewer than two living neighbors, it becomes dead. Finally, living things also die from overcrowding--so let's say that if a living cell has more than three living neighbors, it dies. If we want to see what happens in our grid world, we now have three simple rules we can apply for each tick of the clock. In fact, we can condense them down into just two rules: 1. If a square is dead and has exactly three living neighbors, it becomes live next turn. 2. If a square is alive and has more than three or fewer than two neighbors, it becomes dead next turn. This game is known as The Game Of Life, and was invented in 1968 by John Horton Conway, a mathematician at the University of Cambridge. Initially it was a game played on a board, with counters; nowadays we can program a computer to do all the hard work. Modern computers can handle a grid thousands of squares across, and calculate several turns a second. We can just set up an initial pattern of squares to be alive, then sit back and watch what happens turn by turn. When you first start playing The Game Of Life, what happens is pretty unsurprising. Some patterns of cells die out quickly--either they're too crowded, or the life is spread out too thinly. Other patterns are "just right", and sit there not doing very much. Some patterns expand to fill large areas of the universe, then settle down into clusters of steady patterns. After playing the game for a while, Conway discovered an interesting pattern of five cells which he named a glider.

2 Gliders are a stable repeating cell pattern. That is, the arrangement of living cells changes from turn to turn, but they keep returning to their original pattern after four ticks of the clock. Each time the cells return to that initial arrangement, the pattern has moved one square diagonally on the grid. The cells of the glider pattern go on traveling forever--or at least, until they hit another patch of living cells. The glider is, if you like, a stable moving multicellular entity within the Life universe. Its discovery brought to mind an interesting question: since this ultrasimplistic universe had turned out to contain stable moving cell patterns, was it also possible that it might contain stable cell patterns that created other stable cell patterns? Was there a pattern of cells in the Game Of Life that would, say, spit out gliders? The challenge was printed in the pages of Scientific American magazine, and soon an MIT student named R. William Gosper, Jr had come up with a design for a glider gun. It fired out a new glider every thirty turns, proving that it was possible for a single group of living cells to expand without limit into the Life universe. There are many other interesting kinds of cell patterns in the Game of Life. Some move like gliders, but leave a wall of stable cell patterns behind them. Then at the next level of complexity there are "breeders", which move across the grid leaving a trail of glider guns behind them.

3 Another MIT student, Michael D. Beeler, tried firing beams of gliders produced by a glider gun at various objects in the Life universe. He discovered that if two streams of gliders were directed at each other at right angles and carefully synchronized, they would annihilate each other. If you viewed one of the incoming streams as a binary signal--with a glider being "1" and a missing glider being "0"--then the signal that left the point at which the beams crossed had "1" swapped for "0", and "0" swapped for "1". In other words, the crossing beams of gliders were a binary NOT gate. Before long, eager experimenters had discovered how to build AND gates and memory cells--all the ingredients you need to build a digital computer. This means that, curiously, the universe of The Game Of Life is capable of modeling the computers that we often use to model it. At this point you might be thinking "So what? They build a simulation on a computer, and it turns out that the simulation can model computers. Why is this interesting?" It's interesting because there's nothing inherently computer-related about The Game of Life. You can model its world using counters on a board. Yet two very simple rules, applied to an extremely simple model universe, can result in a great deal of complexity--none of which was intentionally built into the system. Fast computers have certainly made the game more fun to play, though. Before long people began to use computers to look for interesting "organisms" in the Life universe. They started off with random patterns of cells, and programmed the computer to watch for stable repeating patterns, or patterns that moved. Like the glider, the patterns found by computer were discovered rather than invented. They existed implicitly, as a result of the rules of the Life universe; no human decided that they should be there. Obviously, the Life universe is not our universe. Whereas SimEarth attempts to realistically depict the world we inhabit, The Game Of Life makes no attempt to do so, even though the two rules of existence on the grid are inspired by the behavior of real life in the real world. This means that The Game Of Life is not, strictly speaking, a simulation; it does not model cell biology, particle physics, or anything else for that matter. A simulation is a construct designed to resemble a real thing in appearance and behavior--but we can't talk about how closely a given software implementation of the Life universe resembles the real thing, because there is no real thing! Yet in spite of all that, the imaginary universe of the game has a certain reality, in that we can talk sensibly about what happens there. It is what semioticians call hyperreal--a perfect simulation or

