Chaos

A dynamical system is a system in motion (a ball rolling, a star evolving, a sound wave propagating I'm sure you get the idea). Its motion (the systems) is governed by a set of equations (in the former examples these could be respectively Newton's equations of motion ; The diffusion equation coupled to equations describing nuclear burning and hydrodynamic equations {stars are complicated}; hydrodynamic equations) Just think of the state of the system as being a position in some "state space" or some "phase space" The system moves around according to the equations.

Determinism:
If you can use the equations of motion to calculate where the system will be in the state space given as information only where the system currently is then the system is deterministic. Determinism can fail in two ways, in practice and in principle. All systems we know fail practically because we are unable to measure exactly where in the state space a system is. This is because of errors in measurements and the large numbers of degrees of freedom involved in even moderately simple systems. Think of trying to keep track of all of the particles of air in a room in which you wanted to calculate the speed of sound. Pierre LaPlace a French mathematician once said that if he knew the positions and velocities of all of the particles in the universe he could know the future by using Newtons laws of motion. In practice he could never gather all of this information but determinism can also fail in principle.
In Quantum theory the uncertainty principle sets a limit on the amount of information that we can have about any system irrespective of our ability to measure the system. Due to this principle the world is not deterministic. (this is a point that many philosophers seem to have allowed to slip them by in since 1923(4)?, as it makes a discussion of free will of academic interest only (but then again most philosophers are academics and these are the questions that they should be interested in :) ))

Chaos is independent of determinism. The definition of a Chaotic system is a system in which you start with two positions in state space that are as close together as you like , as you apply the equations of motion of the system the two paths in state space diverge. They move away from each other.

Alternatively an stable system is one in which adjacent points in state space remain together as you iterate them in time with the equations of motion.

One might call a system in which all points in state space converge a pathologically stable system, however it is quite common behavior as friction will tend to do this to a system, but that leads one into a discussion of thermodynamics.

The book covers the work of Lorenz, who studied weather forecasting to develop one of the earliest recognizable chaos descriptors in "the Lorenz attractor" (a pattern of periodic behavior where a system orbits around one or more attractors but never reaches it, and never traces the same route twice); Mandelbrot, inventor of the Mandelbrot set, which gave life to fractal geometry; and Feigenbaum, who discovered Feigenbaum's constant, which proved that there is deep underlying commonality across diverse dynamical systems.

Chaos Theory

To those who professionally study the Chaos theory, it is a fundemental way of perceiving the world around them. However, for the rest of us it seems to be a mystery, one that boggles minds while simotaniously stimulating them to great extents. For someone to understand the theory could prove quite revolutionary, as the chaos theory is not obvious at first, rather it is somewhat abstract. Understanding this emmensly complex notion will vastly improve a persons ability to fully comprehend- and appriciate - the universe, which is after all, the main goal of science.

An extremely vital concept of this theory is the "butterfly effect." A man by the name of Edward Lorenz discovered this on his weather simulating computer. Keep in mind that this was in the 1970's and the power of computers at the time was relatively minute compared to their power today... On this computer he could graph the weather patterns (in his computer generated universe) months in advance. The computer read out for the patterns went to four decimal places, a fairly accurate and precise measurement for the time, however when the program was actually operating it would use many more. One day he decided to check the accuracy of his program. Now, Lorenz had great faith in his creation but, as anyone with an anaylitical mind, he wanted to prove to himself just how close to perfection his computer was. He decided to collect a set of data representing all of the current conditions of his "world" and ran the program. Then, when he attempted a repeat of the weather cycle he was very surprised at the results. At first, the graphs of both patterns were very closely related but as more and more time went by, they gradually became more and more different, thus causing the graphs to become more and more dissimilar. Remember how the computer only remembered conditions to four decimal places? This was the cause of the chaos that he experienced. Although the initial conditions in the repeated experiment were exact to one ten-thousandth of one, as the amount of time increased so did the difference in the graphs. This effect came to be known as the butterfly effect. To apply the butterfly effect to a hypothetical situation: Say that something as small as a thunderstorm occurs . In the very distant future, perhaps even thousands of years, the world wide weather will be severely different than it would be had the storm never transpired (remember the word of advice: if you go back in time, don't touch anything). Even in ancient folklore, the butterfly effect is portrayed:

