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Name: Rellik
Country: United States
State: Virginia
Metro: Norfolk
Birthday: 6/22/1900
Gender: Female
Interests: love, hate, fire, blood, sharp things, boys, POETRY, MUSIC ( my life) sex ( don't practice it but I love it neway), thantology, art , vampyrism, ANDROGYNY, food, free things, piercings, tatoos, mY cheMicAL roMAncE, DEPECHE MODE, SWITCHBLADE SYMPHONY, Green Day, THE CURE, S.O.A.D., NEUROTIC FISH, SKINNY PUPPY, Linkin Park, THE BIRTHDAY MASSACRE , Marilyn Manson- Top 11 favourite bands/artists , anime/manga, paranormal phenomena, weird people, stuffed animals, inscence, the dark, rain, lightning, natural disasters, writing, reading, the UK, Japanese Culture , Gothic Lolita, foreign language, forensic science, fashion design, decorating, amusement parks, sleeping, philosophy, psychology, scary movies, random /modnar things, writing things backwards , zen, screaming, I love children..I am adopting at least 4 , witchcraft, tarot cards, romance, new age , mysticism, 60's 70's 80's and 90's pop culture, rotary phones, star trek, theology, golf, football, american football, activism, PETA, mor
Expertise: Dreaming up a better life...solving everyones' problems but my own...worrying...making people angry...doing it all and not giving a damn....yeah that's me ...THE PESSIMIST
Occupation: Artist
Industry: Art
Message: message meEmail: email me
Website: visit my website
AIM:  NoGravityHere
Member Since:
5/25/2005
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They say there is a sound when you hit rock bottom. It sort of rings like freedom, but is underscored by even louder pangs of defeat. Two years ago I felt like I was scraping the bottom and it has taken two years and about a million "a-ha" moments expanding on themselves to form one big epiphany just to get me where I am now, and it will take about a million more to get me where I need to be.
The summer of 2005, was a period of drastic growth and reflection for me. Before that I had been having terrible problems. I started my freshman year at Booker T. Washington High School, a school I was already reluctant to go to because of it's horrid reputation, in September of 2004. From the moment I set foot at the bus stop I could already feel the little cloud of anxiety forming over my head, however I tried to ignore it and remain optimistic. The optimism approach held up approximately a week before things really started to get out of hand. Similar to my experiences nearing the end of eighth grade, I would get dreadful anxiety attacks and end up missing whole classes cowering in a bathroom stall, hyper-ventilating holding my head in my sweaty palms mentally berating myself for being so weak. I was extremely depressed and miserable. I did everything I could to be like the kids I went to school with and nothing was working. I was often pushed around and made fun of. I felt small and inferior and it showed in everything I did ,or rather did not do. I avoided crowds, did not go out much, and spoke in public only when absolutely necessary. I lost interest in almost everything except breathing. I ate little and slept even less. The stress was taking a serious toll on my health as well. I began missing whole days of school until finally, on the twelfth of January 2005, I just stopped going altogether. Finally after talking to one of my teachers, who was very concerned, my mum decided to not only enroll me in the Nexus home schooling program for the remainder of the school year but to also have me " talk to someone" , or in other words she found me a therapist.
It was obvious after the first few sessions with Susan, my therapist, that there was little she could do for me besides offer medication, which I adamantly refused, and offer her advice, which was quite the opposite of helpful. It became evident to me then that I was the only one who could solve my problem. I suppose it was common sense after all, it was my brain, how then could a perfect stranger just waltz in and set everything the way it should be? I suffered...I suffer from a chronic low-grade depression called dysthymia , a condition involving long term and or recurring depressive symptoms that, while not disabling, keep a person from functioning normally. It often interferes with social interactions and enjoyment of life. This type of depression often results from un-conscious negative thinking habits. I’ve been living with it for at least ten years and despite the best medications and all the counseling in the world, no one could change my thinking but me. So in my free time ( I had a surplus of free time given that I'd become so reclusive) I began working to reverse the malignant paradigms that lay in my sub-conscious.
I had a lot of time to study myself sans outside interference. As a result, I was able to see a lot of things I hadn't noticed before. I never realized how unhappy with myself I was until I looked at myself in the "mirror". Everything from the way I thought, to the way I carried myself broadcast my low self-esteem. Then I realized why. I wasn't being myself at all. I was so caught up in being accepted and "trying to be like..." that I had just about lost sight of everything that I cared about. I was afraid to wear the clothes I wanted or openly listen to the music that I liked or speak the way I wanted to for fear of ridicule and rejection. However, even with the phony facade I was still unpopular, I was the fall girl, the push over. I got no respect , I had no friends and I was miserable all the same. That is when I developed the "screw it" attitude.
" It's better to be yourself and be comfortable, even if it's not necessarily "in" than try being someone you're not and being miserable" in other words " I am the way I am and if you don't like it "screw you" " That was the moment I stopped caring, to an extent, what people thought. I started dressing in what I liked , not what was the top trend this week on BET, I started listening to what I liked, doing what I wanted, and completely tuned out the taunts and jeers, ignored the stares and gasps, even laughed at the blatant double takes and the loud whispers of "Christ, look at her she is a freak" until they did not come as much...I actually enjoy the shock now I find it rather amusing . Step one, done.
