If you look on YouTube or any of the other places where amateur film-makers can upload their work, you will find an enormous number of works inspired by or derived from Ray Bradbury's creations. It's nothing new: generations of schoolkids have created their own versions or variations of Bradbury's stories, it's just that it is now easier than ever to put these works into a public forum.
In the past, Bradbury has been asked whether it's permissible for amateurs to make films of his works. His reply has usually been along the lines of "it's okay to make a film, as you long as you don't do anything with it" - by which he means, feel free to flex your film-making muscles, but don't publish unless you've paid for publication rights to the underlying material.
Often the amateur works we find on the web are things made by students as coursework. These are often direct re-presentations of Bradbury's material, as in this piece found on Vimeo, which is essentially a reading of "Kaleidoscope" with added music and visuals.
The creator of the above, Geoff Norman, gives credit to Bradbury for the story and (on the original Vimeo page) gives an explanation of what we are watching and how it came about.
Another type of work often found is something which takes Bradbury's ideas as a springboard and either uses them as the basis of a new creation, or as a reference point for an homage. An example in this category is the short animation Between the Lines, found on Aniboom. It seems to be the work of a small team of people, and does not directly acknowledge Bradbury's work. However, it uses the same premise as Fahrenheit 451 and has a lead character named "Ray".