For want of a nail, the shoe was lost;

For want of a shoe, the horse was lost;

For want of a horse, the rider was lost;

For want of a rider, the battle was lost;

For want of a battle, the kingdom was lost;

After deriving this butterfly effect, Edward Lorenz decided to look for chaos in other places than simply his computer world. This lead him to convection. He took a liquid in a container and place it on a stove, then he turned the heat on. Very early in the experiment the liquid began to boil (this was expected), and by boiling the liquid began to swirl in one direction (this was also expected). As the heat intensified and the liquid approached higher and higher temperatures the boiling liquid went into a frenzy with extreme palpatations and the swirling became faster. A few minutes later as the heat reached even higher levels he noticed that the swirling began to slow down. This surprised him, but not as much as what was to come. Eventually the liquid stopped swirling, this only lasted for a few moments however as the most chaotic action quickly occurred. The liquid began to spin in the opposite direction. The graph of that liquid convection became rather famous in the world of chaos and is known as the Lorenz Attractor. This graph appears to have intersecting lines, however they do not intercept each other due to the fact that it is a three- dimensional graph and the seemingly intersecting lines are actually at different altitudes. This graph was made by using the following variables: rate of spin and the height of the palpatations. This experiment was the first of many to follow, in a way, it was the chaos theory summed up in a graph.

Next, it is important to understand the fractal. These are infinitely iterated geometric series, or infinitely self repeating structures in a finite area. They are yet another way of representing chaos without words. When you see a fractal, at first it may appear to be very confusing and completely random. However, upon further anyilization you will notice that there is organization to it. And, as with everything dealing with chaos, fractals can be seen quite often in nature. For example, in trees, fractals exist in many places. Next time you see a tree, closely examine its branches, notice that each individual branch seems to closely assimilates the one preceding it thus forming one giant fractal. The root system of a tree also follows this same pattern. Even in the leaves of a tree, fractals are frequently found. Another example in a slightly different way would be a rock. As you zoom more and more closely to the surface of a rock, you will eventually notice a very distinctive arrangement of the surface. This you may notice is infinitely self repeating, one of the main aspects of a fractal.

This theory of chaos, an oxymoron in and of itself is a very complicated and confusing idea. However, when broken down into easier terms to understand, anything, including this theory can be addequately understood.

In Warhammer 40k, the Emperor of Mankind, aka The Emperor, is seen by many as the last defence of humanity against Chaos and the Chaos Gods. He was almost killed in a large Chaos rebellion, the Horus Heresy, and has dwelt in the Golden Throne (a life support machine) ever since.

Chaos - The Battle of The Wizards:

8 bit heaven, arguably the greatest computer game ever made

Author: Julian Gollop
Publication: Games Workshop, 1984
Platforms: ZX Spectrum

Disclaimer: this w/u is a unrepentant nostalgia fest. Any time you waste in reading it is your own responsibility.

Historical Context:

In 1982, the ZX Spectrum was released by Sinclair Electronics, a strange looking beast with blue rubber keys and a whacking 48K of memory. This heralded the dawn of the home computer-programming age in Britain, and by 1984 a significant games industry had bootstrapped itself from semi-amateur status. Enter Games Workshop, Britain's biggest fish in the closely-related RPG market, which wanted a slice of this emerging pie. In a flurry of publicity they released a series of computer games (almost all now lost in the mists of time), released one big effort (Eureka!, designed by company founder Ian Livingstone with a team of programmers, a game with a £25 000 prize for the first person to complete it; it sucked) under the Domark title, and then got into a real mess. The two companies split and Domark went on to become the creator of Tomb Raider and similar, while Games Workshop returned to what it did best; giving single, teenage, Iron Maiden T-shirt clad boys a way to feel wanted and creative.

