How is the copyright determined for images that are derived from math formulas?


  • Equal-step gradient graph:

    enter image description here

  • color wheel graph of sin(1/z):

    enter image description here

Who own the rights to images like these?

  • 1
    The concepts of en.wikipedia.org/wiki/Idea-expression_divide and the merger doctrine would seem to apply here.
    – Sean
    Oct 29, 2011 at 23:25
  • @Sean I'm not sure how does it apply here. Afterall, if sin(1/z) is the "idea" and not the "expression", then with that "idea" anyone would derive the same and equal "expression"
    – Pacerier
    Oct 31, 2011 at 15:04

2 Answers 2


The creator of the image is the copyright owner. But, there are a few tricks.

  1. If a program can be used to create the image, and does so in a completely automatic manner, then the creator of the program owns the copyright.
  2. If some work is needed to create the artwork, then the person who did the work to create the image owns it. (Think, if a person draws a picture in photoshop, they own it). In this case, if a person creates a cool formula to create the image, then they would own it.
  3. If a person can generate an image on their own that looks similar, they they own it.

Of the two images, I'd say the first one is generic enough that many people no doubt have created a similar image, and it would be fairly safe to use.

The second shows some real creativity. Anyone who could create the right formula could own the copyright to the image they generated. If a person finds a similar formula, then they own the copyright to produce their new image.

  • But who owns the copyright to the formula sin(1/z) ? Is the formula part of an expression or part of an idea?
    – Pacerier
    Oct 31, 2011 at 15:04
  • I'm guessing for such a simple formula, there isn't anyway to force a copyright question out of it. It's just too difficult for a one-liner to decide. But the image that results from the formula would be copyright by the person who generated it. Of course, multiply generated images would lead to the same essential image being copyright by multiple people... Oct 31, 2011 at 15:31
  • yes this is generally what i'm confused about. if the same formula is used, different people will essentially generate the exact same image, and that image is copyrighted by multiple people...
    – Pacerier
    Nov 1, 2011 at 8:37
  • Substitute formula for recipe, and you have a cooking analog. One might find parts to the recipe, and even successfully reproduce it mostly, but unless they have the exact recipe, then they won't be violating copyright. But a very simple recipe would be beyond any copyright, such as putting flour on chicken to bread it. Nov 1, 2011 at 14:15
  • Nice analogy. ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​
    – Pacerier
    May 26, 2015 at 3:37

Intellectual property laws are constructions of their time. It is becomming increasingly evident that the base asumptions they make do not always apply. You have hit on one of the corner cases.

Who is the inventor/artist when the machine did it? In general its the owner of the program. There are also experiments where the whole job of generation and selection is based on data the computer gathered based on logic that stretches the concept.

It is also possible that the maker of the software owns the rights. In any case if its very generic it may not be owned by anybody. There are 2 questions that govern this.

  1. can you claim ownership of something many people have done and can easily do.

  2. is there any benefit for you to claim this ownership

So yes while you could own the thing. Can you really defend your right and do you want to?

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.