In the last year, people have been experimenting with 3D variations of the Mandelbrot fractal. The first to get a lot of attention was the Mandelbulb, but I didn't like it, it just looks blobby to me, with no apparent self-similarity.
Then in February, a new formula appeared, called Mandelbox. It's a clever two-step formula using folding, first with squares, then with circles. The combination provides a very rich generative source.
Being a 3D structure, you can fly through it:
There's an amazing variety of textures and structures here, reminiscent of many other fractals. Some of the vistas seem like science-fiction sets, but generated by a formula rather than drawn by hand. Fascinating.
Mandelbox is a rich world to explore, and it's really new, so we can expect to see lots more innovation and exploration.