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What at first glance appears to be random behaviour is completely deterministic - it only seems random because imperceptible changes are making all the difference. It was the first chaotic system to be discovered, long before there was a Chaos Theory. 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. A nice way to see this "butterfly effect" for yourself is with a game of pool or billiards. Celebrate Halloween with a tradtional Irish game. Want more great Halloween ideas? Modern fighter jets achieve great manoeuvrability by virtue of being aerodynamically unstable - the slightest nudge is enough to drastically alter their flightpath. Commercial aircraft are aerodynamically stable, so that a small turbulent nudge (possibly butterfly-related) won’t push the plane out of a level flightpath. They must pull the eyeballs out of the tub with their toes and deposit them into a small bowl next to the tub.

These millions of cells must work in sync, contracting in just the right sequence at just the right time to produce a healthy heartbeat. In systems that behave nicely - without chaotic effects - small differences only produce small effects. The game is played with three balls, two white and one red, with one of the white balls having a small red dot, or spot, to distinguish it. Kids love this fast-paced game. A word of note about some of these games sets: Some stores sell versions of the game that don't even remotely resemble the original, so be sure to double-check a product before you buy. Now that you've stirred the cauldron, we'll show you how to play other Magical games in the next section. Additionally, consider chairs with padded armrests for added comfort during those intense games. Chairs made from hardwood frames are known for their sturdiness and longevity. Notice that three points are aligned: the point marking your position, the point on the mirror where you see the reflection of the object and the (imaginary) point behind the mirror where you believe the object to be. To prove our claims above, we are going to exploit this simple idea, the mirror being one side of the billiard table.

While looking at an object in a mirror, you have the impression that the object is behind the mirror. While there is no standard or regulation size for a billiards table, the most popular dimensions for a table measure 4 feet by 8 feet. If you can tease out the pattern’s underlying chaotic systems, you can effect a measure of control over randomness and turn instability into an asset. 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). Have a look at the Geogebra animation below (the play button is in the bottom left corner) and try to figure out how the construction works. If you would like to play the animation again, double click the refresh button in the top right corner. It's also a play on the world googolplex. 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.

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. Comfortingly, what is billiards it takes a large change in the flight controls to effect a large change in the plane’s motion. 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 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. Surprisingly, the solar system is a chaotic system too - with a prediction horizon of a hundred million years. In the case of the weather, the prediction horizon is nowadays about one week (thanks to ever-improving measuring instruments and models). 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.