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'F9F;F>F@FBFDFFFHFRFTFioFgpFfo" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 32 "Create a \"Fibonnacci-SpaceTree\":" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(fibTree, proc (`::`(depth, integer)) local ones, zeros; if \+ depth = 0 then return [0] elif depth = 1 then return [1, seq(op(fibTre e(`+`(depth, `-`(1)))), k = 1 .. 4)] else return [1, seq(op(fibTree(`+ `(depth, `-`(1)))), k = 1 .. 2), seq(op(fibTree(`+`(depth, `-`(2)))), \+ k = 3 .. 4)] end if end proc):" "-I%mrowG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6[q-I#miGF$6%Q(fibTreeF'/%'italicGQ%trueF'/%,mathvaria ntGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separat orGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'a ccentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDF FFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontw eightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6%-F,6%Q&depthF'F/F2-F66- Q-∷F'F9F;F>F@FBFDFFFHFRFT-F,6%Q(integerF'F/F2F9-F,6#Q!F'-I' 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iuF`rFjsF\\v-Fdr6$Q\"2F'F9F9FaqF5F5Fat-Fin6$-F#6,F5Fht-Fin6$-F#6&F5F+- Fin6$-F#6%F]oFcuF]wF9F5F9FaqF5FiuF`r-Fdr6$Q\"3F'F9F\\vF_vF9F9FasFdsFjq FioFgpF5F5F5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5F]rFjqFioF5F_xF5FU- F66-Q\":F'F9F;F>F@FBFDFFFHFRFTFioFgpFfo" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, fullTree(2)):" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q*SPACETREEF'/%'italicGQ%tru eF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&fa lseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movab lelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔ F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q)fullTreeF'F/F2-I(mfe ncedGF$6$-F#6#-I#mnGF$6$Q\"2F'F9F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "fibTree(4):" "-I%mrowG6#/I+mod ulenameG6\"I,TypesettingGI(_syslibGF'6%-I#miGF$6%Q(fibTreeF'/%'italicG Q%trueF'/%,mathvariantGQ'italicF'-I(mfencedGF$6$-F#6#-I#mnGF$6$Q\"4F'/ F3Q'normalF'F>-I#moGF$6-Q\":F'F>/%&fenceGQ&falseF'/%*separatorGFF/%)st retchyGFF/%*symmetricGFF/%(largeopGFF/%.movablelimitsGFF/%'accentGFF/% 'lspaceGQ,0.2777778emF'/%'rspaceGFU" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 24 "Extend a leaf to a node:" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "` :=`(adaptTree, proc (`::`(st, list), `::`(position, integer)) if st[po sition] = 1 then return st end if; return [seq(st[i], i = 1 .. `+`(pos ition, `-`(1))), 1, 0, 0, 0, 0, seq(st[i], i = `+`(position, 1) .. nop s(st))] end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sysli bGF'6O-I#miGF$6%Q*adaptTreeF'/%'italicGQ%trueF'/%,mathvariantGQ'italic F'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)str etchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%' lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2 777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF; F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6*-F,6%Q#stF'F/F2-F66-Q-∷ F'F9F;F>F@FBFDFFFHFRFT-F,6%Q%listF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHF J/FNQ,0.3333333emF'F5-F,6%Q)positionF'F/F2F`o-F,6%Q(integerF'F/F2F9-F, 6#Q!F'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFjp/ %*linebreakGQ(newlineF'-Ffp6&FhpF[qF^q/FaqQ%autoF'F5F5F5-F66/Q#ifF'FXF ZFfnF;F>F@FBFDFFFHFJFMF5-Fin6$-F#6(F]o-Fin6&-F#6#F\\pF9/%%openGQ\"[F'/ %&closeGQ\"]F'F5-F66-Q\"=F'F9F;F>F@FBFDFFFHFRFTF5-I#mnGF$6$Q\"1F'F9F9F 5-F66/Q%thenF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F66/Q'returnF'FXFZFfnF;F>F@F BFDFFFHFJFMF5F]o-F66-Q\";F'F9F;FioF@FBFDFFFHFJFTF5-F66/Q$endF'FXFZFfnF ;F>F@FBFDFFFHFJFMF5FgqFesFepFcqF5F5F5FbsF5-Fin6&-F#66F5-F,6%Q$seqF'F/F 2-Fin6$-F#6-F]o-Fin6&-F#6#-F,6%Q\"iF'F/F2F9FbrFerFfoF5FjtFhrF[s-F66-Q# ..F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'FMF\\p-F66-Q*&uminus0;F'F9F;F>F@ FBFDFFFHF`u/FNFauF[sF9FfoF5F[sFfoF5-F\\s6$Q\"0F'F9FfoFfuFfoFfuFfoFfuFf oF5F_t-Fin6$-F#6/F]oFftFfoF5FjtFhrF\\p-F66-Q\"+F'F9F;F>F@FBFDFFFHF`uFe uF[sF]u-F,6%Q%nopsF'F/F2-Fin6$-F#6#F]oF9F5F9F5F9FbrFerFesFepF5FhsF5FU- F66-Q\":F'F9F;F>F@FBFDFFFHFRFTFepFcqFbp" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, adaptTree(fullTree(2), 4)):" "-I%mrowG6 #/I+modulenameG6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q*SPACETREEF'/ %'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF '/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(larg eopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F 66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q*adaptT reeF'F/F2-I(mfencedGF$6$-F#6'-F,6%Q)fullTreeF'F/F2-FY6$-F#6#-I#mnGF$6$ Q\"2F'F9F9-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F_o6$Q \"4F'F9F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}}{SECT 0 {PARA 209 "" 0 " " {TEXT 203 17 "Sierpinskie Curve" }}{SECT 0 {PARA 210 "" 0 "" {TEXT 203 34 "Helper functions forTurtle-Graphic" }}{EXCHG {PARA 0 "" 0 "" {TEXT 203 30 "Attach an element to the list:" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(attach, proc (li, elem) return [op(eval(li)), elem ] end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6B -I#miGF$6%Q'attachF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF $6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/ %*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ& 0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF '/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDF FFHFJFM-I(mfencedGF$6$-F#6&-F,6%Q#liF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFF FHFJ/FNQ,0.3333333emF'F5-F,6%Q%elemF'F/F2F9-F,6#Q!F'-I'mspaceGF$6&/%'h eightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFap/%*linebreakGQ(newlineF'F 5F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q`o~eval(li)~ist~hier~wicht ig,~weil~li~u.U.~als~Referenz~|^w|gvbergeben~wirdF'F/F2F\\p-F]p6&F_pFb pFep/FhpQ%autoF'F5F5F5-F66/Q'returnF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-Fin6& -F#6'F5-F,6%Q#opF'F/F2-Fin6$-F#6$-F,6%Q%evalF'F/F2-Fin6$-F#6#F]oF9F9F` oFfoF9/%%openGQ\"[F'/%&closeGQ\"]F'-F66-Q\";F'F9F;FcoF@FBFDFFFHFJFTF \\pF5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FU-F66-Q\":F'F9F;F>F@FBFDF FFHFRFTF\\pF`qFio" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 22 "Initialize \+ the turtle:" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(points, [ ]):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6ip-I#miGF$ 6%Q'pointsF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F '/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmet ricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/ %'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5 -I(mfencedGF$6&-F#6#-F,6#Q!F'F9/%%openGQ\"[F'/%&closeGQ\"]F'-F66-Q\":F 'F9F;F>F@FBFDFFFHFRFT-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0em F'/%&depthGFeo/%*linebreakGQ(newlineF'-F,6%Q,init_turtleF'F/F2F5FOF5-F 66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFgpF;F>F@FBFDFFFHFJFM-FV 6$FXF9FZF`o-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F66/Q'globalF'FdpFfpFhpF ;F>F@FBFDFFFHFJFMF5F+-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF 'F5-F,6%Q)stepsizeF'F/F2FcqF5-F,6%Q)TURTLE_xF'F/F2FcqF5-F,6%Q)TURTLE_y F'F/F2-F66-Q\";F'F9F;FfqF@FBFDFFFHFJFTF`oF\\qF5F5F5F+F5FOF5FUFbrF`oF \\qF5F5F5FiqF5FOF5-I#mnGF$6$Q\"1F'F9-F66-Q\"/F'F9F;F>/FAF1FBFDFFFH/FKQ ,0.1666667emF'/FNF^s-Ffr6$Q\"2F'F9FbrF`oF\\qF5F5F5F\\rF5FOF5FerFirF`sF brF`oF\\qF5F5F5F_rF5FOF5FerFir-Ffr6$Q\"4F'F9FbrF`oF5-F66/Q$endF'FdpFfp FhpF;F>F@FBFDFFFHFJFMF5FapF]oF`oF\\qF`oF\\qFZ" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 20 "Let the turtle move:" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(mark, proc () global points, TURTLE_x, TURTLE_y; `:=`(points, attach(points, [TURTLE_x, TURTLE_y])) end proc):" "-I%mrowG6#/I+modul enameG6\"I,TypesettingGI(_syslibGF'6T-I#miGF$6%Q%markF'/%'italicGQ%tru eF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&fa lseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movab lelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔ F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q %boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6#-F,6#Q!F 'F9F]o-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFeo/ %*linebreakGQ(newlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F66-Q\"#F'F9 F;F>F@FBFDFFFHFJFM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F66/Q'globalF 'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q'pointsF'F/F2-F66-Q\",F'F9F;/F?F1F@F BFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q)TURTLE_xF'F/F2F^qF5-F,6%Q)TURTLE_y F'F/F2-F66-Q\";F'F9F;FaqF@FBFDFFFHFJFTF`oF^pF5F5F5F[qF5FOF5-F,6%Q'atta chF'F/F2-Fin6$-F#6'F[qF^qF5-Fin6&-F#6(F5FdqF^qF5FgqF5F9/%%openGQ\"[F'/ %&closeGQ\"]F'F5F9FjqF`oF5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FU-F6 6-Q\":F'F9F;F>F@FBFDFFFHFRFTF`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(move_up, proc () global stepsize, TURTLE_x, TURTLE _y; `:=`(TURTLE_y, `+`(TURTLE_y, stepsize)) end proc):" "-I%mrowG6#/I+ modulenameG6\"I,TypesettingGI(_syslibGF'6W-I#miGF$6%Q(move_upF'/%'ital icGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fe nceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF= /%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*& coloneq;F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%bol dGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6# -F,6#Q!F'F9F]o-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&de pthGFeo/%*linebreakGQ(newlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F66- Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F66/Q 'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q)stepsizeF'F/F2-F66-Q\",F'F9 F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q)TURTLE_xF'F/F2F^qF5-F,6% Q)TURTLE_yF'F/F2-F66-Q\";F'F9F;FaqF@FBFDFFFHFJFTF`oF^pF5F5F5FgqF5FOF5F gqF5-F66-Q\"+F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'/FNFarF5F[qFjqF`oF5-F 66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT F`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(move_down, \+ proc () global stepsize, TURTLE_x, TURTLE_y; `:=`(TURTLE_y, `+`(TURTLE _y, `-`(stepsize))) end proc):" "-I%mrowG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6W-I#miGF$6%Q*move_downF'/%'italicGQ%trueF'/%,mathvari antGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separa torGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%' accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFD FFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+font weightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6#-F,6#Q!F'F9F]o-I'mspac eGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFeo/%*linebreakGQ( newlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFH FJFM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@ FBFDFFFHFJFMF5-F,6%Q)stepsizeF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FN Q,0.3333333emF'F5-F,6%Q)TURTLE_xF'F/F2F^qF5-F,6%Q)TURTLE_yF'F/F2-F66-Q \";F'F9F;FaqF@FBFDFFFHFJFTF`oF^pF5F5F5FgqF5FOF5FgqF5-F66-Q*&uminus0;F' F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'/FNFarF5F[qFjqF`oF5-F66/Q$endF'FXFZF fnF;F>F@FBFDFFFHFJFMF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFTF`oF^pF]o" }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(move_left, proc () global stepsize, TURTLE_x, TURTLE_y; `:=`(TURTLE_x, `+`(TURTLE_x, `-`(stepsi ze))) end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6W-I#miGF$6%Q*move_leftF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF' -I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stret chyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'ls paceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.277 7778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F> F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6#-F,6#Q!F'F9F]o-I'mspaceGF$6&/%'heigh tGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFeo/%*linebreakGQ(newlineF'-Fao6 &FcoFfoFio/F\\pQ%autoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q.opt ion~trace;F'F/F2F`oF^pF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5 -F,6%Q)stepsizeF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF 'F5-F,6%Q)TURTLE_xF'F/F2F^qF5-F,6%Q)TURTLE_yF'F/F2-F66-Q\";F'F9F;FaqF@ FBFDFFFHFJFTF`oF^pF5F5F5FdqF5FOF5FdqF5-F66-Q*&uminus0;F'F9F;F>F@FBFDFF FH/FKQ,0.2222222emF'/FNFarF5F[qFjqF`oF5-F66/Q$endF'FXFZFfnF;F>F@FBFDFF