After successfully completing a big step one, it was time to move on to the next part . Up until then the only social interaction I had was with Susan , family and the few contacts I held out of state, via e-mail and IM. I was extremely lonely and very bored, aside from my constant work at self-improvement and my schoolwork, which really only took about two hours. I spent my time writing poetry, reading, and studying philosophy. Poetry was a great outlet for me. It was like my own sort of therapy. Especially those times when my negative feelings threatened to overwhelm me. My counselor often worried that I would totter over into suicidal territory but I never did, there was a mantra I picked up somewhere and eventually adopted as my own : "When you look at pain as material, it makes all the difference in the world. The pain that is too big to be eased by it's use as material is one I don't want to imagine" There was truth in that for me and I have yet to find too great a pain to ease by it's conversion into art. I harnessed all my anxiety, doubt, fear, and anger ,steering it toward a more creative outlet then I used that as a means to make friends. I joined a few dark poetry groups and was greeted with wonderful feedback, it helped me build confidence as well as meet people who were into some of the same things I was, a first for me. Around that time I decided to sack my doctor, we were spending money on her services yet she was doing nothing for me. By the time school started I was ready to rejoin the social collective a "new" person.
Now I attend a new school, I have met people I like and can really relate to since I have learned that you must exude the qualities you want to attract. There are even times when I can actually say I am happy. I admit everything has not changed, I still have recurring depressive episodes, among other issues that I haven not completely worked through yet but my life is becoming one perpetual "a-ha" moment. Everyday I am enlightened. Everyday I stumble over some new revelation, some new moral with which to better myself. In retrospect the whole ordeal can be viewed as a positive experience and that is how I choose to see it. I believe, and my belief is proven here, that everything happens for a reason. If not for my mental breakdown freshman year I might still be at Booker T. and not Maury. Also, I know for one thing I would not have been forced to take a good look at myself and see what I was doing. I had been adapting to everyone else’s expectations for ten years unconsciously and it took a personal crisis to make me stop and realize it. I also understand now that you are only a victim if you allow yourself to be one. I could just sit and wallow in self-pity over the bad things that happen to me but there is no nobility in that, I would rather learn from it. In Buddhist belief all life is is one big lesson and until you grasp that fact and enlighten yourself you will keep on the same agonizing cycle, Samsara. I am not a Buddhist, however there is much to be learned from their teachings. True, there is a sound when you hit bottom, but for me it is the sound of my nails scraping against weathered stone as I climb up out of this hole, because once you hit bottom there is nowhere to go but up.
Somnambulist’s Elegy
I’m becoming less defined.
This swinging bare bulb twists my vision. My body is no longer mine
Conquest of autonomy
Give in to the black and white silent film behind these eyes
Ragged Mattress
On the floor, this is my home now, forever,
It’s amazing how one moment my body is near to combustion,
Filled to the brim with elation,
Then all at once it’s gone, and all at once the difference between heaven and hell is realized beneath my feet.
Gasping; Grasping; Groping in the darkness,
These tears are stale,
And they burn at my face, but the burning pain inside is much more urgent than the stinging nag of such trivial flames,
My fingers twitch,
My right arm has a mind of it’s own, And I’m afraid to let it roam for fear of what it might do,
Question…
When is a house not a home?
When the very thought of the place saps the cheer from your eyes,
your body gets cold,
And you involuntarily begin to cry,
It’s a feeling,
A sense of foreboding, bad omens, a rush of negative chi
The moment you enter the vicinity,
There is nothing, nothing for me here! No food, no peace, just grief, like cheap karma pooling in these hollow walls.
It doesn’t seem to matter, It’s like I’m already dead,
A mere figment,
Trapped in some halfway house limbo between here, there, and nowhere,
The worst feeling
Is that of un-fulfillment among many,
Fifteen years of life,
Yet not one was spent on living,
And now all the dirty that’s built up inside me like wine bubbles in a corked bottle,
And I just can’t get clean,
Can’t get free of it, Overwhelmed where I can handle no more, Erosion, explosion,
Swinging screen door,
And I’m outside screaming, through the pouring rain, Running in the dark; in the wet,
But I can’t seem to outrun the pain,
No matter where I turn, It’s there, like a grinning Cheshire cat,
Lying on Dr. Just-a-teenage-phase’s couch,
Unctuous bastard,
Sitting up there with your pad and your pen,
Flinging big words about with swift and punning innuendo,
Just to KEEP ME MEDICATED,
Well I think these little green capsules are defective, and your diagnosis full of holes,
I’m trapped in this winding labyrinth of mental dysfunktion,
And there’s not a soul in sight
To show me which way to go. Through these endless hallways, back to my broken room,
On the soggy ground beneath the broken skies, my shattered eyes,
And the light within them fades,
They say the easiest thing to do is to let go,
But they have no idea,
The times that I intend to fall, there’s always one more shiny piece if "hold on it‘s not over yet" ,
And only when I grab it,
Does it seem to loosen and send me six feet deeper down,
From blue sky to red core,
Silence is my veil, that tongue tying mute of your lungs in a static plastic bag,
Screaming " TAKE THIS GUN"!!!