Chaos was one of the short lived Games Workshop Games titles and caused very little impact upon release, internet rumour has it that it was only available on mail order (personally, I have never seen an original boxed edition). Its distinguishing characteristic was its author-designer, Julian Gollop, destined to be the driving force for many of the leading strategy games of the following twenty years (Lords Of Chaos, Laser Squad, UFO: Enemy Unknown, X-COM Apocalypse). Chaos was a slow burner, and only made major waves when released as a covertape (1990) by Your Sinclair, a magazine known to have a circulation of 80 000 per month; its success was proved when, in The Spectrum's twilight years, it was covertaped again (1993), the only game to recieve this status.

Overview:

It's pretty clear that on any superficial level, Chaos isn't very good. It's a Spectrum only game; and I thank Sir Clive for this planning when he built the platform, it's restricted to two colours per character square. This unites with an 8 colour palette; giving the graphics a blocky, semi-monochrome appearance. Further, it's a one-man programming job, and clearly never went through serious testing; the code is a wasteland of bugs. I don't know why, but Julian seemed to love pink and yellow. Later games, (R-Type and Cybernoid), would show that a decent graphic designer could make the Spectrum palette look pretty good. Chaos, however, looks like a 3 year old that has just been unleashed on his first box of Crayola.

It's in the game design that Chaos is untouchable. Fundamentally it's a board game that took advantage of the dynamic scope computers introduced, allowing changing pieces. Based on an empty 10 by 15 board, you could place 2 to 8 human or computer-controlled wizards. A wizard in Chaos is the same as the king in Chess; a weak, easily defeated, low-mobility piece that is the target of the game. Rounds consist of two turns; an opportunity to cast "Spells" followed by a chance to move pieces.

The spells, and planning their use, is the guts of the game. Each player is initially given a random selection (from a range of between 50 and 100), with each spell having an associated, checkable, probability of success. The skill lies in judging these probabilities and planning the use of them. The target is to develop an army and, when fully equipped, to attack the other players on the board, with the resulting tacit alliances and battles this unleashes.

The early Eighties were the height of the Role Playing boom, and this game came from the Games Workshop stable. It took on much of the context of Dungeons and Dragons; yet I see this game more akin to the standardised warfare games such as Chess and Go. While the battles involve standard role playing parameters (Attack, Defence, Magic Resistance, etc), Chaos was more than the sum of these parts, with a Go-like emphasis on tactics and a fractal growth.

Fundamental to Chaos is the ability to alter casting probabilities. Spells are categorised as Chaos, Law or Neutral. This links to the board which also has a changing Chaos/Law score, the casting of spells in these groups cause this status to change; as the board's Chaos score increases, the probability attached to Chaos spells increases, and the inverse for Law. Further, all creature spells can be set to be Illusions, which are guaranteed to work, on the qualifier that they can be destroyed by the Disbelieve spell, which every wizard has an infinite supply of; a risky manoeuvre but one that can seriously pay off.

The Spells

Spells in Chaos break up into groups ('though I've just made these up): Creatures, Board Manipulation, Wizard Alteration, Direct effect and Landscape.

The game is equipped with a huge range of creatures; these are defined by the standard variables one would expect from an RPG: strong, weak, flying, ridable. The creatures were diverse; Dragons, Gorillas, Hydra and Zombies, all are available for a casting probability and a turn.

The other main group are Landscape spells, adding dynamic complexity to the board. The landscape spells result in different setting for each tournament. Fires can rage across the board, castles can materialise beside your wizard, and walls can emerge from the Earth. These act like pawns in chess, giving each game its own flavour.

The rest of the spells are aimed at altering the game, Wizards can gain shields, magic bolts can demolish your foes, creatures can be stolen in their moment of triumph, the dead rise again.

