Apophysis
Get Apophysis, you can also check out a few tutorials, links, and it's a good idea to join the mailing list too. Pick up ApoMap while you're there downloading Apophysis, so you can make your own custom gradients. You might not use it when you first start out with apo, but eventually you'll want it.
Beta releases can be found here, I highly recommend you download the newest version, it is greatly improved over the old one on apophysis.org. Get them both and keep 2.02 or whatever it is as a backup.
Apophysis Resources on the #Apophysis group.
There is a lot more out there but I think that is enough to get anyone started, I have more links and things if anyone wants them, just ask me.
Fractal Explorer
Get Fractal Explorer, also spend some time wandering around that page and clicking links, there's some really useful stuff on there.
Fractal Explorer Turorial - An excellent FE tutorial, it tells you all of the basics and a bit more so you can get working with it. Read it.
Vchira
You can get Vchira here.
Sadly enough, I haven't seen a single tutorial for Vchira but it is similar to Sterlingware (another program by Stephen C. Ferguson), so you may find this tutorial of some use.
Chaoscope
Chaoscope renders 3D strange attractors, it is fun to play with and some people manage to do some truly amazing things with it.
You can get Chaoscope here, also navigate around that page for tutorials and things to help you get started.
The GIMP
The GIMP is an open source graphics creation and editing program, with many of the capabilities you'd find in Photoshop. The best part: it's free to download and use.
You can get the GIMP here: [link]
That's all for this time, mainly because I'm tired of typing at the moment. I'll add more next time I update my journal, of course. That should be enough for anyone that's looking at fractal work and trying to figure out how to get started with it.
Most importantly, roll up your sleeves and start PLAYING! The best way to learn anything is by experience. Experiment and have fun.
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You're welcome for the links, I hope you find them useful.