I can’t use it anymore, just a user trying to use a tool for what it’s supposed to be used for,
Nearing the climax now,
Ambient music growing stronger, Mascara bleeds like gasoline,
Procrastination of life,
Disappointment fuels the fire, and I’m TRYING, clawing my way out before this heart expires,
I’ve got a heedful of doubt and a fist full of matches,
Armed with a solemn smile and a wrist full of scratches,
A noble death,
In stark contrast to a frivolous life, but never once believed,
For there is no nobility in suicide,
But what does it matter? It never happened and It never will,
Because " you were never gonna do it anyway"
So don’t waste your flowers laying them across my damn life,
Being dragged by the hair,
Back to the bleak house, echoing modified lies,
Back inside the broken room,
All the walls are painted red, Writhing on a ragged mattress in the middle of the floor,
Trying to reclaim the quiet,
From the boisterous voices in my head, Talking in my sleep,
Whispering prayers and seeping sins,
The windows are all covered, and the bulb is swinging bare,
And they’re rapping at the door now,
And they’re coming up the stairs,
The last thing I remember was the bitter cold, the lights were flashing red and blue,
Distant crying,
And I thought I heard someone say " I love you",
Then the lights just went away,
A moribund life,
And all that is left, etched on countless pages, the malfunction of her head.
::Fin:: | | |
| IT IS BELIEVED that Jesus was born in the spring or early fall, and that it was fourth-century Christians who chose to celebrate Christmas on Dec. 25, the date of the Roman pagan holiday Dies Natalis Invicti Solis, or "birthday of the unconquered sun."
SOLSTICE MEANS "sun standing still," reflecting the time of year when the sun appears to hold its place at the highest or lowest point in the sky for a few days, around June 21 and Dec. 21.
MODERN PAGAN beliefs include the equality of men and women, the individual's ability to communicate with deities, the right to pursue happiness without hurting others and the idea that people's actions, good or bad, return to them threefold. | | |
| I am not abandoning xanga, but I have left in a sense to persue Myspace, xanga is now a head quarters for my philosophies and my studies....my myspace is www.myspace.com/the_shady_jane
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What exactly is chaos? The name "chaos theory" comes from the fact that the systems that the theory describes are apparently disordered, but chaos theory is really about finding the underlying order in apparently random data.
When was chaos first discovered? The first true experimenter in chaos was a meteorologist, named Edward Lorenz. In 1960, he was working on the problem of weather prediction. He had a computer set up, with a set of twelve equations to model the weather. It didn't predict the weather itself. However this computer program did theoretically predict what the weather might be.
One day in 1961, he wanted to see a particular sequence again. To save time, he started in the middle of the sequence, instead of the beginning. He entered the number off his printout and left to let it run.
When he came back an hour later, the sequence had evolved differently. Instead of the same pattern as before, it diverged from the pattern, ending up wildly different from the original. (See figure 1.) Eventually he figured out what happened. The computer stored the numbers to six decimal places in its memory. To save paper, he only had it print out three decimal places. In the original sequence, the number was .506127, and he had only typed the first three digits, .506.
By all conventional ideas of the time, it should have worked. He should have gotten a sequence very close to the original sequence. A scientist considers himself lucky if he can get measurements with accuracy to three decimal places. Surely the fourth and fifth, impossible to measure using reasonable methods, can't have a huge effect on the outcome of the experiment. Lorenz proved this idea wrong.
This effect came to be known as the butterfly effect. The amount of difference in the starting points of the two curves is so small that it is comparable to a butterfly flapping its wings.
The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does. (Ian Stewart, Does God Play Dice? The Mathematics of Chaos, pg. 141)
This phenomenon, common to chaos theory, is also known as sensitive dependence on initial conditions. Just a small change in the initial conditions can drastically change the long-term behavior of a system. Such a small amount of difference in a measurement might be considered experimental noise, background noise, or an inaccuracy of the equipment. Such things are impossible to avoid in even the most isolated lab. With a starting number of 2, the final result can be entirely different from the same system with a starting value of 2.000001. It is simply impossible to achieve this level of accuracy - just try and measure something to the nearest millionth of an inch!
From this idea, Lorenz stated that it is impossible to predict the weather accurately. However, this discovery led Lorenz on to other aspects of what eventually came to be known as chaos theory.
Lorenz started to look for a simpler system that had sensitive dependence on initial conditions. His first discovery had twelve equations, and he wanted a much more simple version that still had this attribute. He took the equations for convection, and stripped them down, making them unrealistically simple. The system no longer had anything to do with convection, but it did have sensitive dependence on its initial conditions, and there were only three equations this time. Later, it was discovered that his equations precisely described a water wheel.
At the top, water drips steadily into containers hanging on the wheel's rim. Each container drips steadily from a small hole. If the stream of water is slow, the top containers never fill fast enough to overcome friction, but if the stream is faster, the weight starts to turn the wheel. The rotation might become continuous. Or if the stream is so fast that the heavy containers swing all the way around the bottom and up the other side, the wheel might then slow, stop, and reverse its rotation, turning first one way and then the other. (James Gleick, Chaos - Making a New Science, pg. 29)
The equations for this system also seemed to give rise to entirely random behavior. However, when he graphed it, a surprising thing happened. The output always stayed on a curve, a double spiral. There were only two kinds of order previously known: a steady state, in which the variables never change, and periodic behavior, in which the system goes into a loop, repeating itself indefinitely. Lorenz's equations were definitely ordered - they always followed a spiral. They never settled down to a single point, but since they never repeated the same thing, they weren't periodic either. He called the image he got when he graphed the equations the Lorenz attractor. (See figure 2)
In 1963, Lorenz published a paper describing what he had discovered. He included the unpredictability of the weather, and discussed the types of equations that caused this type of behavior. Unfortunately, the only journal he was able to publish in was a meteorological journal, because he was a meteorologist, not a mathematician or a physicist. As a result, Lorenz's discoveries weren't acknowledged until years later, when they were rediscovered by others. Lorenz had discovered something revolutionary; now he had to wait for someone to discover him.
