{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } } {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "with(plottools):\nwi th(geom3d):\nwith(JavaViewLib):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1278 "# A variation on Sierpinski Gasket\n# \n# This code will all ow the recursive construction of a cube with the \n# middle thirds rem oved. Actual structure of the cube is determined\n# by the alteration variable entered to the procedure. Interesting\n# variations on this can be created by changing this structure.\n#\n# Author: K G Hare\n# \+ Original Designer: Sierpinski (?)\n\nglobal_var := 1:\n\nCubes := proc (x_pos,y_pos,z_pos,radius,level,alterations)\n \n option remember:\n \n local new_radius,new_level,picture,silly,temp,s,Silly:\n global g lobal_var:\n\n if level = 0 then \n silly := global_var: global_va r := global_var + 1:\n cube(cat(`t`,silly),point(o,x_pos,y_pos,z_po s),evalf(radius)):\n RETURN (\{cat(`t`,silly)\}):\n fi;\n\n new_r adius := radius / 3:\n new_level := level-1:\n \n temp := map(pro c(d,x_pos,y_pos,z_pos,new_radius,new_level) \n \+ Cubes(x_pos+new_radius*d[1],\n y_po s+new_radius*d[2],\n z_pos+new_radius*d[3 ],\n new_radius*d[4],new_level) end, \n \+ alteration,\n \+ x_pos,y_pos,z_pos,new_radius,new_level):\n\n Silly := \{\}:\n for s in temp do \n Silly := s union Silly:\n od:\n RETURN (Silly):\ne nd:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1032 "lvl:=2:\nalteratio n := \{[1/sqrt(3)*2,1/sqrt(3)*2,-1/sqrt(3)*2,1],\n [1/sq rt(3)*2,1/sqrt(3)*2,1/sqrt(3)*2,1],\n [1/sqrt(3)*2,-1/sq rt(3)*2,-1/sqrt(3)*2,1],\n [1/sqrt(3)*2,-1/sqrt(3)*2,1/s qrt(3)*2,1],\n [-1/sqrt(3)*2,1/sqrt(3)*2,-1/sqrt(3)*2,1] ,\n [-1/sqrt(3)*2,1/sqrt(3)*2,1/sqrt(3)*2,1],\n \+ [-1/sqrt(3)*2,-1/sqrt(3)*2,-1/sqrt(3)*2,1],\n [-1/ sqrt(3)*2,-1/sqrt(3)*2,1/sqrt(3)*2,1],\n [0,-1/sqrt(3)*2 ,-1/sqrt(3)*2,1],\n [0,-1/sqrt(3)*2,1/sqrt(3)*2,1],\n \+ [0,1/sqrt(3)*2,-1/sqrt(3)*2,1],\n [0,1/sqrt( 3)*2,1/sqrt(3)*2,1],\n [-1/sqrt(3)*2,0,-1/sqrt(3)*2,1], \n [-1/sqrt(3)*2,0,1/sqrt(3)*2,1],\n [1/sq rt(3)*2,0,-1/sqrt(3)*2,1],\n [1/sqrt(3)*2,0,1/sqrt(3)*2, 1],\n [-1/sqrt(3)*2,-1/sqrt(3)*2,0,1],\n [ -1/sqrt(3)*2,1/sqrt(3)*2,0,1],\n [1/sqrt(3)*2,-1/sqrt(3) *2,0,1],\n [1/sqrt(3)*2,1/sqrt(3)*2,0,1]\}:" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 95 "draw(Cubes(0,0,0,4,lvl,alteration),view=[-4. .4,-4..4,-4..4],style=patch ,lightmodel=light1);" }}{PARA 13 "" 1 " " {GLPLOT3D 400 300 300 {PLOTDATA 3 "6`dl-%)POLYGONSG6)7&7%$\"+x5S4B! \"*$\"+!f.!)p(!#5$!+#f.!)p(F-7%F($\"+)>,gc#F-F.7%F(F1$!+)f+IG\"F*7%F(F +F47&7%$\"+Q3?'z\"F*F+F.7%F9F+F47%F9F1F47%F9F1F.7&F'F6F;F87&F0F=F,gc#F-$\"+ )f+IG\"F*7%Fjo$!+!f.!)p(F-F^p7%FjoFap$\"+#f.!)p(F-7%FjoF\\pFdp7&7%FJF \\pF^p7%FJF\\pFdp7%FJFapFdp7%FJFapF^p7&FioFfpFipFhp7&F`pF[qFjpFcp7&Fio FhpF[qF`p7&FcpFjpFipFfpFB-F$6)7&7%F(F\\pFjo7%F(FapFjo7%F(FapFJ7%F(F\\p FJ7&7%F9F\\pFjo7%F9F\\pFJ7%F9FapFJ7%F9FapFjo7&FcqFfqFiqFhq7&FdqF[rFjqF eq7&FcqFhqF[rFdq7&FeqFjqFiqFfqFB-F$6)7&7%FJFJF\\p7%FJFSF\\p7%FJFSFap7% FJFJFap7&7%FSFJF\\p7%FSFJFap7%FSFSFap7%FSFSF\\p7&FcrFfrFirFhr7&FdrF[sF jrFer7&FcrFhrF[sFdr7&FerFjrFirFfrFB-F$6)7&7%F(F+FJ7%F(F1FJ7%F(F1FS7%F( F+FS7&7%F9F+FJ7%F9F+FS7%F9F1FS7%F9F1FJ7&FcsFfsFisFhs7&FdsF[tFjsFes7&Fc sFhsF[tFds7&FesFjsFisFfsFB-F$6)7&7%F.F(F97%F.F9F97%F.F9FN7%F.F(FN7&7%F 4F(F97%F4F(FN7%F4F9FN7%F4F9F97&FctFftFitFht7&FdtF[uFjtFet7&FctFhtF[uFd t7&FetFjtFitFftFB-F$6)7&7%F(FJ$\"+'>,gc#F-7%F(FSFdu7%F(FS$!+'>,gc#F-7% F(FJFhu7&7%F9FJFdu7%F9FJFhu7%F9FSFhu7%F9FSFdu7&FcuFjuF]vF\\v7&FfuF_vF^ vFgu7&FcuF\\vF_vFfu7&FguF^vF]vFjuFB-F$6)7&7%F.F.F(7%F.F4F(7%F.F4F97%F. 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ompresssion) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "runJavaVie w(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QMZ:\\DEVELOPMENT\\JavaViewLi b\\mpl/JVLExport.mpl6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 246 "You c an now easily display this light, single geometry using the light vers ion of JavaView. For a pedagogical demonstration, you might want to ma nually construct the next level of the serpinsky fractal. Do this in r ealtime right off of the web. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "set(w=1000,h=1000,axes=off,dc=off):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "runApplet(\"c:\\\\temp\\\\smserp.mpl\");" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#QJZ:\\DEVELOPMENT\\JavaViewLib\\htm/smserp.h tm6\"" }}}}{MARK "0 0 0" 49 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }