Yin Yang Fire

Might there be a kind of Yin Yang Fire burning in our universe?

Introduction

Cellular Automaton

Chaos Theory

Scientific Aspects

Pictures/Animations

Products



Introduction

Until recently science has always been centered around linear aspects of nature, as it turns out to be, the non-linear aspects of nature are much more important and much much more interesting. In fact, nothing in nature has anything to do with linear aspects, nature is all about non-linear aspects. The most beautiful thing about nature is life and as such, it is a very complex non-linear system, in fact it is a selforganizing system. Or to be more precise, many biological life-forms are selforganizing systems of selforganizing systems of selforganizing systems etc..

A field which is build around the non-linear aspects of nature is the so called chaos-theory, it is relatively new and still in it's infancy, much is to be discovered yet. One of the subfields which relate to the subject is the study of cellular automata, it is the field which tries to isolate the basic aspects of dynamical systems, of which selforganization might be the most interesting aspect. Selforganization is the ability of a dynamical system to produce patterns/structures which organize themselves. It can be studied by dividing a certain system in a lot of cells which interact with eachother, thus allowing the researcher to study the dynamical behaviour of the system in detail. The most general way to do this is by means of a computer, a computer can easily maintain a large grid of cells and display them on a display, thus making it possible to view to state of the system in one glance. The most famous cellular automaton is the program Life from John Conway, it exhibits many aspects of non-linear systems and has been studied extensively. However there are much more interesting cellular automata to be studied yet ...

During the development of a simple graphical demo (small computer program to demonstrate something), I was baffled by the accidental discovery I made when the demo didn't work. I changed some parameters -in a sense useless changes-, but just before quitting the demo and concluding that I had to make real fundamental changes, to make the demo work, strange structures emerged out of nowhere! I looked for more than two hours, although very tired, from 5:00 am to 7:00 am, wondering where the seemingly random and beautiful pictures came from. Because some years ago I searched very hard for an algorithm to turn random dots into beautiful pictures and didn't succeed then, I immediately realised that I found (at least) one of my holy grails. I didn't just get a static picture, I got a kind of infinitely random creation of beautiful pictures without using any randomness or complexity in the algorithm itself! I called the cellular automation "Yin Yang Fire" for several reasons, one of the most important being the fact that the system reminded me of the dynamical aspects the yin yang symbol stands for.

Viewing the Yin Yang Fire effect on a computerscreen can best be described as quantum fluctuations where things emerge out of nothing and will die out again to make room for new structures. In this way the effect perfectly visualises the yin yang concept, where in the ultimate of yin is the origin of yang and in the ultimate of yang is the origin of yin. Hence the name Yin Yang Fire. The ancient yin yang principle is not so easy to explain in a few words, it takes time to really understand the principle. It normally is visualized with a Tai Chi or Yin Yang symbol as seen in the picture above. It must be interpreted as a highly dynamical process where the white (yang) and black (yin) areas are constantly changing and keeping the whole in a kind of balance. However nowadays the symbol itself is overpopularized (certainly in the Western world) and got a meaning of its own (being just a symbol), which has not much to do with the real meaning of the tai chi diagram. In order to understand the yin yang principle, one has to recognize it in the real world, an example that is easy to understand is the following; suppose a body builder who is cultivating his body and builds up strength (yang), the more he trains the more strength he develops and the more powerful his body becomes, however at the same time his body gets weaker and weaker in another area. How so ...? Well, suppose he wounds himself and gets an ugly scar, he would be much more devistated than someone who isn't so busy with his body ...

The algorithm behind the Yin Yang Fire effect is almost as simple as adding 1 and 1 together! The algorithm contains only some basic binary operations (8 bit arithmetic is enough!) and can be calculated fast enough such that the pictures can be animated in realtime (2 to 4 pictures/s with a 640x480 resolution on a 100MHz Pentium)! Seeing the Ying Yang Fire is almost as fascinating as real fire (nothing can beat real fire!). The psychedelic pictures and the animations have almost a hypnotic effect and if symmetric pictures are generated, faces can occur, look at the alien above for example! Viewing the animated Yin Yang Fire on a computerscreen is like watching real fire, it looks very different but in a way it is exactly the same. And yet the fire is only "driven" by a very simple algorithm! The Yin Yang Fire algorithm is comparable to the algorithm of the program Life and is almost as simple as that. The Yin Yang Fire algorithm probably will enable scientists to study different basic aspects of very complex dynamical systems, without using very complex and timeconsuming higher mathematics to simulate these processes.

Every living creature in nature lives by means of interactions with its living and non-living environment. The most basic way to simulate this concept on a computer is by means of a cellular automaton. It is a long time ago (1970) since John Conway invented the very popular cellular automaton: Life. Life is a computer-program which simulates a very simple form of "life" by representing squares on the computer-screen as cells and those cells die and live by applying a very simple algorithm. When considering a grid of cells and assuming that either a cell is alive or dead, the new state of a cell is determined by the following rules: If it has less than 2 or more than 3 neighbouring cells (out of a total of 8) it will die, if it has exactly 2 neighbours no change occurs and with 3 neighbours a cell will be born (if it was dead). When repeatedly applying these very simple rules on every cell in a large grid, every time a new large grid can be calculated and shown on the computer-screen. Very often a random starting grid is chosen and then the rules are applied, this sometimes results in very beautiful and complex dynamic figures. In this way many interesting "lifeforms" have since been discovered. The main disadvantage of the program Life however is the fact that it needs a random or interesting starting position to start with. But to make it even worse, the pictures (almost) always will die out to non-interesting forms after a certain number of iterations (repeated calculations). This is where the newly discovered "Yin Yang Fire"-effect comes to life and supersedes every cellular automaton seen before ...

At this moment nothing can be said about what implications the Yin Yang Fire algorithm will have. It looks like anything seen in nature but on the other hand it cannot really be linked to any physical process (yet) ...





Alien

It is unbelievable that this figure can spontaneously emerge from (almost) nothing, using only a very simple algorithm! It is even more special if you view the picture upside down! This picture will be used as the symbol for the Yin Yang Fire effect.






Cellular Automaton


What is a cellular automaton? A better question is what is not a cellular automaton? Apart from any official and strict definition, one can state that a cellular automaton is a system that consist of multiple "cells" which interact with eachother using certain rules. Using this broad definition means that almost everything is a cellular automaton, any object build up from atoms (which we can regard as cells in the above definition) is therefore a kind of cellular automaton. However, normally the term cellular automaton is used for simulated systems on computers where a large grid is taken and where the individual cells interact with eachother using a certain algorithm. Another general rule is that every cell is considered equal and on every cell the same algorithm is applied.


New value of Y as a function of its surroundings cells



Consider for example a large grid of square cells where every cell has a certain value, lets say a value in the range of 0 to 255 (representable by a single byte). And the value itself stands for a certain quantity, lets call it health. If you choose a grid of say 640x480 cells, you can easily visualize the total state of the system at any time on a screen with 640x480 pixels and 256 colors. To let the automaton work, you just need a certain starting state and an algorithm to apply on the individual cells. The normal way is to check every cell of the grid and its surrounding cells and calculate a new value for that particular cell. These new values will form a new grid and this will be used as the original grid for the next iteration, etc.. In the example above the new value of a particular cell (Y) is a function of the the value Y and the values X1 through X8. But remember that more distant neighbouring points might be taken as input parameters. To illustrate the working of the cellular automaton consider the following function: Ynew=(X1+X2+..+X8)/8, this function is the same as saying that the new value will become the average of the surrounding cells, something like: adapt thyself to the environment! What will happen with such an algorithm? This will point out another point, you can only answer this question if you know the starting values of all the cells, if they are all equal nothing will happen! If the cells have a random value it seems logical that when applying the algorithm above results in a dull averaging of all the cells until a certain stable state has been reached. The interesting point however is that there are an infinite number of possible algorithms and starting conditions ...

Another important point is that if you apply an algorithm on every cell in the grid you run into problems at the edges of the large grid because the border-cells have fewer neighbouring cells. This is normally solved in two different ways; either you let the border cells be unchanged or you use a cyclic grid in which the right side connects to the left and the upper side connects to the bottom. Even with these two possibillities you still have an enormous number of variations. You can let the border-cells maintain their initial values or you can vary them with a certain border-algorithm or even change them randomly. Needless to say that the most interesting cellular automata of the sheer infinite possible automata are the ones where chaotic behaviour is present or where a great contrast between complexity and simplicity exist. The Yin Yang Fire is a pure cellular automaton which exhibits chaotic behaviour and has a very high contrast between a simple algorithm and a seemingly eternal (ever changing) burning fire ...


Random

This is an example of a picture that can emerge when no symmetry is used. The number of pictures that can emerge from the yin yang fire effect is infinite, this picture is just a snapshot and can therefore not give a good impression of the seemingly random emerging and dying out of a wide variety of figures. Note that the algorithm itself entails no randomness whatsoever! Everything is created out of (almost) nothing!






Chaos Theory


During several centuries "real" scientists have always neglected non-linear aspects of phenomena they observed, only the linear and highly mathematical aspects were studied extensively. Typical examples of the non-linear phenomena science neglected are: friction, turbulence, many body systems (like gas molecules) or almost all natural processes seen in nature. Only since the last 20 years or so, these non-linear aspects got some of the scientific attention they deserve. An important new theory that is build around these non-linear phenomena is the so called chaos-theory. It is not easy to explain the fundamentals of the chaos-theory, because there are no clear laws or postulates, and yet the understanding of the theory is not very difficult. Maybe the best and shortest explanation of the theory is: Chaos is not really chaos! This means that chaotic systems, like the weather for example, are not a total mess. Chaotic systems obey to some very basic laws like any other linear system. The dynamics of the weather for example highly depends on certain conditions and only at some extreme conditions the system behaves like a real mess, at other conditions weather behaves in a very logical and even predictable way.

Another important aspect of chaotic systems is that the state of the system, at any time, highly depends on the initial conditions. A very famous example to explain this effect is the so called butterfly effect, which states that the wings of a flying butterfly in Brazil can cause a hurricane at the other side of the earth within one or two weeks. This example however confuses many people because they cannot really visualize flow of air and the influence of small air-flows on bigger air-flows etc.. I personally prefer a much easier example. Take for example a certain rat at the time when the plague played the role of the grim reaper in Europe. This certain rat could have had the choice between two barns where the grain for certain families had been stored. One barn belonging to the ancestors of Hitler and the other belonging to an arbitrary family. At that time that rat could directly determine whether or how world war II began! The point however is that if one looks a little bit further back in time, a flee which has the choice between two rats can on its turn determine the fate of world war II. But there are millions or billions of rats and flees and only time can determine whether one flee or rat will have such an impact on history. The fact is that one flee CAN determine the course of history, but it might as well not ...

An important discovery which can be regarded as the foundation for the modern chaos theory is done by Edward Lorenz. He tried to simulate some weather phenomena and used a computermodel. By coincidence he tried some simulations twice with two different starting conditions (only very slighty different, Lorenz didn't even know that the conditions were different) and he came up with two very different results! This turned out to be a very basic aspect of chaotic systems; very high dependancy on initial conditions. This effect can prove that even if the weather obeys very simple mathematical rules and if one can determine every condition of the current weather very accurately, it still is impossible to predict the weather more than about three days. To exaggerate this a little bit; even if one measures the temperature, airflow, pressure etc. at every cubic centimeter of the atmosphere at the highest possible accuracy, it can only enhance any prediction by a few days. And yet the weather is not totally unpredictable ...

The link with the Yin Yang Fire effect is that the Yin Yang Fire is a real chaotic system, it can also visualize the high dependancy on initial conditions perfectly. Below you see two very slightly different -differing with only 1 pixel- random starting conditions and some subsequent states of the system (after 32, 480, 720 and 1000 iterations). It can be seen that only one pixel can cause a totally different state after only a very limited amount of iterations. At first glance the bottom pictures look almost the same, but if you imagine that the initial difference is just one value of one pixel in the original 640x480x256 picture, which is about 1/(128*640*480)*100 = 0.0000025 percent, the resulting difference is suprising. For comparison: Suppose that the pictures are weather-expectations (which they are not!) and you are living around the middle of the picture and that the initial difference is due to a small inaccuracy of a single thermometer!


Yin Yang Fire after 32, 480, 720 and 1000 iterations

(Note: To save space and download-time, the first two pictures point to the same file)

Click on the cell-picture below to see a more extended sequence and how this cell appears!



The first four states above show the starting phase of the Yin Yang Fire (starting with a random state) and after it the fire will burn in its more normal pseudo-random way. Although the fire exhibits a kind of random nature it is surprising that the total state of the automaton (in this case the total sum of the cells) shows a very stable periodic signal. As can be seen in the picture below, the state S resembles a kind of AM-modulated signal, where the modulation itself (the ripple on the periodic signal) also is surprisingly stable (meaning: varies only with a small amount). What does this mean? I don't know (yet), but further research is done to visualize a certain attractor ...


Statevector of YYF-automaton (S=sum of all cells)


(Note: The graph shows S for the left variant above. Where A,B,C and D stand for the four pictures)

Long term Statevector of YYF-automaton (S=sum of all cells)



The graph above shows a very strange effect, after about 50,000 iterations (about 120 periods of about 428 iterations) the variation of the statevector suddenly decreases with a significant amount. The highly stable periodic effect of the statevector in itself is very strange, but that the amplitude suddenly drops and stays about the same for at least 1,800,000 iterations (not all shown) is at least very weird. It is like a stable heartbeat which suddenly pumps much less blood ...