4 representation of something that does not exist, so that in a sense the representation itself becomes the real thing. However, it was a simulation of life in our own world that led to the invention of a hyperreal world showing the power of natural selection. In 1968 a biologist named Aristid Lindenmeyer came up with a set of mathematical rules that modeled the growth of real plants. The basic idea is very simple. Start with a single piece of stem; a "shoot", if you like. Now, each tick of the clock you take each shoot in turn, and replace it with a sequence of three shoots joined together, with another shoot protruding from each join, as shown to the right. Finally, you can take each unconnected tip of a shoot, and draw a leaf there. Basically, you are assuming that each piece of plant stem will try to grow and branch off new pieces of stem. If you repeat this basic recipe a few more times, what you end up with looks remarkably like a real plant. You can change the rules slightly, and get different sorts of plant. You can also add refinements such as varying the angles of the branches, and making the stem segments longer according to how many turns old they are.

5 These algorithms are known as L-systems, and the computer-generated L-plants are now used in movie special effects as realistic looking vegetation. In 1985, Richard Dawkins wanted to demonstrate pure natural selection, much as The Game of Life had demonstrated pure cell interactions. He decided to write a program that used L-systems to generate plants. He picked nine variables for the system--length of "stem" pieces, angles, and so on; and he started with a random L-plant. The software "mutated" the nine parameters of the initial plant, and displayed the nine "offspring" in a grid. Dawkins would select one of them, and nine more variants would be bred from that specimen, and so on. He called the shapes "biomorphs". Dawkins confirmed that if he picked the most "treelike" biomorph each time, the process of selection and mutation would result in a treelike shape after only a few generations. He could then select for "bushyness", and see the shape evolve into a bush. All of these variations were produced from random mutation, through a process much like real-world natural selection. After a while, though, Dawkins noticed biomorphs that had lines that crossed back on themselves. In fact, a few had protrusions that looked rather like legs or wings sprouting from tight clusters of lines that looked like bodies. Although he hadn't designed the code to draw anything but plants, suddenly he was breeding insect shapes! Before long the biomorph bestiary had expanded to include spiders, birds, frogs, alphabet letters, castles, spacecraft, and even a chalice shape which Dawkins named the "Holy Grail". The biomorph world teaches us that when a hyperreal world is given natural selection, the results can be extremely unexpected. Similar lessons were to be

6 learnt later on in the field of software engineering; but first, we need to take a detour back to the early days of computers. Early computers were so expensive that it was unthinkable that you would have an entire computer to yourself. Instead, many people would use a single "timesharing" computer system. Unfortunately, early primitive operating systems lacked technologies like memory protection. If a program accidentally malfunctioned, it would sometimes end up crashing other programs, or the operating system itself. Computer scientists tend to have a strange sense of humor, and some of them decided to make competitive program-crashing into a sport. Rather than crashing the actual computer, they built software that modeled a much simpler virtual computer, designed so it could run malicious programs without damaging the real operating system--much like the Java virtual machine in many web browsers. The game became known as Core War, named after the "core memory" used in early computers; it was first described in detail by A.K. Dewdney and D.G. Jones in The virtual machine used for the game had a very simple instruction set called RedCode. Competitors would write RedCode programs that attempted to copy themselves elsewhere in memory and then run the extra copies. Programs would also try to find and overwrite competing programs and make them crash. Some Core War code would carefully take over the competing software, stealing its allocation of CPU time like a virus. Eventually, the last program left running would be the winner. By the late 80s, Core Wars had become a cult pastime amongst computer programmers, with several versions of the software existing. There are even tournaments held over the Internet. However, it would take a biologist to make the next imaginative leap. ;redcode ;name Dwarf ;author A.K. Dewdney bomb DAT #0 dwarf ADD #4, bomb MOV JMP dwarf END dwarf

7 Tom Ray had studied evolution in the real world, but found it a frustrating subject. He wanted to be able to watch its effects on thousands of generations of organisms, evolving there in front of him. Years before, an MIT computer hacker had introduced him to the idea of self-replicating computer code in a virtual machine. He wondered if he might be able to build some kind of artificial life or a-life software, that would let him run experiments in evolution. He built a computer program to model a virtual computer similar to the one in the Core Wars game, and called his virtual world Tierra. However, Ray added a new feature to the virtual world that had been missing from Core Wars: mutation. Computers are generally programmed in textual languages of words, symbols and numbers that humans can understand--languages like C, Java and BASIC. However, the integrated circuit at the heart of the machine only understands a much simpler language of binary numbers. To add two numbers together, you might need to read them from memory into spaces called registers, add the two registers together, and then write the result out to memory again. Each of those small steps would be represented by a series of binary numbers. Your web browser software consists of millions of binary instructions. They were assembled automatically by software called a compiler, following instructions written in the original programming language--the "source code". It's possible to write machine code directly, but only if the program is fairly small. The programs in Core Wars and Tierra are only a few tens of bytes, maybe a couple of hundred at most, and are written in machine language. Ray altered the Tierra system to simulate a computer with a slight flaw. Every now and again, the machine code instruction which copied data between memory cells would randomly flip one of the bits during copying. If the data being copied was the machine code of the program itself as it tried to reproduce, the result would be a slightly different mutant program. High-end computers use special error-correcting memory, specifically to avoid bits getting flipped. They do this because if you flip bits in the machine code of a piece of software, it will almost certainly crash. Conventional wisdom before Tierra was that randomly flipping bits of a machine code program could never result in improvement to that program--the chances against it were astronomical. Like in the real world, Tierra had natural selection. Mutant programs that crashed were eliminated as unfit. In addition, a process called The Reaper would pick off the oldest programs to free up space--meaning this new virtual world had death, as well. Ray decided to start his Tierra system off with a population of the most 80: 04 zero 02 or1 03 sh1 03 sh1 18 mov_cd 1C adrb 07 sub_ac 19 mov_ab 1D adrf 08 inc_a 06 sub_ab 1E mal 16 call 1F divide 14 jmp 05 if_cz 0C push_ax 0D push_bx 0E push_cx 1A mov_iab 0A dec_c 05 if_cz 14 jmp

8 After the unexpected success of Tierra, computer scientists began to explore whether similar techniques could be used to evolve real, useful code. Today, the state of the art is Genetic Programming or Evolutionary Programming, invented (and patented) in 1992 by John R. Koza of Stanford University. Like Tierra, the "DNA" of Genetic Programming is a set of equations and operations, not just parameters; but instead of reaping the code that crashes and rewarding the code that copies itself in the smallest space, Evolutionary Programming measures how well each program does at solving a particular problem. The programs that do the worst are eliminated, and new strains of program code are bred by recombination, either with or without mutation. The solutions produced by evolutionary programming resemble the solutions we find in the real world in several ways. To start with, they are very hard (or even impossible) to understand: the code makes no sense whatsoever to a human mind. It may use functions that seemingly have no logical relevance to the problem, like using trigonometry to solve a binary arithmetic problem. Typically evolved programs will consist of one long line of code, with literally hundreds of nested expressions. Another characteristic of evolved solutions is that they're messy. They may include obviously unnecessary operations in one part of the code, yet be much more compact than any human programmer can achieve elsewhere. Think of the human eye: it has a far greater sensitivity than the best camera man can build, yet the retina is wired in backwards. The nerve cell wiring is on the inside of the eye, in the way of the light path; the brain processes the gaps out of the sensory data later on. If cameras were built like that, there would be wires going across the film, and you'd paint out the gaps on the prints when you got them back. Intelligent design? Hardly. The very idea is crazy. Yet to the blind process of evolution, it's perfectly adequate. A third thing evolutionary solutions have in common is that they're unpredictable. Because we don't really understand how the evolved code works, we also don't know what conditions might make it stop working. A piece of evolved code that computed the best way to drive between two cities in the USA might behave bizarrely if asked about a city a mile across the border in Canada. Yet at the same time, evolved code is often much more robust than programmed code, so long as it has been tested against a wide enough range of sample problems. Because the code is evolved rather than designed, it doesn't have built into it all the assumptions a human programmer would make--and the Y2K problem is a good example of the value of not making obvious assumptions. Robustness is good, but the single biggest advantage of Evolutionary Programming is the final thing it has in common with biological evolution: it can

