CELLULAR AUTOMATA TEXTS




...By picking the right rules Conway believed that he was, in some less complicated way, rerunning a process that takes place in our own universe. At some point (perhaps Planck time) everything was set up, the rules were established and the whole thing was left to run. The same rules determined what happened to new generations of organisms in our universe. - Mark Ward

Mark Ward
VIRTUAL ORGANISMS
Pan Books 1999


pg 75:...Conway thought that the most important aspect of von Neumann's automaton was the fact that it could act as a universal computing machine. This is part of the reason that it took a long time to find the ideal set of roles for Life. Conway had to tinker in order to ensure his version did the same job. In doing this he was trying to establish a profound connection between living things and the logical world.

By picking the right rules Conway believed that he was, in some less complicated way, rerunning a process that takes place in our own universe. At some point (perhaps Planck time) everything was set up, the rules were established and the whole thing was left to run. The same rules determined what happened to new generations of organisms in our universe.

The use of the same rules over and over again, recursively, has once again produced ships, loafs and beehives. This time though they are not made up of squares on a computer screen; instead they are tea clippers, French sticks and homes for honeymaking insects. Cellular automata are at the heart of ALife. The ideas underpinning them are what makes ALife worth doing.

They forge a link between the complexity of the world we find ourselves in and an artificial world that is easier to study but reveals much about both. The central point is this: living organisms are physical systems made up of elements operating to a set of rules. There is no need, or room, for non-physical forces such as souls to get involved. Some of the rules operating in living things we know about, others are proving harder to grasp and uncover. The number of rules operating, the number of elements involved and the ways they can interact make it difficult to understand what is happening in actual organisms. The blooming, buzzing confusion makes it hard to pick out what is relevant and what is superfluous.

What we need is a way to remove all the extraneous elements to reveal the essence, what it is about living things that keeps them going. CAs are that way. They remove the muscle, flesh and bone and leave the essential rules exposed. Although in the case of CAs the number of rules operating are fewer than in living organisms, nothing, apart from the superfluous, should be lost. Despite the fact that there are only a few rules the complex forms that result and the fact that they emerge out of a system that is computationally universal lends weight to the claim that by studying a CA you are studying life: life in the raw and life that is much more tractable than doing experiments with fruit flies, cats or rats.

The connection between CAs and life is not purely computational. There is evidence that some cells in the body act like computers and process information. A convincing case can be made for a link in this sense but it is not one that CA researchers pursue. They leave that to the robot makers (see Chapter Three). The connection is phenomenological, which essentially means that living things and CAs do the same things. The complex dynamic activity you find in fruit flies, societies and cells is also found in CAs. Using CAs to model these moving targets makes them easier to study. Boston University physics professor Tom Toffoli thinks that the only reason CAs are worth studying is because of this connection with real life. Toffoli says that mathematically CAs are not that interesting. Although it must be said that the mathematics of CAs are easier to work with than those of other dynamic systems like water flowing round a propeller or air over a wing. Toffoli is another alumnus of Arthur Burks' Logic of Computer group at Michigan. It was there that he did his PhD thesis on what CAs were worth saving for. The conclusion of his thesis was that the saving grace of CAs was their close affinity with reality. Before Toffoli did his research many thought that CAs had little connection with the real world because the basic physics of the two worlds differed widely. But Toffoli was able to show that in fact there were strong affinities between the two. The connection showed that both worked in the same way. As such they could legitimately be used to model and study problems in this field. Once he had got his PhD Toffoli became the first staff member of the newly formed Information Mechanics Group at MIT. The research group was set up by Ed Fredkin one of computer science's oldest hackers who has made enough money out of the field to buy his own Caribbean island. Fredkin also has an abiding interest in CAs. He set up the Information Mechanics Group as a way of exploring his contention that all physical phenomena are rooted in information.



JOHN CONWAY GAME OF LIFE


Steve Grand

CREATION
Life and How to Make it

Phoenix 2001

pg 46

John Conway Game of Life

Patterns in the Game of Life

.... the results can be quite startling. Sometimes the whole pattern will flicker for a few ticks of the clock then quickly died out. Other times, stable patterns - persistent phenomena - will emerge. Some of these or trivial and boring.


For example a group of four lit bulbs in a square will just remain in the same state forever.

The lines of three in adjacent lights are slightly more interesting, because the alternate endlessly between two patterns: one horizontal and one vertical. Such shapes are dubbed "spinners".

