How does a chain fountain work?

A chain fountain is the name given to the phenomenon where a chain flows upward against gravity and pours out of its container. This might appear illogical and almost magical, but it is governed by the same physics as everything else.
Let's define a chain first since its unique properties make this phenomenon possible. A chain is a flexible series of links and is usually made of metal. These interconnected links can give a chain the appearance of a string, but it is functionally distinct because the metal links that make up the chain are actually rigid rods and not flexible on their own. This is very important to the function of the chain fountain because it is the qualities of an inflexible rod that create the fountain effect as the chain flows out of its container.
When the chain fountain experiment begins, someone lifts the end of the chain out of its container and pulls it. Before someone pulls the chain out of the container the system is at rest, so it is important to note that this action imparts some energy to the system.
Back to the idea of an inflexible rod. When the chain is lifted out of the container and let go, it might appear like a string, but remember it is a series of rods that can't bend. Only the linking sections bend. Now that the system is in motion let's examine what is going on with each individual link.
Imagine a rod laying on a table. If you pull it up on one end, you might think you are only lifting it; however, you are also rotating the rod. It is the surface it sits on which prevents the rod from rotating around its center like it would want to (imagine if you pushed one end of a rod sitting on a table with no friction).
Newton's Third Law states that every action has an equal and opposite reaction. The end that is in contact with the surface is pushing down due to gravity, but this also means that the surface it is sitting on is pushing up. This end which is in contact with the surface is the secret to the chain fountain and provides the gravity-defying appearance of the chain fountain. 
The experimenter's initial application of force by pulling the chain out of the container means that individual link is pushing down on the link next in line, which is itself pushing back on the first link. Each link only interacts with the link immediately next to it. This gives the experiment the appearance of a fountain.
1. The beginning section of chain is pulled, starting the chain fountain.
2. This pull causes the first link on the pile of chain to be pulled (rotated) at one end.
3. The link gets an equal but opposite force as stated by Newton's Third Law, meaning the end that is pushing down on the surface it sits on will also be pushed up by the same surface.
4. This causes the chain to bounce up out of its container while still looking like a string because of the unique properties of a chain. 
5. The pull of the initial segment of chain means the weight of each link (from gravity) is pulling down on the chain. This weight pulls the chain down and gives the rigid links the characteristic chain fountain arc.
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