There is a term known as "fair use" when it comes to copyright. It mean that certain types of use are considered legal even if a person holds a copyright to a work. For example, if a student is reviewing a copy of Lord of the Rings and wants to quote what Gandalf says in one scene to make his point, he doesn't need to write the estate of JRR Tolkien to get permission to use that quote. He provides the quote in the context of the review and it is considered fine. You can quote short paragraphs of content for uses such as book reviews, school reports, news stories, and so on. You always have to say who wrote it and give credit, but you don't have to ask permission before you do that.
Related to this is the world of parody. Parody is considered fair use when the entire new work is the words and phrases of the new author - but it is obviously parodying a created work by an original author. The original author and title are always credited - to be sure, the whole point of a parody is that people know and love the original work and are going to enjoy the parody version because of that. Nobody is going to confuse "Bored of the Rings" as being a new work by JRR Tolkien. If anything, it encourages people to buy the original version to understand better how the parody is being done.
The US Supreme Court has seen cases on parody and has held that it was OK. They said parody "is the use of some elements of a prior author's composition to create a new one that, at least in part, comments on that author's works."
Remember, the key is that you're not trying to write a new book set in an existing universe. You can't write a "fourth book" of Lord of the Rings, telling how Aragorn and Arwen raise their child, how the elves build more tree-houses and how Samwise the Great takes over his little corner of the Shire. You can't write a new book in the Harry Potter series, giving more storyline to characters. That would be infringing on copyright. Likewise, you cannot rewrite The Hobbit from Smaug's point of view, giving the dragon's take on events. Again, copyright infringement. You can't write a new Lord of the Rings story where Legolas falls in love with you and you raise a bevy of little elven children.
On the other hand, you can do a parody of Lord of the Rings (called, as mentioned above, Bored of the Rings) where Legolas becomes "Legolam" and Frodo becomes "Frito". The characters all act in extremely silly versions of their real personalities and the book in general pokes fun at Tolkein's way of writing. Yes, I have the 1969 original printing of the book and love it :).
For example, in the real books, Merry and Pippin are almost interchangeable as the "two minor hobbit friend characters". The parody plays this up greatly, making them mindless simpletons who always repeat each other's words. In a scene that both involves this and Tolkien's love of adding songs into his story, they are preparing to head out and want a good marching song. The next thing you know, the hobbits are singing
it's off to work we go,
Heigh-ho, heigh-ho, heigh-ho, heigh-heigh,
heigh-ho, heigh-ho ..."
"Good! Good!" yipped Moxie.
"Yes, good! Especially the 'heigh-ho' part," added Pepsi.
In another scene, the two hobbits are hiding in a pair of sacks, and "Spam" is grumpy with his furry-footed friends. Spam walks by and kicks each sack in turn.
"Grouchy, he is," said one.
"Grouchy and mean," said the other.
Note that I was able to display the above content from the Bored of the Rings book because of "fair use", for my educational article here :). Bored of the Rings was written by the Harvard Lampoon. All rights reserved :).
Parody vs Fan Fiction
As hopefully you can see from the above examples, parody differs from fan fiction in that fan fiction is generally written by someone who wants to stay true to the original world and just extend a few scenes, or "insert themselves into the story" (usually as a love interest). Fan fiction usually tries to imitate the original author's works and appear a seamless extension of that world. So in a sense, it is deceptive, trying to pass itself off as a legitimate part of that author's world.
A fan fiction work is in a way no different than George Lucas asking someone to write a new Star Wars story that explains the background of Boba Fett ... except that George Lucas did not give the fan fiction author permission to use his universe. So you CAN write Space Balls - parodying Star Wars - but you CANNOT write Star Wars Episode 10, describing how the new republic grows and expands and begins to take on aspects of the old Empire.
If you wonder why an author would NOT want fan fiction written, there have been cases when authors were lenient about fan fiction in their universe. As a result, fan fiction flooded the market. After a while, the author decided to write a new story about their characters. Once the author did, a FAN then sued the author claiming that the new "real" story had borrowed ideas from a fan fiction story.
If you have 10,000 people in the world all writing fan fiction in the Eragon universe, and then the actual author of Eragon decides to do a sequel, it's probably likely that at least some of those 10,000 people have mentioned an idea or two found in the sequel. It's common sense - how many realistic storylines could you write that were 100% unique? If the fan author then sues - now the real author is stuck, because even if he never even heard of the fan fiction story, it's hard to prove that. Plus, the fan fiction person is going to be out to get lots of money from this "rich" author and loses nothing by suing.
It must be pretty scary for an author to realize he cannot write about his own world any more, because a fan fiction writer will sue him for theft.
The key here is to write a parody and not fan fiction. Remember, a parody does not need to be just of one book or series. Yes, Spaceballs parodied Star Wars and Bored of the Rings parodied Lord of the Rings. Weird Al generally does one song at a time, turning it into a fresh, new song. However, Samurai Cat parodied a number of different books in each story. The Scream series made fun of bunches of horror movies in each movie. Weird Al does "Polkas" which mix together a whole set of songs of a theme or genre. Shrek has parodies of many fairy tales and movies in it.
So when you write your parody, first think about the original characters, words, settings and other aspects of the work, and then think of how you can play up or tease certain aspects of the characters. Merry and Pippin were both minor hobbit characters that seemed to speak alike - so in the parody they are pretty much twins who parrot each other inanely. In Star Wars, Vader had a deep, rasping voice and breathing pattern. This is made fun of in SpaceBalls and in "George Lucas in Love".
Find what makes a character unique and expand it to make it even more silly. Use scenes that are familiar, but twist them around. Combine together stories that did not belong together. Make sure you use your own wording and descriptions. You are not copying the original author's works - you are writing your own version, something that will make people who have read the original laugh and see the exaggeration you are showing.
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