Wow, XaoS. That brings back memories.
When I was quite young, somehow I stumbled across a copy of Fractint, an old proto-Free-software app for MS-DOS that was clearly made by a bunch of people who thought fractals were cool - it supported a whole bunch of different fractal algorithms, and for each one there were pages of tweakable settings, and of documentation about how the fractal worked and why it looked the way it did, and often special-purpose rendering tweaks—for example, it knew that the Mandelbrot set is symmetric about the X axis, so if the X axis was somewhere in the range being rendered, it would render up to it, then just copy pixels across to the other side instead of re-calculating them.
Anyway, Fractint kept me busy reading about mathematics and tweaking settings for a while, until I eventually grew frustrated with how, even with fixed-point integer calculations and all the tricks in the book, it took so long to render fractals, and I put it aside.
Until a few years later, where I bumped into XaoS, which did in realtime what had previously taken seconds, and I was blown away, and started exploring fractals all over again.
To my intense surprise, it seems that Fractint is still a thing, and the latest release dates to 2015, and compiles out of the box on Linux. I am staggered. Even XaoS is still a thing, although it was only updated in 2014. The nostalgia is heavy, tonight.
Somehow XaoS seems to not have been ever mentioned here.
Looking at XaoS and NextFractal is also highly recommended, they are applications to run locally but they can draw more different fractals.
On the more artistic side, I also really enjoy Frax for IOS: http://fract.al/