9 solve problems that humans are unable to solve, or come up with solutions better than any human solution. In the biological world, animals can climb stairs, avoid obstacles, catch prey, and do many other things that humans have failed to get a robot to do well. In the a-life world, there are evolved programs like the 22s in Tierra. Lockheed Martin have evolved code that works out how to maneuver spacecraft from one orientation to another. It achieves the goal within 2% of the theoretical minimum time -- which is around 10% faster than any human-written code can manage. Imitating nature even more closely may lead to further advances in genetic programming. One recent innovation is the development of Field-Programmable Gate Arrays, or FPGAs. Whereas a normal computer chip cannot have its design changed once it has been built, FPGAs are completely reprogrammable--you can actually change the wiring of the circuits on the chip. Some researchers are now using this technology to investigate whether it's possible to evolve hardware, rather than software. In one experiment, a chip was evolved that would digitally decode a binary signal sent over a telephone line, without using any of the external analog components found in devices such as modems. All digital circuits have "rough edges" where they don't quite behave exactly like perfect digital components; whereas human engineers try to filter out these irregularities, evolution exploited them. It came up with an almost perfect solution to the problem; it would have been almost impossible for a human electronics expert to build a similar circuit from the same components. What, if anything, does all this prove? Is it meaningful to draw a comparison between a-life and real life, or is it a false analogy? The Game of Life shows us that an incredibly simple system can exhibit complex behavior. All that's needed are two simple rules inspired by cell biology. Somehow, all of the cell patterns that move across the Life universe, all the machines which breed gliders and glider guns, all the logic gates needed to model a digital computer, they're all a necessary consequence of those two rules; nobody designed them there. You can play with the hyperreal universe of the Game of Life using a computer, using counters, or just using pen and paper, and the result is the same; but change the rules, and the complex patterns and structures change. So, complex behavior and elaborate structures don't require a designer, and don't even require a complicated explanation. Just two simple mathematical rules might be all it takes. The lesson is shown again in the world of L-plants, where the actual growth of real plants is modeled accurately by repeating the same straightforward operations over and over again.

10 Biomorphs show us the power of taking that simple iterative system, and adding in selection and mutation. Suddenly the artificial life forms start to act in unexpected ways, and almost seem to exploit the system they live in according to some hidden plan--producing insects in a world built to contain only plants. Tierra more closely resembles the biological world, and as a result the power of evolution is shown even more strongly. Whole new species appear from nowhere, with no human input at all; they evolve ways to reproduce that are better than any human can design. Finally, Genetic Programming astounds us with solutions so bizarre that they are obviously not the product of any human mind; yet at the same time, they are efficient and often robust, like the biological solutions in the real world which outdo our greatest feats of engineering. All of this is achieved without even hinting to the computer how it should solve the problem. To put it another way: A sophisticated computer program that is way too complex for humans to understand can now be evolved from random numbers! This completely destroys the Creationist argument that complexity cannot arise without a designer. If evolution can work this way on something as simple as a string of numbers or a chip full of transistors, it clearly ought to work for more complicated systems such as chemical molecules. In fact, it's hard to read about all of this A-life research and not be struck by the amazing, almost magical power of evolution. Suddenly life--the real kind--looks a little less inexplicable. Assignment Questions 1. Summarize the essay into a single paragraph (2-3 sentences). 2. How does a program like SimEarth differ from something like Jon Conway s Game of Life? What makes Game of Life so much more interesting in terms of its a-life potential? 3. What is a glider gun? How many different glider guns have been discovered/created so far? 4. In the previous question, why have I indicated uncertainty as to whether the appropriate term should be discovered or created? 5. With faster computers and larger computer screens, even more interesting things can begin to happen in the Game of Life World. Make some educated guesses as to the kinds of things that might happen. 6. Describe L-systems. 7. Describe Richard Dawkins program Biomorphs. 8. See if you can find an online Java applet or Flash program which does Biomorphs. What is the URL? 9. Using this Biomorphs program, a) how many generations does it take you to evolve a bat-like object? b) How man generations does it take to go from this bat to a tree-like object? (Approximate numbers are o.k.) 10. Describe Core Wars.

11 11.How is Core Wars relevant to a-life? 12.Any system that involves replicators (things that spontaneously make copies of themselves) involves the occasional imperfect replication. An act of imperfect replication will usually result in a thing that can no longer function. But once in a rare while, the error will result in a thing that can copy itself better. By better, we mean faster and/or with less error. Soon these better replicators will take over the population, and the replicating power of the general population will have been ratcheted up a notch. As this process mindlessly continues, more complicated life forms can develop. The algorithm can be thought of as: 1. replication 2. random mutation 3. selection 4. goto 1 With this simple looped algorithm in mind, can you think of two other examples (real or made up) of such a process in action? 13. What is a 1-D cellular automata? Find a working version online and provide the URL. 14. A famous (and rich) mathematician named Steven Wolfram has some very interesting thoughts about 1-D cellular automata. In fact, a few years ago he wrote a big fat book on the topic. It s called A New Kind of Science. See if you can find some reviews/summaries of this book. Write Wolfram s big idea in a sentence or two. 15. Interesting point: Wolfram believes that the universe itself just might be a 3-D cellular automaton that has just 4 or 5 rules. Wow!