Another system in which sensitive dependence on initial conditions is evident is the flip of a coin. There are two variables in a flipping coin: how soon it hits the ground, and how fast it is flipping. Theoretically, it should be possible to control these variables entirely and control how the coin will end up. In practice, it is impossible to control exactly how fast the coin flips and how high it flips. It is possible to put the variables into a certain range, but it is impossible to control it enough to know the final results of the coin toss
A similar problem occurs in ecology, and the prediction of biological populations. The equation would be simple if population just rises indefinitely, but the effect of predators and a limited food supply make this equation incorrect. The simplest equation that takes this into account is the following:
next year's population = r * this year's population * (1 - this year's population)
In this equation, the population is a number between 0 and 1, where 1 represents the maximum possible population and 0 represents extinction. R is the growth rate. The question was, how does this parameter affect the equation? The obvious answer is that a high growth rate means that the population will settle down at a high population, while a low growth rate means that the population will settle down to a low number. This trend is true for some growth rates, but not for every one.
One biologist, Robert May, decided to see what would happen to the equation as the growth rate value changes. At low values of the growth rate, the population would settle down to a single number. For instance, if the growth rate value is 2.7, the population will settle down to .6292. As the growth rate increased, the final population would increase as well. Then, something weird happened. As soon as the growth rate passed 3, the line broke in two. Instead of settling down to a single population, it would jump between two different populations. It would be one value for one year, go to another value the next year, then repeat the cycle forever. Raising the growth rate a little more caused it to jump between four different values. As the parameter rose further, the line bifurcated (doubled) again. The bifurcations came faster and faster until suddenly, chaos appeared. Past a certain growth rate, it becomes impossible to predict the behavior of the equation. However, upon closer inspection, it is possible to see white strips. Looking closer at these strips reveals little windows of order, where the equation goes through the bifurcations again before returning to chaos. This self-similarity, the fact that the graph has an exact copy of itself hidden deep inside, came to be an important aspect of chaos.
An employee of IBM, Benoit Mandelbrot was a mathematician studying this self-similarity. One of the areas he was studying was cotton price fluctuations. No matter how the data on cotton prices was analyzed, the results did not fit the normal distribution. Mandelbrot eventually obtained all of the available data on cotton prices, dating back to 1900. When he analyzed the data with IBM's computers, he noticed an astonishing fact:
The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent on scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two World Wars and a depression. (James Gleick, Chaos - Making a New Science, pg. 86)
Mandelbrot analyzed not only cotton prices, but many other phenomena as well. At one point, he was wondering about the length of a coastline. A map of a coastline will show many bays. However, measuring the length of a coastline off a map will miss minor bays that were too small to show on the map. Likewise, walking along the coastline misses microscopic bays in between grains of sand. No matter how much a coastline is magnified, there will be more bays visible if it is magnified more.
One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve. To create a Koch curve, imagine an equilateral triangle. To the middle third of each side, add another equilateral triangle. Keep on adding new triangles to the middle part of each side, and the result is a Koch curve. (See figure 4) A magnification of the Koch curve looks exactly the same as the original. It is another self-similar figure.
The Koch curve brings up an interesting paradox. Each time new triangles are added to the figure, the length of the line gets longer. However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area.
To get around this difficulty, mathematicians invented fractal dimensions. Fractal comes from the word fractional. The fractal dimension of the Koch curve is somewhere around 1.26. A fractional dimension is impossible to conceive, but it does make sense. The Koch curve is rougher than a smooth curve or line, which has one dimension. Since it is rougher and more crinkly, it is better at taking up space. However, it's not as good at filling up space as a square with two dimensions is, since it doesn't really have any area. So it makes sense that the dimension of the Koch curve is somewhere in between the two.
Fractal has come to mean any image that displays the attribute of self-similarity. The bifurcation diagram of the population equation is fractal. The Lorenz Attractor is fractal. The Koch curve is fractal.
During this time, scientists found it very difficult to get work published about chaos. Since they had not yet shown the relevance to real-world situations, most scientists did not think the results of experiments in chaos were important. As a result, even though chaos is a mathematical phenomenon, most of the research into chaos was done by people in other areas, such as meteorology and ecology. The field of chaos sprouted up as a hobby for scientists working on problems that maybe had something to do with it.
Later, a scientist by the name of Feigenbaum was looking at the bifurcation diagram again. He was looking at how fast the bifurcations come. He discovered that they come at a constant rate. He calculated it as 4.669. In other words, he discovered the exact scale at which it was self-similar. Make the diagram 4.669 times smaller, and it looks like the next region of bifurcations. He decided to look at other equations to see if it was possible to determine a scaling factor for them as well. Much to his surprise, the scaling factor was exactly the same. Not only was this complicated equation displaying regularity, the regularity was exactly the same as a much simpler equation. He tried many other functions, and they all produced the same scaling factor, 4.669.
This was a revolutionary discovery. He had found that a whole class of mathematical functions behaved in the same, predictable way. This universality would help other scientists easily analyze chaotic equations. Universality gave scientists the first tools to analyze a chaotic system. Now they could use a simple equation to predict the outcome of a more complex equation.
