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So except for the occasional maverick glittery soul, the colors of billiard balls will likely stay as they are, each set specific to their game, for the foreseeable future. The key to unlocking the hidden structure of a chaotic system is in determining its preferred set of behaviours - known to mathematicians as its attractor. The purpose of a defibrillator - the device that applies a large voltage of electricity across the heart - is not to "restart" the heart cells as such, but rather to give the chaotic system enough of a kick to move it off the fibrillating attractor and back to the healthy heartbeat attractor. A chaotic system will also move predictably towards its attractor in phase space - but instead of points or simple loops, we see "strange attractors" appear - complex and beautiful shapes (known as fractals) that twist and turn, intricately detailed at all possible scales. Our editors will review what you’ve submitted and determine whether to revise the article.

Obviously, as the black ball is worth the highest number of points, players will try to pot the black as often as possible after a red ball. This means that the ball will bounce infinitely many times on the sides of the billiard table and keep going forever. To prove our claims above, we are going to exploit this simple idea, the mirror being one side of the billiard table. The table sizes, balls and cues used in both pool and billiards are different. The table size of the pool game is three and a half feet by seven feet. Lorenz famously illustrated this effect with the analogy of a butterfly flapping its wings and thereby causing the formation of a hurricane half a world away. Once this computer program was up and running, Lorenz could produce long-term forecasts by feeding the predicted weather back into the computer over and over again, with each run forecasting further into the future.

All the three games involve the use of a cue stick and balls over a table covered in cloth with rubberised or leather cushions on the edges. All of the sides, or rails, of the table are bound in cushions and no pockets are present. The table and the cushioned rail bordering the table are topped with a feltlike tight-fitting cloth. The balls used are smaller and the table is pocketed. Clouds are not spheres, mountains are not cones … Consequently, they are equipped with on-board computers which constantly and delicately adjust the flight surfaces to cancel out the unwanted butterfly effects, leaving the pilot free to exploit his own. Two weeks is believed to be the limit we could ever achieve however much better computers and software get. But the important thing, I repeat, about this kind of chant is that it’s quite different from the ordinary religious exercise that, say, we have in our churches, where we are interminably talking and thinking, and we never get to contemplation. It is worth noting that the laws of physics that determine how the billiard balls move are precise and unambiguous: they allow no room for randomness. The cloth used in billiards is fast making the balls move more swiftly on the table.

One thing that I think it brings to the table is that it allows us to intuitively understand a curious property of ellipses. It is a mathematical toolkit that allows us to extract beautifully ordered structures from a sea of chaos - a window into the complex workings of such diverse natural systems as the beating of the human heart and the trajectories of asteroids. Though the dance of the planets has a lengthy prediction horizon, the effects of chaos cannot be ignored, for the intricate interplay of gravitation tugs among the planets has a large influence on the trajectories of the asteroids. The large rectangular table typically is twice as long as it is wide. Each time the ball passes through one of the foci, it reflects off the elliptical table and passes through the other focus. The game is played with 22 balls, made up of one white ball (the cue ball), 15 red balls, and six numbered coloured balls including one yellow 2, one green 3, one brown 4, one blue 5, one pink 6, and one black (valued at 7 points). Billiards is a reference name given to three different cue sports. A nice way to see this "butterfly effect" for yourself is with a game of pool or billiards.

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