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. 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. In this case, Lorenz’s equations were causing errors to steadily grow over time. This meant that tiny errors in the measurement of the current weather would not stay tiny, but relentlessly increased in size each time they were fed back into the computer until they had completely swamped the predictions. He created a mathematical model which, when supplied with a set of numbers representing the current weather, could predict the weather a few minutes in advance. Chaotic systems are an intimate mix of the two: from the outside they display unpredictable and chaotic behaviour, but expose the inner workings and you discover a perfectly deterministic set of equations ticking like clockwork. Other accessories like bridge sticks, cue gloves, cue cases, and scorekeeping tools can further enhance your game and make it more enjoyable. In a variety of the game called three-cushion billiards, the cue ball must also touch a cushion or cushions three or more times to complete a carom.

No matter where it starts, the ball will immediately move in a very predictable way towards its attractor - the ocean surface. Imagine taking a ping-pong ball far out into the ocean and letting it go. Each red ball when pocketed remains in the pocket, while the colours when pocketed, as long as any reds remain on the table, are placed on their respective spots. Interestingly, what we get is an elliptical caustic curve that shares the same foci as the elliptical table, and so these are confocal ellipses. If you then slide the pencil while keeping the string tight, then the shape that you get is an ellipse. You can visualise it like this: put a loop of string around pins located at the foci, then pull the string taut at one point using a pencil. In play, the object is to stroke the cue ball so that it hits the two object balls in succession, scoring a carom, or billiard, which counts one point. Thicker cloth tends to last longer but may affect ball speed slightly.

Most billiard tables use either woolen or worsted cloth. The table and the cushioned rail bordering the table are topped with a feltlike tight-fitting cloth. 3. What are the symmetries of the arithmetic billiard path (as a geometrical figure)? At the centre of Chaos Theory is the fascinating idea that order and chaos are not always diametrically opposed. Explainer: what is Chaos Theory? In 1887, the French mathematician Henri Poincaré showed that while Newton’s theory of gravity could perfectly predict how two planetary bodies would orbit under their mutual attraction, what is billiards adding a third body to the mix rendered the equations unsolvable. One way of defining an ellipse is in terms of two points, each of which is called a focus point. The behaviour of the system can be observed by placing a point at the location representing the starting configuration and watching how that point moves through the phase space. In phase space, a stable system will move predictably towards a very simple attractor (which will look like a single point in the phase space if the system settles down, or a simple loop if the system cycles between different configurations repeatedly). If released above the water it will fall, and if released underwater it will float.

Once there it clings to its attractor as it is buffeted to and fro in a literal sea of chaos, and quickly moves back to the surface if temporarily thrown above or dumped below the waves. There are numerous varieties of each game-particularly of carom and pocket billiards. Clouds are not spheres, mountains are not cones … What at first glance appears to be random behaviour is completely deterministic - it only seems random because imperceptible changes are making all the difference. And how can we tell the difference between pure randomness and orderly patterns that are cloaked in chaos? If you want to add a pop of color or make a statement, opt for bold patterns or vibrant shades that reflect your personality. Lastly, choose a color that complements your playing environment and enhances visibility. Playing billiards often involves long hours of sitting and focusing on every shot. Sitting for extended periods can cause discomfort if the chair lacks proper cushioning. No matter how consistent you are with the first shot (the break), the smallest of differences in the speed and angle with which you strike the white ball will cause the pack of billiards to scatter in wildly different directions every time.