[math-fun] Peano polygons
If Peano maps the unit interval onto the complex unit square, we get the canonical diagrams by stepping by powers of 1/4, connecting points offset by 1/6 of a step: Graphics[Polygon[{Re[#],Im[#]}&/@Join[{1,0},Table[Peano[(k+1/6)/256],{k,0,255}]]]] gives http://gosper.org/peano256+1536s.gif . With zero offset, joining every fifth point gives http://gosper.org/peano1024o5+0.gif, which by startling coincidence is the Foo Dynasty ideogram for "My hovercraft is full of eels." --rwg ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ
Bill: You might consider patenting certain types of "curves" like this. They could make excellent power & clock distribution circuits for IC's. Henry Baker hbaker1@pipeline.com At 12:54 PM 4/22/2008, you wrote:
If Peano maps the unit interval onto the complex unit square, we get the canonical diagrams by stepping by powers of 1/4, connecting points offset by 1/6 of a step: Graphics[Polygon[{Re[#],Im[#]}&/@Join[{1,0},Table[Peano[(k+1/6)/256],{k,0,255}]]]] gives http://gosper.org/peano256+1536s.gif . With zero offset, joining every fifth point gives http://gosper.org/peano1024o5+0.gif, which by startling coincidence is the Foo Dynasty ideogram for "My hovercraft is full of eels." --rwg
participants (2)
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Bill Gosper -
Henry Baker