New Rome by MakinMagic

The best way to start is via Ultra Fractal even though it is a commercial program, it by far has the friendliest user interface and can be used free for 30 days after which you should pay for it or stop using it, though it doesn't cease to function - note that the drawback is that until paid for any saved images will have "evaluation copy" or similar written over the image.
Initially stick to a limited number of fractal formulas and colourings - e.g. stick to plain z^p+c for the formula (Standard Mandelbrot or Julia) and stick to the colouring formulas available in the "standard" colouring folder.
Beyond that Ultra Fractal also has the best in-built help section of any current fractal software.
If you get the fractal bug but don't want to pay for software yet (or ever) then once you've got the general idea of how to zoom around, change colourings, play with formula parameters etc. then the closest free software to UF is ChaosPro.
For 3D fractals the best options at the moment are Mandelbulber and Mandelbulb3D both freeware found via www.fractalforums.com
For 3D IFS fractals the best software is Xenodream (commercial).
For flames the best software is Apophysis (freeware).
For Orbital/Strange Attractors the best software is Chaoscope (free I think).
Other notables:
Fractint (the "father" of all fractal software, still relevant but a little behind the times).
Fractal Explorer (you may need to ask for help getting a copy of this)
Various programs (3D mostly) by Terry Gintz (Mystic Fractal I think) e.g. QuaSZ - these are good for those wanting to export meshes to Bryce, 3D Studio etc. (Xenodream can also do this)
Various program by Stephen Ferguson.

All the above should be fairly easy to Google

For more information/help on fractals generally see:

[link]

For up-to-the-minute developments and a place to ask questions:

[link]

Also all the resources linked via the Ultra Fractal pages are very useful as is the very friendly and obliging membership of the Ultra Fractal mailing list.

Thanks !
There aren't that many starter params for my UF formula in circulation and I haven't really adapted any from Mandelbulber, Mandelbulb3D or any other software because since my last UF render (Disaster Strikes the Diner) I really haven't had the time I would like for creating images - I've been working on code only whenever I get free fractalling time - unfortunately not related to my currently released 3D formulas.
Of course my UF formula also pre-dates the custom software for 3D fractals as it was the first publicly released code for the Mandelbulb (and possibly the Mandelbox) but because of my lack of spare time it's now quite a way behind in terms of formula advances and of enhanced 3D lighting techniques in particular.
If you want sample UPRs I think there are some in the thread relating to my UF formula here:

[link]

though one or two may be out of date with respect to the current released version of the formula.
I think I may have posted one or two more examples on ff elsewhere but the number of posts/threads on there is so vast I couldn't point you directly at them
If you'd like some example UPRs just ask by mailing me at:
makinmagic@tiscali.co.uk
And I'll sort some out when I get chance (if I get an hour or so I should now be able to get quite a few examples done with the speed of this beastie).
Initially bib (Jeremie Brunet) did quite a lot of work using my formula for UF so you could ask him if there are some parameter files that he'd be prepared to share.

You probably write your own...

Finally got around to checking, "At the forest's edge" took 36mins at 2880*2880 pixels and "New Rome" took 1hour 8mins at 3840*2880 pixels.

Those times are on my ancient 3GHz P4HT which is approximately 3* slower than an average 2GHz core2duo.

In both cases setup and artistic creation was probably somewhere between 3 and 6 hours but to be honest I lose track when working and don't usually make a point of noting when I start (if I do then I tend to feel under pressure and don't "go with the flow" as much).

Thank you

Thanks.