The recent discussions about fractal parameters, copyright, and image theft, I felt the need for a little education was in order.
I use a fractal generating program called Ultra Fractal. It has many hundreds of formulas which in turn can be combined with hundreds of other formulas. In each of these formulas, there are many, and in some, hundreds of different parameters which can be changed. Each of these parameters has a different effect on the image. The program also has capabilities similar to Photo Shop, in that you can use multiple layers with the ability to include transparencies, and change the way these layers interact with each other. You also have color gradients which can be adjusted in very complex ways. When I make a fractal image, each layer will be worked on individually and adjusted to interact with each other layer to end up with the final image. In some layers, I will have very few visible elements, but depending on where they are located in the layer stack, they can have a very large effect on the final image. Creating fractal art is in no way a simple matter of just plugging a random series of numbers into a formula, and then pushing a button to see what comes out. Creating fractal art is a very painstaking process of fiddling with many small pieces of an image, sometimes tweaking one parameter for hours until the artist ends up with the creative result they desire. One could spend hours just tweaking one gradient until it looks right. When you save the parameters of the final image you end up with a series of number, letters, and symbols which are the codes for all the (sometimes into the hundreds) parameters for each layer, the locations, how each layer interacts with all the other layers, and the code that makes each gradient. Some fractal artists have images that are made up of hundreds of these layers and the code can be incredibly long. For anyone who has never seen what the parameters look like, here is just a small snippet of one:

geoGnarly1b3 {
; Copyright © 2007 by Mary C. Thornton.
::13fuvin2szzyOOOSydfAm/Bh6iX7GV1KzkJfYDeYme22+g9udu7gB76LNokoo02SkcoYrSqw
+x7IfFRks61ww+gtBq6Q3RkxDmMelkRqk7na2O3c6f87/uVrmPOfqt+hu2hVd9NTnuvSsR9w
qnPub+QtWve1h2jdHmdgnau3OdpWItCudqd3x5L1P8v1Md f1Hea1PfYYqfeo/fq49Kx7lrXX
8w3/dORcXotNjzHH6rf4f1qv2+HWNM2s9489apc152pu2zD7arHu2OBC99f35mxxj9 deZb7n
bnqfc9TZZaZWF836163D4rzrcoVw/rXduprvWU9UmoIrI/7/u9DTn/6pGnOO3c7oVJi1r2f8
UbfzZ42+PO30vrZa3Tfd/5HWBXlp72bo+dtn2MNM/wqxPfZuZaue97XbVy4nHHeGUi89rB4N
NHPN81ZwgU+9f3x+LH316tpTN9X2Ds1P03u6ywpj7qzkwENvQWp/+vDk518e6Yfbz03cut9E
O3+p29Nf90MYZ7ma2dEG1plLnHGA/192LrgpdjzQLWdEuPuVve12hTDwcWbv0ebOXo+BkR0j
YZ9b46+gVRr+hd/lveZ+MctJfoY9amT8wlTN7293yHqyFefoS68hCly7Dz0/fQfo3v8/aOtM
FExr+vpj7c78hhd1g9b+4YzlLskQLPrkkDsSx8f7OuHu7a732+t9hC9TKhyGR/e1TiKtuqAm
kVef36n0lZgPuaVTfHUb5Rh6p8q8yvtrUCOh2ptH a3+l6h97Zmy5zNSnP1yewSee+RXVqfTX
f7g4v/dzntuXokxFnx7JFgt/UzVwyJc+97wEQEc7OMJRQVLBwhx6bv7OAM12cCQe4fwqyjwt
Cg8IA2/VA4deV0IqzeKHyltXoGZtEQ05abckoW9UZmwSYjl QBAsTUbjx2JrDThDwAPZnAHkB
gLbbsTRACckCXI55Iw4NbMrl0d7IeVc+ek69A1LHa2ZDGsqIKa7t7IkAhkkaavpwhzQINClj
QFIUJCNC

The idea that anyone could "accidentally" create the same fractal image by plugging in the "same numbers" is quite impossible as you can see. The only way one could get a similar image is to actually copy the exact parameters, which can be quite complex.

If you examine the code, you will see my copyright is embedded right in it. When an artist shares their parameters with the Ultra Fractal mailing list, they will usually also embed in the code a comment of whether they will allow tweaks of their parameters. Many state that they do allow them, but only for posting back to the list for all to see and learn. Most parameters are posted to the list for "learning" purposes and many formula writers will post example parameters to show folks how to use their formulas. Some folks who post to the list will state that no tweaks are allowed on their parameters, but that anyone is free to study and learn from them. There are rules for the mailing list which are posted each week and which are very clearly stated. Most have no trouble following them. Because fractal artists love to share the creative joy of this art form, they take the risk of their parameters being used in a dishonest way. That is the hazard of sharing parameters with the mailing list. But sometimes the wish to share overpowers the fear of having one's parameters misused, so many still post their parameters. And then there are those who have stopped posting at all because of this very real hazard. That is very sad in my opinion.