Many scientists were exploring equations that created fractal equations. The most famous fractal image is also one of the most simple. It is known as the Mandelbrot set (pictures of the mandelbrot set). The equation is simple: z=z2+c. To see if a point is part of the Mandelbrot set, just take a complex number z. Square it, then add the original number. Square the result, then add the original number. Repeat that ad infinitum, and if the number keeps on going up to infinity, it is not part of the Mandelbrot set. If it stays down below a certain level, it is part of the Mandelbrot set. The Mandelbrot set is the innermost section of the picture, and each different shade of gray represents how far out that particular point is. One interesting feature of the Mandelbrot set is that the circular humps match up to the bifurcation graph. The Mandelbrot fractal has the same self-similarity seen in the other equations. In fact, zooming in deep enough on a Mandelbrot fractal will eventually reveal an exact replica of the Mandelbrot set, perfect in every detail.
Fractal structures have been noticed in many real-world areas, as well as in mathematician's minds. Blood vessels branching out further and further, the branches of a tree, the internal structure of the lungs, graphs of stock market data, and many other real-world systems all have something in common: they are all self-similar.
Scientists at UC Santa Cruz found chaos in a dripping water faucet. By recording a dripping faucet and recording the periods of time, they discovered that at a certain flow velocity, the dripping no longer occurred at even times. When they graphed the data, they found that the dripping did indeed follow a pattern.
The human heart also has a chaotic pattern. The time between beats does not remain constant; it depends on how much activity a person is doing, among other things. Under certain conditions, the heartbeat can speed up. Under different conditions, the heart beats erratically. It might even be called a chaotic heartbeat. The analysis of a heartbeat can help medical researchers find ways to put an abnormal heartbeat back into a steady state, instead of uncontrolled chaos.
Researchers discovered a simple set of three equations that graphed a fern. This started a new idea - perhaps DNA encodes not exactly where the leaves grow, but a formula that controls their distribution. DNA, even though it holds an amazing amount of data, could not hold all of the data necessary to determine where every cell of the human body goes. However, by using fractal formulas to control how the blood vessels branch out and the nerve fibers get created, DNA has more than enough information. It has even been speculated that the brain itself might be organized somehow according to the laws of chaos.
Chaos even has applications outside of science. Computer art has become more realistic through the use of chaos and fractals. Now, with a simple formula, a computer can create a beautiful, and realistic tree. Instead of following a regular pattern, the bark of a tree can be created according to a formula that almost, but not quite, repeats itself.
Music can be created using fractals as well. Using the Lorenz attractor, Diana S. Dabby, a graduate student in electrical engineering at the Massachusetts Institute of Technology, has created variations of musical themes. ("Bach to Chaos: Chaotic Variations on a Classical Theme", Science News, Dec. 24, 1994) By associating the musical notes of a piece of music like Bach's Prelude in C with the x coordinates of the Lorenz attractor, and running a computer program, she has created variations of the theme of the song. Most musicians who hear the new sounds believe that the variations are very musical and creative.
Chaos has already had a lasting effect on science, yet there is much still left to be discovered. Many scientists believe that twentieth century science will be known for only three theories: relativity, quantum mechanics, and chaos. Aspects of chaos show up everywhere around the world, from the currents of the ocean and the flow of blood through fractal blood vessels to the branches of trees and the effects of turbulence. Chaos has inescapably become part of modern science. As chaos changed from a little-known theory to a full science of its own, it has received widespread publicity. Chaos theory has changed the direction of science: in the eyes of the general public, physics is no longer simply the study of subatomic particles in a billion-dollar particle accelerator, but the study of chaotic systems and how they work.
..
An employee of IBM, Benoit Mandelbrot was a mathematician studying this self-similarity. One of the areas he was studying was cotton price fluctuations. No matter how the data on cotton prices was analyzed, the results did not fit the normal distribution. Mandelbrot eventually obtained all of the available data on cotton prices, dating back to 1900. When he analyzed the data with IBM's computers, he noticed an astonishing fact:
The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent on scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two World Wars and a depression. (James Gleick, Chaos - Making a New Science, pg. 86)
Mandelbrot analyzed not only cotton prices, but many other phenomena as well. At one point, he was wondering about the length of a coastline. A map of a coastline will show many bays. However, measuring the length of a coastline off a map will miss minor bays that were too small to show on the map. Likewise, walking along the coastline misses microscopic bays in between grains of sand. No matter how much a coastline is magnified, there will be more bays visible if it is magnified more.
One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve. To create a Koch curve, imagine an equilateral triangle. To the middle third of each side, add another equilateral triangle. Keep on adding new triangles to the middle part of each side, and the result is a Koch curve. (See figure 4) A magnification of the Koch curve looks exactly the same as the original. It is another self-similar figure.
The Koch curve brings up an interesting paradox. Each time new triangles are added to the figure, the length of the line gets longer. However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area.
To get around this difficulty, mathematicians invented fractal dimensions. Fractal comes from the word fractional. The fractal dimension of the Koch curve is somewhere around 1.26. A fractional dimension is impossible to conceive, but it does make sense. The Koch curve is rougher than a smooth curve or line, which has one dimension. Since it is rougher and more crinkly, it is better at taking up space. However, it's not as good at filling up space as a square with two dimensions is, since it doesn't really have any area. So it makes sense that the dimension of the Koch curve is somewhere in between the two.
Fractal has come to mean any image that displays the attribute of self-similarity. The bifurcation diagram of the population equation is fractal. The Lorenz Attractor is fractal. The Koch curve is fractal.
During this time, scientists found it very difficult to get work published about chaos. Since they had not yet shown the relevance to real-world situations, most scientists did not think the results of experiments in chaos were important. As a result, even though chaos is a mathematical phenomenon, most of the research into chaos was done by people in other areas, such as meteorology and ecology. The field of chaos sprouted up as a hobby for scientists working on problems that maybe had something to do with it.
