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. A nice way to see this "butterfly effect" for yourself is with a game of pool or billiards. What Is the Difference Between Pool and Billiards? According to recent stats, about 46 million people across America play pool regularly. Some players mark the out of bounds line with chalk or other material that doesn't interfere with game play. A rotation along this line would result in a roll - the plane would start doing barrel rolls. The plane either climbs or dives, depending on the direction of the pitch. Commercial aircraft are aerodynamically stable, so that a small turbulent nudge (possibly butterfly-related) won’t push the plane out of a level flightpath. On the other hand, this stability is somewhat of an inconvenience to fighter pilots who prefer their aircraft to make rapid changes with minimal effort.

Louis XI, who loved the sport, commanded the creation of a table to play inside without needing to worry about the weather. Now that you've stirred the cauldron, we'll show you how to play other Magical games in the next section. In our next section, we'll show you how to play the Halloween version of the game, Ghost out of Water. Kid's Halloween Costumes: Pirate or princess? Want more great Halloween ideas? That’s why our great games all need solid pool balls. Modern fighter jets achieve great manoeuvrability by virtue of being aerodynamically unstable - the slightest nudge is enough to drastically alter their flightpath. UK standard pool tables are 7ft in length, but come in 6ft and 8ft too, (unlike American pool tables, with their standard tournament table size being 9ft). UK pool tables use napped felt, which causes friction and slows down the balls. Snooker is normally played using fifteen red balls, six colored balls, and one cue ball, all of which are significantly larger than pool balls. Phase space may seem fairly abstract, but one important application lies in understanding your heartbeat.

Though we may not be able to predict exactly how a chaotic system will behave moment to moment, knowing the attractor allows us to narrow down the possibilities. The millions of cells that make up your heart are constantly contracting and relaxing separately as part of an intricate chaotic system with complicated attractors. The main benefit to having a chaotic heart is that tiny variations in the way those millions of cells contract serves to distribute the load more evenly, reducing wear and tear on your heart and allowing it to pump decades longer than would otherwise be possible. The rate at which these tiny differences stack up provides each chaotic system with a prediction horizon - a length of time beyond which we can no longer accurately forecast its behaviour. In this case, Lorenz’s equations were causing errors to steadily grow over time. 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.

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). It also allows us to accurately predict how the system will respond if it is jolted off its attractor. No matter where it starts, the ball will immediately move in a very predictable way towards its attractor - the ocean surface. 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. 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. The best we can do for three bodies is to predict their movements moment by moment, and feed those predictions back into our equations …

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