In China, nine people sitting in the path of an air conditioning vent in a restaurant all got sick , most likely from one person, as the duct blew viral particles across their faces. Small things could have changed these outcomes. The clubber could have decided to watch TV instead of going out dancing.
If the choir practice was rescheduled for the next day, maybe the person would have felt sick and stayed home. The air conditioner in the restaurant could have been turned off.
And scientists have a name for systems that operate like this: chaos. But it can also help us appreciate why this uncertainty need not be so debilitating. Its movement is explained by the laws of motion written by Isaac Newton hundreds of years ago.
But slight changes in the initial condition of the pendulum — say it starts its swing from a little higher up, or if the weight of the pendulum balls is a little heavier, or one of the pendulum arms is a bit longer than the other — lead to wildly different outcomes that are very hard to predict. Is it too late for celebrations? Here is a very colorful second animation of 20 pendulums starting from the exactly same position, just with just 20 gram difference in mass.
The double pendulum is chaotic because the motion of the first pendulum influences the motion of the second, which then influences the entire apparatus. A one-gram change to the weight of a pendulum ball can result in a very different swing pattern than a two-gram change. It teaches us to understand the mechanics of a system — the science of how it works — without being able to precisely predict its future. Complicated ones, then? God knows. Myriad chains of events, operating in overlapping networks, conspire to chart its course.
Chaotic systems are everywhere and, in fact, dominate the universe. Stick a pendulum on the end of another pendulum, and you have a very simple but very chaotic system. The population of species over time is a chaotic system. Chaos is everywhere. This sensitivity to initial conditions means that with chaotic systems, it's impossible to make firm predictions, because you can never know exactly, precisely, to the infinite decimal point the state of the system. And if you're off by even the tiniest bit, after enough time, you'll have no idea what the system is doing.
There are a number of surprising features buried in this unpredictability and chaos. They appear mostly in something called phase space, a map that describes the state of a system at various points in time. If you know the properties of a system at a specific "snapshot," you can describe a point in phase space. As a system evolves and changes its state and properties, you can take another snapshot and describe a new point in phase space, over time building up a collection of points. With enough such points, you can see how the system has behaved over time.
Some systems exhibit a pattern called attractors. This means that no matter where you start the system, it ends up evolving into a particular state that it is especially fond of. For example, no matter where you drop a ball in a valley it will end up at the bottom of the valley. That bottom is the attractor of this system. When Lorenz looked at the phase space of his simple weather model, he found an attractor. But that attractor didn't look like anything that had been seen before.
The oven is eaten by rust, and the batter is to stale! Most of the new-born Cakes don't make it. Skelecake Grunt :. Story 4 Pastry Cookie :. Thirty seven. Thirty Eight! Foul creatures, I release you from your sweet temptations! Ferocious Cake Wolf :. Cake Boomerang Warrior :. Ah, and so the little nosy gnat has shown herself. How typical of a gnat to be attracted to sweet things Did Pomegranate Cookie say to "crumble" the intruder? Was there such a command?
You there! Do you wish to work for me? I can be merciful enough to pardon your foolish intrusion! We provide accommodations AND let you sleep in. And you, little nosy gnat, looks like you need both. Ha ha! What you see is what you see: nothing else, nothing more. Ah, can you here these sounds? That is the cake factory working day and night! I am Pastry Cookie , a devotee sworn to preserve the order of this world!
Story 5 Red Velvet Cookie :. Pet Cake Hound :. The Tower is composed of Trays , which are special challenges with both a set of enemies to be defeated and a set of restrictions for your team composition to follow. Most Trays consist of different enemy compositions from World Exploration , with a few being PvP battles against preset Cookie teams. In order to challenge a Tray, a player must have the required number of Searing Keys. As players ascend the Tower by clearing Trays, the rewards will become greater; however, enemies will also become stronger and restrictions will become tighter, requiring more heavily-invested Cookies.
Some Tray levels have two options instead of one, and clearing either Tray allows further progression. Some of these forks will be Chaotic Treasure Chests instead of levels, which contain a valuable amount of rewards if their Searing Key costs are paid.
While either Chest can be unlocked to progress, the more-expensive Chest typically contains rarer rewards.
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