Later, a scientist by the name of Feigenbaum was looking at the bifurcation diagram again. He was looking at how fast the bifurcations come. He discovered that they come at a constant rate. He calculated it as 4.669. In other words, he discovered the exact scale at which it was self-similar. Make the diagram 4.669 times smaller, and it looks like the next region of bifurcations. He decided to look at other equations to see if it was possible to determine a scaling factor for them as well. Much to his surprise, the scaling factor was exactly the same. Not only was this complicated equation displaying regularity, the regularity was exactly the same as a much simpler equation. He tried many other functions, and they all produced the same scaling factor, 4.669.
This was a revolutionary discovery. He had found that a whole class of mathematical functions behaved in the same, predictable way. This universality would help other scientists easily analyze chaotic equations. Universality gave scientists the first tools to analyze a chaotic system. Now they could use a simple equation to predict the outcome of a more complex equation.
Many scientists were exploring equations that created fractal equations. The most famous fractal image is also one of the most simple. It is known as the Mandelbrot set (pictures of the mandelbrot set). The equation is simple: z=z2+c. To see if a point is part of the Mandelbrot set, just take a complex number z. Square it, then add the original number. Square the result, then add the original number. Repeat that ad infinitum, and if the number keeps on going up to infinity, it is not part of the Mandelbrot set. If it stays down below a certain level, it is part of the Mandelbrot set. The Mandelbrot set is the innermost section of the picture, and each different shade of gray represents how far out that particular point is. One interesting feature of the Mandelbrot set is that the circular humps match up to the bifurcation graph. The Mandelbrot fractal has the same self-similarity seen in the other equations. In fact, zooming in deep enough on a Mandelbrot fractal will eventually reveal an exact replica of the Mandelbrot set, perfect in every detail.
Fractal structures have been noticed in many real-world areas, as well as in mathematician's minds. Blood vessels branching out further and further, the branches of a tree, the internal structure of the lungs, graphs of stock market data, and many other real-world systems all have something in common: they are all self-similar.
Scientists at UC Santa Cruz found chaos in a dripping water faucet. By recording a dripping faucet and recording the periods of time, they discovered that at a certain flow velocity, the dripping no longer occurred at even times. When they graphed the data, they found that the dripping did indeed follow a pattern.
The human heart also has a chaotic pattern. The time between beats does not remain constant; it depends on how much activity a person is doing, among other things. Under certain conditions, the heartbeat can speed up. Under different conditions, the heart beats erratically. It might even be called a chaotic heartbeat. The analysis of a heartbeat can help medical researchers find ways to put an abnormal heartbeat back into a steady state, instead of uncontrolled chaos.
Researchers discovered a simple set of three equations that graphed a fern. This started a new idea - perhaps DNA encodes not exactly where the leaves grow, but a formula that controls their distribution. DNA, even though it holds an amazing amount of data, could not hold all of the data necessary to determine where every cell of the human body goes. However, by using fractal formulas to control how the blood vessels branch out and the nerve fibers get created, DNA has more than enough information. It has even been speculated that the brain itself might be organized somehow according to the laws of chaos.
Chaos even has applications outside of science. Computer art has become more realistic through the use of chaos and fractals. Now, with a simple formula, a computer can create a beautiful, and realistic tree. Instead of following a regular pattern, the bark of a tree can be created according to a formula that almost, but not quite, repeats itself.
Music can be created using fractals as well. Using the Lorenz attractor, Diana S. Dabby, a graduate student in electrical engineering at the Massachusetts Institute of Technology, has created variations of musical themes. ("Bach to Chaos: Chaotic Variations on a Classical Theme", Science News, Dec. 24, 1994) By associating the musical notes of a piece of music like Bach's Prelude in C with the x coordinates of the Lorenz attractor, and running a computer program, she has created variations of the theme of the song. Most musicians who hear the new sounds believe that the variations are very musical and creative.
Chaos has already had a lasting effect on science, yet there is much still left to be discovered. Many scientists believe that twentieth century science will be known for only three theories: relativity, quantum mechanics, and chaos. Aspects of chaos show up everywhere around the world, from the currents of the ocean and the flow of blood through fractal blood vessels to the branches of trees and the effects of turbulence. Chaos has inescapably become part of modern science. As chaos changed from a little-known theory to a full science of its own, it has received widespread publicity. Chaos theory has changed the direction of science: in the eyes of the general public, physics is no longer simply the study of subatomic particles in a billion-dollar particle accelerator, but the study of chaotic systems and how they work.
One biologist, Robert May, decided to see what would happen to the equation as the growth rate value changes. At low values of the growth rate, the population would settle down to a single number. For instance, if the growth rate value is 2.7, the population will settle down to .6292. As the growth rate increased, the final population would increase as well. Then, something weird happened. As soon as the growth rate passed 3, the line broke in two. Instead of settling down to a single population, it would jump between two different populations. It would be one value for one year, go to another value the next year, then repeat the cycle forever. Raising the growth rate a little more caused it to jump between four different values. As the parameter rose further, the line bifurcated (doubled) again. The bifurcations came faster and faster until suddenly, chaos appeared. Past a certain growth rate, it becomes impossible to predict the behavior of the equation. However, upon closer inspection, it is possible to see white strips. Looking closer at these strips reveals little windows of order, where the equation goes through the bifurcations again before returning to chaos. This self-similarity, the fact that the graph has an exact copy of itself hidden deep inside, came to be an important aspect of chaos.
