September something, 2001 Lots of variations of automata exist. I use this note to jot down what my thoughts on ca are currently about the CA's I'm using. Well after spending lots of time locating 3dCA resources and finding some, it seems that 3dca using traditional rules isn't quite the answer I'm looking for. Fantastic software out there, but the available rules just don't seem capable of what I'm looking for. Mabye I don't even know what I'm looking for. After investigating lots of traditional 3dca rulesets, it seems that the patterns are either going to die out too soon or grow infinitely. Sure, there are rulesets that produce games similar to life. A cell is the smallest most indivisible element in the CA universe. Its equivalent in the real world probably hasn't been found yet. It takes billions of atoms and whatever the heck makes them up, to make up the simplest gene, which many see as a prerequisite to life. So, in a CA world, patterns of LOTS of cells are required to function as a self contained entity. Something that appears very rare in a random CA field, most have been engineered. People differ on what the definition of life is. I would say that any naturally occurring system that is capable of responding to external stimuli could be seen as a lifeform, natural meaning a system that comes about without human intervention. In order for life to maintain itself, it must also have a mechanism for producing offspring and sending information about itself to the offspring. This is called genes in nature of course. In nature, there is no such thing as a perfect copy, and the resulting imperfect copies is part of what gives rise to evolution, and what in turn can give rise to life. In the real work, if you look at a stationary object, well it's not moving. If you could get closer and closer too it and magnify the parts that it's made of eventually you'd see billions of things moving at near light speed. In a CA, I think one that is capable of containing enough complexity to result in lifelike behavior this level of abstraction is needed. In otherwords, most of us view CA at the greatest possible magnifications meaning we see the smallest elements that make up the CA world (cells). But zoom out. A lot. Eventually, one stationary nearly motionless pixel will represent thousands of cells that are moving at lightspeed (in CA terms). If there were any lifelike behavior really going on in CA, I think it would be nearly impossible to interpret when you are seeing the smallest particles in the CA universe. Think of what a mess we'd be in if everything was magnified so much that we could actually make out muons and other subatomic particles. That means we need a lot more computing power. How this relates to CA.. Well with the 3dca rulesets I've used as I said, patterns either die out or grow forever. A few produce lots of pretty patterns, gliders and things, but none that I found produce patterns that grow to a certain point and stay at that same approximate size. So what I plan on doing when I grow up and learn a little more programming, is write a 3dca that will allow rulesets that I THINK might allow a pattern to grow to a certain size and stay about the same size. This makes it possible for self contained systems to exist within the CA field that aren't going to grow forever and aren't made up of just a handful of cells. The whole point here is that it's going to take A LOT more than a handful of cells to contain a pattern that is able to function as any type of genetic material, which I consider the simplest mechanism that is required to have life come about in a CA field. The rules, I imagine, will allow you to not select what happens to a cell when it has 2 neighbors on or 4 neighbors off, but what will happen to a cell if it has X cells of type Y within a distance of Z from the cell in question. X is the count of neighboring cells, Y is the cell type. I plan on having multiple colors, the more the better, and each color will have it's own ruleset. Z is the distance between the cells in question. For example, one rule might say if the cell in question is red and it has 3 or 6 neighbors that are within 8 cells of this one and are blue then turn the cell yellow. Being able to specify a distance is what I believe will give us the ability to have patterns that can grow in size but not indefinitely. I'm sure that this has been tried before, and I'm interested in the results, but my mathematical capabilities don't go much beyond the basics. November 10, 2001 Another thought. Life can?t exist without evolution. For millions of years things have been getting better and better at existing within their environments, but what?s evolution? Most people say it?s a species tendancy toward developing more fine-tuned abilities at surviving and breeding (we?ve gotten really good at the latter). How about something a little more specific though. When inseption takes place, and it doesn?t matter if we?re talking about a worm, an elephant or a human, there?s a LOT of chemical things happening, billions of chemical processes and reactions are going on. Copies of genetic material are taken from mother and father. But again these are chemical processes, not logical ones. A perfect copy with this number of processes happening might be something of a miracle. It?s this imperfection that gives us what we in the macroscopic world would call evolution. Without it, life would never have started. The first signs of life- a chemical process that could reproduce itself, would at it?s very best simply reproduce itself perfectly over and over, with no changes. It would remain a chemical process for billions of years. It?s the chemical imperfection that results in evolution. Just as this evolution would be referred to as chemical imperfection at smaller scales, at still smaller scales, the same effect would be referred to as entropy (us humans are always playing word games with ourselves). I?m not a physicist or a mathematician, so take this all with two grains of salt. Entropy is, from the physicist?s point of view, our inability to know everything about anything. There?s always some element of chance going on and it?s this randomness (for lack of a better word)that keeps things from being completely predictable. My intuitive guess is that there isn?t really such a thing as randomness. Our fabulous complicated sophisticated super powerful mathematical abilities are MODELS of a physical process, not the process itself. And so when we use our algorithms to probe deeper and deeper into reality, the errors produced by the model become more and more apparent. That?s why there?s such radically different types of math at different levels of magnification i.e. at macroscopic we can use basic algebraic equations to predict the speed of a ball moving down a hill, but the math gets a lot more complex at we zoom in on matter, probably because just as we are zooming in on matter, we are also magnifying any errors or inconsistencies in the mathematical models themselves. Blablabla but that?s another story. The main idea is that what physicists call entropy in subatomic physics translates into what biologists call evolution in the macroscopic world. Without entropy in a 3dca, we aren?t likely to find life. Then again, without a computer that is thousands of times faster than that currently available, we aren?t able to maintain 3dca fields large enough to contain the complexities we would need to search for life, and so the question of entropy probably isn?t an important one for a decade or so. Entropy in currently useable field sizes would do us less than no good without the computer power to take advantage of enormous field sizes. To get an idea of what size of 3dca we might need to search for life, it might be useful to examine the 3d sizes of life-as-we-know-it. The smallest element of what we generally call lifelike material is the gene- it reproduces, it defends itself, it repairs itself, it becomes better at surviving with each generation. We need to compare apples to apples. In cellular automata, the cell is the absolute smallest particle in its universe. To compare apples to apples, we need to know what we are comparing exist i.e. what is a 3dca cell?s counterpart in the real world? In the real world, it used to be thought that the atom was the most fundamental particle, but later science tells us there are other particles that make up atoms. We may never know for sure what the smallest particles are. But lets pretend that an atoms is the smallest, and so we can say that an atom?s counterpart in a 3dca is a 3dca cell. Now we have a basis for comparison, even though it probably won?t be quite right. In real life, how many billions of atoms does it take to make up the simplest known gene? That?s a rough guess at how many 3dca cells it might take to contain the complexity required to perform basic lifelike functions. Too many to be practical anytime soon.