Quite a large number of initial patterns indulge in rather more spectacular behaviour. They transform themselves into a pattern after pattern, never quite repeating themselves, and usually growing to fill large area of the grid. Such patterns are persistent but not immortal, and they are fascinating things to study.

But the pattern that knocked me off my chair when I first saw it on a computer screen is a rather simpler one. It is made up of five asymmetrical lit bulbs. It's posh name is the R-pentomino, but it is commonly known as a "glider", because that describes exactly what it does.

The glider continues to alternate between four states, and with each cycle moves one square across the board. The thing that really startled me about this, and stilled spooks me today, is that something is clearly moving across the board, and yet no thing is moving! The lightbulbs don't move; they just switch on and off. There is no central control deciding where to put the pattern next (like those displays of moving text you sometimes see in airports); it just emerge as all by itself. The glider is a thing - and yet it is not separate from or superimposed on that space. It is simply a self-propagating disturbance in the space created by these little rule following lightbulbs.

It seems to me that the natural world is rather like this too. Space is not really like a grid of lightbulbs, and the phenomena that persist in physical space are different from those that emerge Conway's game. But in both cases

...we see phenomena arising out of local disturbances, and many of those phenomena persist. We can classify them in terms of how and why they persist, and the more complex phenomena can "hitch a ride" on simpler ones, so that every new class of phenomena opens the door to the creation of further classes. Whether we are dealing with the simplest or the most complex phenomenon, the same basic concepts and mechanisms apply - everything is a self-maintaining pattern in a sequence of cause and effect. The universe is not made of stuff but of events and relationships.

...hierarchies of persistent phenomena

Now that we finally put matter in its proper place, we can start to look at how whole hierarchies of these persistent phenomena, including many that have hitherto been relegated to the realms of the intangible and thus beyond the pale for science, can come into existence and persist for extended periods. Among these phenomena, besides particles and atoms, we shall discover life, intelligence and mind.

Among these phenomena, besides particles and atoms, we shall discover life, intelligence and mind







STEPHEN WOLFRAM Interview Weltwoche 41/02

Wolfram's survey was empirical rather than analytical but it seems to have revealed some qualitative differences between CAs. His results have been independently corroborated and extended by others in the ALife field. The survey has important implications for anyone who believes that CAs can be used to study complexity or analyse some biological phenomena. Wolfram believes that organisms often unknowingly employ CA type systems to create some of their characteristics. One of the most striking examples of this can be found on the shell of the mollusc Natica enzona. Anyone comparing the patterns on the shells of these molluscs and some of the patterns that form in a CA would be hard pressed to deny some sort of connection. If it is the case that recursive systems are widely used in nature, then starting to classify them could also help us to understand them. At the very least they could be used to model them. It is unlikely, though, that living systems use only one sort of dynamic system. Wolfram is convinced that Class III and IV CAs are most lifelike

Mark Ward
Virtual Organisms

The Startling World of Artificial Life
Pan Books
pg 72




Mark Ward

BEYOND CHAOS
The Underlying Theory Behind Life, the Universe, and EverythingThomas Dunne Books 2001
pg 97

Cellular Automata




GEORGE JOHNSON
A Shortcut Through Time
The Path to the Quantum Computer
New York 2003

Turing Machines and Cellular Automata




Steve Grand
Creation
pg 73

Keywords : emergence - interactions - When populations of interacting structures become arranged in certain configurations, and something new and surprising comes into existence, we call this an emergent phenomenon - Conway's Game of Life: glider - logical reasoning - prediction - we could, in principle, predict the existence of a glider from the rules of Life, but only by actually carrying these rules out, simulating the system - Matter is just one link in the chain of being . Atoms are no more real than societies or minds. Hardware is a subset of software - self-sustaining patterns in space and time - The interconnectedness of all things - self-organizing chains of cause and effect - 'problem' of how mind has influence over matter is spurious. Since the two are not distinct, the idea that one can affect the other should not be at all difficult to accept - purposeful action - cause and effect act in webs, not chains - think of the information acting upon the brain at least as much as we think of the brain acting on the information - gestalt: form, the whole that is greater than the sum of its parts - Life, we discover, is a loose coalition of selfmaintaining eddies in a flowing stream. When the whole becomes more than the sum of its parts something new and perfectly real comes into existence. This gestalt is not mysterious, but neither is it a figment of our imagination - the basic buildin blocks of cause and effect





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