Playing the Game

This was the first "beer and pretzels" computer game in the UK (1 year before Bomberman); friends would converge on each others house with pizza and gorge on 5 hour Chaos festivals; crocodiles, giants, lions and wraiths raging upon each other; alliances, betrayals and accidents in epic wars of attrition.

The game is bug ridden, but once the player becomes well acquainted with these they almost become an asset; each bug is systematic and repeatable. The result is that these just add more dimensions to game play: riding an undead horse leaves your Wizard undead, destroying your own creature upon the corpse of a more powerful one will bring that creature to life under your control.

The AI isn't bad either, they possess multiple levels. True, these increase the wizards physical stats rather than intelligence, but still provides variation in difficulty. The AI is relatively predictable; however, an idiot with a hand grenade can still kill you, and seven idiots with a fistful of grenades usually prove a real challenge. Real fun occurs when you pit 4 humans against 4 computers. It is common that one of the humans will betray another, only to find themselves receiving a computer attack.

The game has an emergent quality, due to the freedom of rules, whereby after about 10 rounds, a unique board will develope. This leaves almost limitless scope. Further, with fixed casting probabilities, and Chaos and Law values to alter them, there is little "luck", just the opportunity to play the percentages. The only random component is the initial hand of spells, and even then it is possible to play a poor hand and win.

Personal History:

I was 6 when this came out, and I got my hands on a copy at 8. It wasn't an original, so i learnt with no manual. Immediately I was hooked, and I played Chaos pretty much continually, til the Spectrum Age ended. My close friends and I were raised by it, feeling our way with no understanding of statistics. This game devoured more hours of my life than sleep for a while.

The years bring a constant dribble of ports, proving I'm not the only obsessive out here. Checking Google, I find people have even written fan fiction! The best port was for the Atari ST, although, like most ports, it changed the probabilities and stripped out the bugs, leaving Chaos less balanced. Over the years there were sequels; Lords of Chaos was superb, but fundamentally different, Magic and Mayhem was abysmal: Chaos was not meant to be real time. Chaos remains the most playable because it is still, fundamentally, a board game.

However, even without nostalgia it is clear that this is extremely well designed, holding up as the best of the 8 bit era. I've been playing it in research for this node, and even friends I introduced to it recently enjoy it. Download an emulator, load a virtual tape in the spirit of Retro Gaming, you won't regret it. And if the desire comes upon you to produce another port, please do it properly, one day this game will re-emerge... And I am waiting for it.

I am a child of the eighties, and I am not ashamed!

And now, due to the wonders of java, I give you, Chaos on the web! http://www.spectrum.lovely.net/Chaos.html

Introduction

According to the poet Hesiod, the first power in the Universe was vast void named Chaos. The word Chaos is derived from the Greek chaino, "to gape, yawn". Chaos was the source of the first deities;

Gaia: Earth

Eros: Love

Nyx: Night

Contrasts with Christian Creation Stories

In the Biblical Creation story, the Earth was "without form, and void; and a darkness was on the face of the deep"1, and the Universe is created by God shaping this void. However, in Greek mythology, Chaos is the originating force.

The greatest triumph of Zeus was seen to be the establishment of a firm rule over the primal, disorderly forces of Chaos. Greek mythology favours these Gods as they are seen to be more powerful and orderly.

1. Genesis, King James Version.

Cha"os (?), n. [L. chaos chaos (in senses 1 & 2), Gr. , fr. (root ) to yawn, to gape, to open widely. Cf. Chasm.]

1.

An empty, immeasurable space; a yawning chasm.

Between us and there is fixed a great chaos. Luke xvi. 26 (Rhemish Trans. ).

2.

The confused, unorganized condition or mass of matter before the creation of distinct and order forms.

3.

Any confused or disordered collection or state of things; a confused mixture; confusion; disorder.

© Webster 1913.