Brecciated Jasper slabs can be very interesting, and colorful. They formed as a result of tectonic shifting over an extended period of time. Jasper would form, then be broken apart or shattered. It would then fill in with new minerals, perhaps more jasper, sometimes chalcedony, and macrocrystalline quartz. This process probably occured repeatedly, thus yielding to us a wide variety of colors and patterns.
As with any microcrystalline quartz, it is hard, and takes an excellent polish with cerium or tin oxide. Mohs hardness around 7.