Modifying Fractal Formulas

Greetings. Back in the days of the old mailing list, there were so many discussions about what it took to make a fractal image one's own, but not nearly so much discussion relating to modifications of fractal formulas in UFM files. Most of us have modified z = z^2 + c many times without a thought, but what about other fractal formulas? Many of us have been asked for permission to modify our formulas, or have ourselves asked others for permission. I have in the past never refused, nor been refused, such permission. But math formulas are free to use for anyone, so I would be interested in hearing your thoughts about formula modifications in general. How different does one need to make a formula before you believe that it is OK to proceed?

I waited a week hoping others would respond, but I guess not. For what it's worth (I'm not a lawyer), here's my opinion:

As you say, math formulas are free to use for anyone. If you are just coding a math formula (as you did in another thread for the catseye formula from XaoS), no permission should be needed. Credit to whoever came up with it should be given (if known).

More complex algorithms used in many formulas and colorings are a different story. They are subject to copyright, so permission is needed to include a chunk of code from someone else in your own formulas and colorings. Reverse engineering an algorithm to understand how it works and then rewriting it yourself, with your own creative insights and quirks, might be OK.

I would say it is OK to copy and modify someone else's formula for private use. However, before you upload your variation to the formula database or share it in some other way, you should contact the original formula author to ask for permission.