# How much do figures need to differ to avoid copyright claims?

It sometimes arise that I need to use, for an article, a book chapter or any other written work, figures that I have already published (not figures published by others). These are usually schematic figures explaining what a chemical or physical system look like, how an algorithm works, etc. Thus, instead of reusing the exact same figure, I can easily create another one, conveying the same message with (more or less subtle) differences in presentation.

However, I have no idea how to answer the following question: how different need two figures be to avoid the second one infringing on the copyright of the first? What is a good rule of thumb to be used? Is it enough to change one of the following:

• color scheme
• viewpoint of a 3D visualization
• moving around blocks in a 2D diagram (or mind map)
• changing axis properties (labels, tick mark positions, etc.) in a graph

In general, I would argue that the new plot needs to do one of two things:

• present materially different content relative to the old image
• present the same material in a different context.

Graphs are generally visual representations of numerical data. The numerical data itself cannot be copyrighted (because the data are "facts"), only the presentations thereof. However, simply changing axis labels or colors, and other similar "gloss" changes, don't really make the graph any different. Rotating a 3D graph, or changing significantly the relationship of blocks in a mind map or diagram to show off different features would represent a change in the message and presentation, and therefore would be OK.

However, chemical structures and mathematical equations are not normally considered subject to copyright, as they represent "facts," and cannot be arbitrarily drawn or represented; there's only so many "legal" ways to write them. That said, cutting and pasting somebody's figure from another article would be a copyright violation; recreating it yourself would not. (Otherwise, we would never be able to write E = mc^2 without it being a copyright violation!)

If there are doubts, however, you can always try to contact the journal in question. If needed, you can ask for permission to reuse a figure, especially if it's one you've already created. Most journals already permit self reuse, so long as you include an appropriate credit and citation of the original.

• Graphs are visual representations, but not necessarily of numerical data. The OP mentioned "schematic figures", in particular those may not relate to numerical data at all, but rather to processes or concepts. And mathematical graphs probably rarely represent numerical data. – gerrit Oct 20 '12 at 21:50
• A figure showing mathematical formulae or concepts is probably very tough to copyright, since then you're visually illustrating a "fact" which has a precise definition. Then you're pretty much limited to not taking somebody else's artwork and passing it off as your own. But I've edited the text slightly accordingly. – aeismail Oct 21 '12 at 7:26
• @aeismail the question is specifically about figures/artwork that you have produced… not lifting figures from other people’s work – F'x Oct 21 '12 at 8:51
• If you're reusing your own work, then look at the last paragraph of my answer: the journal in which you publish may let you write: "Figure reprinted from [citation] with permission," or something to that effect. You may be able to reuse the same artwork. Check the journal's online information about the rights of authors to the work they've published in that journal. – aeismail Oct 21 '12 at 11:13
• And yet, there are illegal prime numbers... en.wikipedia.org/wiki/Illegal_prime – Federico Poloni Oct 21 '12 at 12:13

First up, a disclaimer. I am not a lawyer. This does not constitute legal advice.

I assume that your earlier work has been published and that the copyright to that work vests with your publisher.

I see two relevant possibilities here.

1. Your new work does not differ substantially from the earlier work.

A later work which is substantially similar to an earlier copyrighted work may infringe that copyright. From Wikipedia (yes, but the reference is to case law):

See, for example, Castle Rock Entertainment, Inc. v. Carol Pub. Group, 150 F.3d 132, 137 (2d Cir. 1998) ("Since the fact of copying is acknowledged and undisputed, the critical question for decision is whether the copying was unlawful or improper in that it took a sufficient amount of protected expression from Seinfeld as evidenced by its substantial similarity to such expression.")

What substantial similarity means in your case will turn on the facts. I would not be comfortable saying that your proposed alterations to your previous work would result in a sufficiently different work.

2. Your new work has some element of originality over the first work

In this case, your new work might be considered a derivative work:

Only the owner of copyright in a work has the right to prepare, or to authorize someone else to create, a new version of that work. The owner is generally the author or someone who has obtained rights from the author.

I've written this from a US law perspective. I am more familiar with UK copyright law but the basic points above are broadly similar.