An employee of IBM, Benoit Mandelbrot was a mathematician studying this self-similarity. One of the areas he was studying was cotton price fluctuations. No matter how the data on cotton prices was analyzed, the results did not fit the normal distribution. Mandelbrot eventually obtained all of the available data on cotton prices, dating back to 1900. When he analyzed the data with IBM's computers, he noticed an astonishing fact:
The numbers that produced aberrations from the point of view of normal distribution produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent on scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two World Wars and a depression. (James Gleick, Chaos - Making a New Science, pg. 86)
Mandelbrot analyzed not only cotton prices, but many other phenomena as well. At one point, he was wondering about the length of a coastline. A map of a coastline will show many bays. However, measuring the length of a coastline off a map will miss minor bays that were too small to show on the map. Likewise, walking along the coastline misses microscopic bays in between grains of sand. No matter how much a coastline is magnified, there will be more bays visible if it is magnified more.
One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve. To create a Koch curve, imagine an equilateral triangle. To the middle third of each side, add another equilateral triangle. Keep on adding new triangles to the middle part of each side, and the result is a Koch curve. (See figure 4) A magnification of the Koch curve looks exactly the same as the original. It is another self-similar figure.
The Koch curve brings up an interesting paradox. Each time new triangles are added to the figure, the length of the line gets longer. However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle. Essentially, it is a line of infinite length surrounding a finite area.
To get around this difficulty, mathematicians invented fractal dimensions. Fractal comes from the word fractional. The fractal dimension of the Koch curve is somewhere around 1.26. A fractional dimension is impossible to conceive, but it does make sense. The Koch curve is rougher than a smooth curve or line, which has one dimension. Since it is rougher and more crinkly, it is better at taking up space. However, it's not as good at filling up space as a square with two dimensions is, since it doesn't really have any area. So it makes sense that the dimension of the Koch curve is somewhere in between the two.
Fractal has come to mean any image that displays the attribute of self-similarity. The bifurcation diagram of the population equation is fractal. The Lorenz Attractor is fractal. The Koch curve is fractal.
During this time, scientists found it very difficult to get work published about chaos. Since they had not yet shown the relevance to real-world situations, most scientists did not think the results of experiments in chaos were important. As a result, even though chaos is a mathematical phenomenon, most of the research into chaos was done by people in other areas, such as meteorology and ecology. The field of chaos sprouted up as a hobby for scientists working on problems that maybe had something to do with it.
Later, a scientist by the name of Feigenbaum was looking at the bifurcation diagram again. He was looking at how fast the bifurcations come. He discovered that they come at a constant rate. He calculated it as 4.669. In other words, he discovered the exact scale at which it was self-similar. Make the diagram 4.669 times smaller, and it looks like the next region of bifurcations. He decided to look at other equations to see if it was possible to determine a scaling factor for them as well. Much to his surprise, the scaling factor was exactly the same. Not only was this complicated equation displaying regularity, the regularity was exactly the same as a much simpler equation. He tried many other functions, and they all produced the same scaling factor, 4.669.
This was a revolutionary discovery. He had found that a whole class of mathematical functions behaved in the same, predictable way. This universality would help other scientists easily analyze chaotic equations. Universality gave scientists the first tools to analyze a chaotic system. Now they could use a simple equation to predict the outcome of a more complex equation.
Many scientists were exploring equations that created fractal equations. The most famous fractal image is also one of the most simple. It is known as the Mandelbrot set (pictures of the mandelbrot set). The equation is simple: z=z2+c. To see if a point is part of the Mandelbrot set, just take a complex number z. Square it, then add the original number. Square the result, then add the original number. Repeat that ad infinitum, and if the number keeps on going up to infinity, it is not part of the Mandelbrot set. If it stays down below a certain level, it is part of the Mandelbrot set. The Mandelbrot set is the innermost section of the picture, and each different shade of gray represents how far out that particular point is. One interesting feature of the Mandelbrot set is that the circular humps match up to the bifurcation graph. The Mandelbrot fractal has the same self-similarity seen in the other equations. In fact, zooming in deep enough on a Mandelbrot fractal will eventually reveal an exact replica of the Mandelbrot set, perfect in every detail.
Fractal structures have been noticed in many real-world areas, as well as in mathematician's minds. Blood vessels branching out further and further, the branches of a tree, the internal structure of the lungs, graphs of stock market data, and many other real-world systems all have something in common: they are all self-similar.
Scientists at UC Santa Cruz found chaos in a dripping water faucet. By recording a dripping faucet and recording the periods of time, they discovered that at a certain flow velocity, the dripping no longer occurred at even times. When they graphed the data, they found that the dripping did indeed follow a pattern.
The human heart also has a chaotic pattern. The time between beats does not remain constant; it depends on how much activity a person is doing, among other things. Under certain conditions, the heartbeat can speed up. Under different conditions, the heart beats erratically. It might even be called a chaotic heartbeat. The analysis of a heartbeat can help medical researchers find ways to put an abnormal heartbeat back into a steady state, instead of uncontrolled chaos.
Researchers discovered a simple set of three equations that graphed a fern. This started a new idea - perhaps DNA encodes not exactly where the leaves grow, but a formula that controls their distribution. DNA, even though it holds an amazing amount of data, could not hold all of the data necessary to determine where every cell of the human body goes. However, by using fractal formulas to control how the blood vessels branch out and the nerve fibers get created, DNA has more than enough information. It has even been speculated that the brain itself might be organized somehow according to the laws of chaos.
