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