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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT 257 19 
"Sierpinski triangle" }}{PARA 0 "" 0 "" {TEXT -1 2 "  " }}{PARA 0 "" 
0 "" {TEXT -1 234 "     If you have loaded the procedures from the Lpi
ctures.mws file, you can try defining some affine contractions, draw t
he L-picture, and then generate the fractal.  We show it here for Sier
pinski's triangle.  (The isoceles version.)" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "f1:=P->AFFINE1(P,
.5,0,0,.5,0,0);\n      #shrink by .5 and don't translate \nf2:=P->AFFI
NE1(P,.5,0,0,.5,.5,0);\n      #same shrink, and translate 0.5 to the r
ight\nf3:=P->AFFINE1(P,.5,0,0,.5,.25,.5);\n      #shrink, then displac
e by [.25,.5]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "TESTMAP([f
1,f2,f3]);" }}}{PARA 0 "" 0 "" {TEXT -1 52 "     Since the template is
 correct, we may proceed. " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
47 "S:=\{[0,0]\}:#initial set consisting of one point" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "3^9; #good to keep point numbers we
ll below 100,000,\n     #so as not to strain Maple's memory" }}}{PARA 
0 "" 0 "" {TEXT -1 68 "     Based on the computation above I will do n
ine iterations below:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "for
 i from 1 to 9 do\nS1:=map(f1,S);\nS2:=map(f2,S);\nS3:=map(f3,S);\nS:=
`union`(S1,S2,S3);\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "
pointplot(S,symbol=point,scaling=constrained,\n    title=`Sierpinski t
riangle`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2
 0" 234 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }