[Edit 13-February-19]
Proto version 12u: smoother interpolations, other fixes
This version fixes at least one bad bug, and some internal changes were made.
Use of the script has not changed perceptibly. In the zip file with the script, I've added a text document that may help to understand the use of rotation segments. There is a composite animation with 8 panes showing different types of rotations between interpolation segments. That animation can be downloaded here: [link]
The same instruction text is also included in that zip file with the animation, along with the keyframes used to make it.
I hesitate to upload that composite animation to YouTube because I think it just wont work on YT that well.
I hope the animation example will be helpful. But I realize people will not be able to watch all 8 panes at once to really compare the differences. Animations will always work differently with different keyframe sets. The 8 examples in the composite animation all use the same keyframe parameters. So it's intended to show how different kinds of motion can be created with the same set of keyframes. The only differences between the 8 examples are the rotation settings at the top of Apophymator and that is what is explained in the text file with the download.

[Edit 12-Oct-06]
Proto version 12f: small change.
Changed one line to prevent script from running in Apophysis 7X 15d: the script input box is still hosed. *Use the script with 7X version 15b*. Flames constructed in 7X 15c or 15d could present problems even when used with 7X 15b... it might help to save any such flames with 15b before trying to use them with the script.

[Edit 12-July-02]
I've uploaded another proto version that fixes several earlier flaws. The new proto is version 12d.
It's working for me, although I left off work on the script about 2 weeks ago. If errors are encountered please drop me a note, or leave a comment. I still expect to get the script in better shape in the coming days. My time is being consumed by unnecessary distractions though. Wish me luck with those. I wish you luck and enjoyment in your fractal pursuits.

[Edit 12-June-07]
I apologize profusely to the few people who downloaded this earlier. It was the wrong script. That's been corrected. The version of the script is now 12b and I changed the title to only use the number without the letter. I'm still going to have to do some changes so the letter will change a few more times at least. The rest of the info below still applies. I just changed any "12a" to "12b".

[Edit 12-June-04]
So here [link] is one reason I released the script as a prototype. But I'd like to emphasize that the problem is in the appearance of the dialogs and does not effect the way animation frames are calculated or rendered. So please, if you use the 10x version of Apophymamtor update to this version. I will fix what I show at that link asap. But I'm anxious to move on to getting the documentation ready because this script is a great deal more capable than 11x. Until I get the docs done though, I'm the only one who knows about those new capabilities. :-/
[The previous description follows.]

I'm nearing completion of a new Apophymator version.
I've decided to upload what I have at this point as version 12b.
I tacked "Proto" on to the end of the script name.
But it's fully functional, and it's quite stable in my testing - not really a "prototype" at all.
There's some cosmetic stuff I still have to change, so it's a "proto" in that sense.
Right now I've only put the script in my scraps, but it will get a new feature page once I have the whole bag of materials ready.
I will update the version letter at that time.

I've added a lot of info to the dialogs.
I hope the info will make it easier for people to understand the various settings.
I've also changed the general look of the input dialogs so they have a better appearance in the 7X and JK versions of Apo.
I still need to rearrange the menus for Apo 3D hack... but in 11x they didn't look near as bad as they did in the other Apo versions.
For 3D hack I mainly just have to get the text of the menus centered.

I also still have a lot to update in the Apophymator 11x pdf to bring the document up to date for 12b and beyond.
Some info in the 11x doc does not apply to the 12b version. Mainly though, all of the illustrations need to be replaced with illustrations of the new input dialogs.

I've disabled the script for all 7X-15c versions, which may be a bummer for some people.
But internal changes to 15c have made interpolated flame animation all but impossible.
The script works fine in 7X-15b versions, and there isn't much about 15c that 15b doesn't have.
I can provide some semi-technical reasons why animations won't work (well) with 15c if anyone wants to know.

I don't have a lot more to add at this point.
But I've been anxious to upload what I have because I think it's a significant improvement over 11x.
Otherwise I wouldn't make it available.

Just download the script to wherever you save your scripts.
Run it like you would any other script.

Oh, and... Apophymator starts up rather slowly - it depends a lot on how many plugins are in your plugins folder.
The script checks for missing plugins in the flames you're trying to use with it, and that takes a while.
The actual work section of the script runs rather slowly too. Unfortunately the scripter software is not multi-threaded.
It doesn't help that I don't know any sophisticated code optimization techniques either, and that's also surely a factor in the script's performance.
But I'm confident that Apophymator will reliably accomplish its purpose, which is to produce animation frames.

Naturally I'm interested in feedback and comments if anyone has any.
I will post a more complete package on a feature page once I get the package ready.