When viewing the animated Yin Yang Fire with a 428 iteration interval (about the period of the Yin Yang Fire automaton) one can see that the individual cells phase up or synchronize with eachother in some way. This effect becomes apparent across the complete 640x480 picture at about 50,000 iterations. This means that the reduction of amplitude in the graph above is a result of cells synchronizing with eachother in some way. It is also around the moment when the cell-like picture appears (at about 42,444 iterations) in the first sequence. The cell-like structure in fact is just an intermediate result (at least so it seems) of this synchronizing effect. This also means that the more random looking pictures of the typical fire, compared to the earlier states (which look much more regular), are in fact much more synchronized (or should I say organized?).




Scientific Aspects


The Yin Yang Fire has been discovered more or less accidentally while developing a simple graph-demo and at this point it is not clear whether the effect has any important scientific significance. It is already more or less clear that the algorithm is unique in that its use results in a very complex and highly dynamical non-linear system, fortunately in a very beautiful way. The quotation at the top of this page "Might there be a kind of Yin Yang Fire burning in our universe" is a kind of philosophical remark concerning the fact that empty space might have a kind of bubbling nature. The main scientific question being; How does it bubble? What do quantum fluctuations look like? The Yin Yang Fire has a bubbling nature, might quantum fluctuations be something like the bubbling nature of Yin Yang Fire? Not meaning the exact way the Yin Yang Fire works, because nature itself is not a cellular automaton, but might the general aspects of the fire look something like the bubbling nature of empty space? Note: These are not scientifical statements, it are just remarks to point out what direction the research is pointing towards ...

Even without extensive research the following statements are very plausible:

At this point more research is needed to determine the real scientific significance of the Yin Yang Fire, the research will initially be focused on the following points:
(This section will be updated during the research)



Funny Bear

Or ape? Just for fun ... These pictures really appear if you wait long enough! Can you imagine a better screensaver?





Symmetry

This example shows the possibility of a highly symmetric Yin Yang Fire effect.






Pictures/Animations


The Yin Yang Fire can produce an endless amount of pictures and animations, at the link below more pictures and a simple animation can be found. Note however that all the pictures together exceed 1 MB (this means: View only if you are interested).

More Pictures ...

The following link points to a small b/w mpeg Yin Yang Fire animation file which has been shown on MTV's Top Selection on June 10 1999.

Yin Yang Fire animation (mpeg-file: 1.2MB)




Notes


It has been decided -in order to do more research- not to reveal the Yin Yang Fire algorithm (yet), which also means that the programs concerning the Yin Yang Fire will not be released in the near future. There are several reasons not to reveal the algorithm, the most important being the fact that I could not forgive myself if someone else discovers something important from it, which I could have discovered myself. However in order to receive the free demo for the Yin Yang Fire (including the algorithm) as soon as the programs are released, one can still send an email to yyfire@ramos.nl with the text "Yin Yang Fire" in the subject or text (the demo will not exceed 50 kB). To give an idea, the alien-picture and animation are produced with a program with a size of about 2 kB! But I want to ask patience from the people who are interested, I have to pay for my own research, and in order to do this, I have to work on other things too ...

January 2000, Jack Ruijs jack@ramos.nl

As mentioned above, I have to fund my own research, this means making time free for research, research that doesn't pay any bills. For this reason I invested in some stocks at the end of 1999 ..., and at that time I worked for 3 days a week as an independent contractor, and planned to stop this work and do the research fulltime for a longer period. But anyone who invests in stocks, knows what happened ..., something went wrong ... I accepted a regular job and worked more than ever and also worked for another company as an independent contractor, just to fund my investments. And as everyone can guess, it is not possible to do the research next to two jobs. However, the stock-prices are rising again and all my loss is gone, but I still cannot afford to quit my regular job, and continue the research to the Yin Yang Fire algorithm.

Occasionally I get emails about the time it takes before anything new is mentioned on the Yin Yang Fire site and that I am egocentric and arrogant because I keep the algorithm to myself. Maybe this is true, but there is some reason for this. After discovering the Yin Yang Fire effect, I tried to contact several universities/persons that are working on the field of self organizing system / computer-algorithms etc.., but apart from a reaction from one of the greatest minds on a related field, I am still waiting for the first reaction from the "lesser" persons (talking about arrogance). I stopped the fruitless quest trying to contact other people and decided to do everything myself. I also have mixed feelings about the scientific world, I embrace the thought that although science is very beautiful, the scientific world itself is not. The greatest scientific discoveries are made by neglecting the scientific world!

May 2004, Jack Ruijs jack@ramos.nl




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April 1999 : Selected as site of the month by the Dutch math magazine Pythagoras

June 10 1999 : Yin Yang Fire animation shown on MTV's program: Top Selection


Ruijs Automation Home Page / Yin Yang Fire / RAMOS / Favourite Links / jack@ramos.nl / revised May 2004