STL file: http://www.geekhaus.com/makerhome/day60_peanocurve.stl
Tinkercad link: https://tinkercad.com/things/91KlFCcna1X-day-60-peano-curve/edit
Thingiverse link: http://www.thingiverse.com/thing:171911
Settings: On MakerWare "low" setting, each layer of the curve prints as one continuous curve! It takes a bit over an hour to print.
Technical notes: The image of the Peano curve was opened in Inkscape and then "Path/Trace Bitmap" was applied before saving as an .svg file that Tinkercad could import and extrude.
Stuff you might want to change: This model is not stable for use as a dish that you want to carry around; since it is one continuous path, it unfolds quite a bit when you pick it up! However you can get the Peano curve part of the design out of the Tinkercad link and put it onto something more stable. Perhaps tomorrow...