Chaos even has applications outside of science. Computer art has become more realistic through the use of chaos and fractals. Now, with a simple formula, a computer can create a beautiful, and realistic tree. Instead of following a regular pattern, the bark of a tree can be created according to a formula that almost, but not quite, repeats itself.
Music can be created using fractals as well. Using the Lorenz attractor, Diana S. Dabby, a graduate student in electrical engineering at the Massachusetts Institute of Technology, has created variations of musical themes. ("Bach to Chaos: Chaotic Variations on a Classical Theme", Science News, Dec. 24, 1994) By associating the musical notes of a piece of music like Bach's Prelude in C with the x coordinates of the Lorenz attractor, and running a computer program, she has created variations of the theme of the song. Most musicians who hear the new sounds believe that the variations are very musical and creative.
Chaos has already had a lasting effect on science, yet there is much still left to be discovered. Many scientists believe that twentieth century science will be known for only three theories: relativity, quantum mechanics, and chaos. Aspects of chaos show up everywhere around the world, from the currents of the ocean and the flow of blood through fractal blood vessels to the branches of trees and the effects of turbulence. Chaos has inescapably become part of modern science. As chaos changed from a little-known theory to a full science of its own, it has received widespread publicity. Chaos theory has changed the direction of science: in the eyes of the general public, physics is no longer simply the study of subatomic particles in a billion-dollar particle accelerator, but the study of chaotic systems and how they work.
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| I feel heavy like a lead weight , it's own mass dragging it deeper into the
sea... all my motivations left me, the just slowly fell away , left lonely my
vacant soul...
Strangely enough this is no poem, therein lies the irony, this is my life ...
and I cannot help but throw myself a pity party...more like a Grand
Lamenteurs Ball... for my anxiety never travels alone...hardships journey in
clusters magnifying grief tenfold...
At 4:35 am when I should be in bed asleep and dreaming dreams of
grandeur ... I am awake tense...in a darkened living room, lit only by the
almost blinding light of this monitor...every sound beckons for my attention,
and I cannot think of anything but the noise inside my head ...driving me to
tears...sleep never comes and instead I would lie on my back ..hands clasped
together across my chest...an ominous foreshadowing of my future...ranting to
my dark quarters as a madwoman would, my sermon faling upon deaf ears...and I
can find no solace in school and it's taxing demands on my already unstable
being...for whom could I rest on without the weight of my distress dragging
us both spiraling down into the abyss ...there is no one...and none it seems
would understand...I live a double life...my shadow side only rearing its
ugly head in the company of myself, the rest of the time I wear a mask...so
as not to spread my contagion amongst the self actualized, self made success
stories...I suffer the belladonna complex...there is none so sweet as the
venom of my lips ... one has only to taste it ... To consort with me is to
consort with admirable pleasures , however in consorting with me one runs the
risk of falling into chaos with me...I'm poison...
I don't want to wake today, although I'm already up, Somehow I've fallen
behind and though I try to behave nonchalantly..I am frightened...frightened
of a relapse into ,y cliche'd past, frightened of the ramifications of my
actions, be they from sloth or from anxiety, from depression or demons that
dwell in the heart and mind of the dreamer to torment them into madness...I'm
failing ...secummbing to the norm. to the below average standard of our
age...I disgust myself while at the same time I sympathize because I know
that something is wrong...but how long will that excuse exemplify me...there
is only a small timeframe for allowance on mental dysfunction before one is
permanantly condemned...I do not wish to lead a damned life... | | |
| 
\ Arachnimancia: Tragic Romance of the Black Widow©
- Rellik ( ShaneceJ.)
Rock steady. my trembling hands,
delving impressions in your flesh, and cold as death pallor is spoiled by contrast of royal red...
Your regal head, hangs low...Your eyes sunken to deep black holes,...courtesy of my sharpened thumbs... as you shriek in protest of sweet REDRUM ...innebriated and intoxicated, I suffocated you...skinned you with my scissor hands, and your skin will serve as suit...Wearing you to your own wake, crying like I care...they'll NEVER find your body, I know your caskets empty, and your corpse will never make it there... Penetration drags you down, In your own blood, I watched you drown...I'll pluck your stillborn heart out from your chest...Iron clad Irony...Grinning pleasure with every bit of blood soaked love I ingest...
You're so pretty decked out in red and blue...you remind me so much of a dead prostitue...that I dug up just to fuck one more time...but you were a gift I never wanted, the illustration of that fact so divine, I was never yours to keep, but I MADE YOU MINE
My lover unconcious, I love you unconcious.... slowly dying in the dark, peaceful absence of your cries, lucid silence only broken by my satisfied sigh,
Pretty lover uncosious, I LOVE you unconcious
Petty lover unconcious , I LOVE YOU UNCONCIOUS!!
Morbid self expression... I'll paint the walls with your blood,
The saccharine sweet of your blood on my lips, naive whore that you were, I think, as your post mortem self gives a sudden twitch... Cup of caffine and a stick of nicotene, slowly exhale and revel in the fog...as I lick my ruby stained fingertips, recline and close my eyes...
" We COULD mate...but then you'd have to die"
::Fin::
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On a less psychopatic note, here are more happy pictures of my favourite current day band ever!! YAY
 It
 
See if you can spot Gerard in this pic haha...
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Erika Made This Layout Rock
