{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {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 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 6 "ACCESS" }}{PARA 259 "" 0 "" {TEXT -1 9 "July 2001" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 257 0 "" }}{PARA 256 "" 0 "" {TEXT -1 22 "crystal/forest fractal" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 103 "An example from the book \"Fractals - Endlessly repeated geometric figures\", by Hans Lauwerie r, page 94." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Digits:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "AFFIN E1:=proc(X,a,b,c,d,e,f)\nRETURN(evalf([a*X[1]+b*X[2]+e,\n \+ c*X[1]+d*X[2]+f]));\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "f1:=P->AFFINE1(P,0,-.7,.7,0,0,0);\n #rotate by Pi/2 rads, and scale by .7\nf2:=P->AFFINE1(P,.7,0,0,.7,1,0);\n #just scale by fa ctor of .7, and translate\n #to the right by 1\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f1Gf*6#%\"PG6\"6$%)operatorG%&arrowGF(-%(AFFINE1G 6)9$\"\"!$!\"(!\"\"$\"\"(F3F0F0F0F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2Gf*6#%\"PG6\"6$%)operatorG%&arrowGF(-%(AFFINE1G6)9$$\"\"(! \"\"\"\"!F3F0\"\"\"F3F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "S:=\{[0,0]\}; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"SG<#7$\"\"!F '" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "for i from 1 to 12 do \nS1:=map(f1,S);\nS2:=map(f2,S);\nS:=`union`(S1,S2);\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "pointplot(S,symbol=point,scaling=co nstrained,\n title=`Figure 1.5, page 94 book by Lauwerier`);" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{MARK "11" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }