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With all the emphasis on image quality, is it really possible to create decent work on a phone with a 2 inch screen?

The Rev

It is on the higher res. ones - e.g. the latest iPhone/iTouch devices have a resolution of 960*640 which is plenty.
Of course that's assuming you're young enough to have good eyesight (unlike me - I'll stick to PCs and maybe an iPad if I'm ever rich).

I would think the most limiting factor would be the phones processing power.

With respect to processing power, if you're just trying to create fractal art rather than doing something more specific such as deep zooming then you only need float accuracy and most phones (and simliar devices) now have shader 2 GPU hardware so fractal generation can be done using shader fragments - this makes say an iPhone at least as fast at generating 2D fractals as Ultra Fractal is on my 3GHz P4HT, obviously not up to say a core2duo or better but pretty quick and definitely useable :)
I've just started on a UF-style project using shader 2 code (OpenGL ES2) for the iPhone/iTouch/iPad, the advantage of this is that the compiler for any formula authors is already there as part of the OS/OpenGL, all I have to do is write a decent parser to convert from *very* user-friendly source to source compilable by the OS/OpenGL eg. writing library code for complex arithmetic etc. (basically as macros).
The drawback is not the speed but the amount/complexity level of the fractal code so I'll be sticking to something more similar to UF4 and earlier style rather than the class-based method of UF5, though I am adding the ability to use macro libraries - in fact the handling of complex math will initially be done in this way as I want to release "something" ASAP so will not be adding "native" handling of the complex type untli later releases of the program.

I can get some amazing fractals on my motorola smartphone with its large 3.5 inch screen, running on Android OS!