You like zoning out in front of fractals, right? Of course you do!
FractalJS is the easiest fractal zoomer yet: just pinch-zoom or scrollwheel and watch it go. There are several sets to choose from, a smoothing option, lots of color schemes, and it's all open-source.
Alternatives: Calvin Metcalf's Leaflet has Google Maps-style controls and Alson Kemp's WebFract3D renders sets in three dimensions for an especially bizarre experience.
Bonus: Here's a Mandelbrot set being generated on a 50-year-old IBM mainframe.
Found any cool fractal stuff on the web lately?