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MathGroup Archive 1992

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Filled Gosper curve

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Filled Gosper curve
  • From: Michael.Trott at physik.tu-ilmenau.de
  • Date: Tue, 1 Dec 1992 16:23:32 +0000

 Hi MathGroup,

 I have a little graphics problem.
 Say you have the coordinates of a hexagonal Gosper curve..
 Displaying it with Show[Graphics[Line[ GosperCurve[i]]]]
 works fine for orders up to 5. (More is very time and memory consuming.)
 Now I would like to "fill" the GosperCurve like in
 M.Gardner: PENROSE TILES TO TRAPDOOR CIPHERS (Freeman 1989) 
 on page 38. Up to order three the Following works
 Show[Graphics[Polygon[FilledGosperCurve[i]]]].
 Here FilledGosperCurve is GosperCurve and four outer vertices
 of the "rectangle".
 But order 4 , which has 2405  verices (order 3 has 344)
 gives a very hard crash on my Mac IIfx with Mma 2.1. 
 Now my question. Is there an upper bound for the number of 
 vertices of an 2d- Polygon. Is it caused because the resulting filled area is
 higly branched?
 It seemed to me that the crash is caused by the PostScript interprete, 
 Show[Graphics[Polygon[FilledGosperCurve[4]]],
      DisplayFunction->Identity]
works well.

Any ideas how to display the fourth order?

Thanks for an solution

Michael Trott

trott at physik.tu-ilmenau.de







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