FHFJFMF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFTF`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(move_right, proc () global stepsize, TUR TLE_x, TURTLE_y; `:=`(TURTLE_x, `+`(TURTLE_x, stepsize)) end proc):" " -I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6W-I#miGF$6%Q+mov e_rightF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F 3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetric GF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'r spaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F6 6/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(m fencedGF$6$-F#6#-F,6#Q!F'F9F]o-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widt hGQ&0.0emF'/%&depthGFeo/%*linebreakGQ(newlineF'-Fao6&FcoFfoFio/F\\pQ%a utoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q.option~trace;F'F/F2F` oF^pF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q)stepsizeF'F /F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q)TURTLE_x F'F/F2F^qF5-F,6%Q)TURTLE_yF'F/F2-F66-Q\";F'F9F;FaqF@FBFDFFFHFJFTF`oF^p F5F5F5FdqF5FOF5FdqF5-F66-Q\"+F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'/FNFa rF5F[qFjqF`oF5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FU-F66-Q\":F'F9F; F>F@FBFDFFFHFRFTF`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 " `:=`(move_ne, proc () global stepsize, TURTLE_x, TURTLE_y; `:=`(TURTLE _x, `+`(TURTLE_x, `*`(`/`(1, 2), `*`(stepsize)))); `:=`(TURTLE_y, `+`( TURTLE_y, `*`(`/`(1, 2), `*`(stepsize)))) end proc):" "-I%mrowG6#/I+mo dulenameG6\"I,TypesettingGI(_syslibGF'6Z-I#miGF$6%Q(move_neF'/%'italic GQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6/Q\"~F'/%%boldGF1/F3Q%boldF '/%+fontweightGF " 0 "" {XPPEDIT 19 1 "`:=`(move_sw, proc () global stepsize , TURTLE_x, TURTLE_y; `:=`(TURTLE_x, `+`(TURTLE_x, `-`(`*`(`/`(1, 2), \+ `*`(stepsize))))); `:=`(TURTLE_y, `+`(TURTLE_y, `-`(`*`(`/`(1, 2), `*` (stepsize))))) end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI (_syslibGF'6Z-I#miGF$6%Q(move_swF'/%'italicGQ%trueF'/%,mathvariantGQ'i talicF'-I#moGF$6/Q\"~F'/%%boldGF1/F3Q%boldF'/%+fontweightGF " 0 "" {XPPEDIT 19 1 "`:=`(move_nw, proc () global stepsize, TURTLE_x, TURTLE _y; `:=`(TURTLE_x, `+`(TURTLE_x, `-`(`*`(`/`(1, 2), `*`(stepsize))))); `:=`(TURTLE_y, `+`(TURTLE_y, `*`(`/`(1, 2), `*`(stepsize)))) end proc ):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6Z-I#miGF$6% Q(move_nwF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6/Q\"~F' /%%boldGF1/F3Q%boldF'/%+fontweightGF " 0 "" {XPPEDIT 19 1 "`:=`(move_se, proc () global stepsize, TURTLE_x, TUR TLE_y; `:=`(TURTLE_x, `+`(TURTLE_x, `*`(`/`(1, 2), `*`(stepsize)))); ` :=`(TURTLE_y, `+`(TURTLE_y, `-`(`*`(`/`(1, 2), `*`(stepsize))))) end p roc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6Z-I#miGF $6%Q(move_seF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6/Q\" ~F'/%%boldGF1/F3Q%boldF'/%+fontweightGF " 0 "" {XPPEDIT 19 1 "`:=`(fine, proc (`::`(xshift, float), `::`(yshift , float)) global stepsize, TURTLE_x, TURTLE_y; `:=`(stepsize, `+`(`*`( `/`(1, 2), `*`(stepsize)))); `:=`(TURTLE_x, `+`(TURTLE_x, `*`(xshift, \+ `*`(stepsize)))); `:=`(TURTLE_y, `+`(TURTLE_y, `*`(yshift, `*`(stepsiz e)))) end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibG F'6cp-I#miGF$6%Q%fineF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#m oGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyG F=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspace GQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778 emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FB FDFFFHFJFM-I(mfencedGF$6$-F#6*-F,6%Q'xshiftF'F/F2-F66-Q-∷F' F9F;F>F@FBFDFFFHFRFT-F,6%Q&floatF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ /FNQ,0.3333333emF'F5-F,6%Q'yshiftF'F/F2F`oFcoF9-F,6#Q!F'-I'mspaceGF$6& /%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFgp/%*linebreakGQ(newlin eF'-Fcp6&FepFhpF[q/F^qQ%autoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F, 6%Q.option~trace;F'F/F2FbpF`qF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFF HFJFMF5-F,6%Q)stepsizeF'F/F2FfoF5-F,6%Q)TURTLE_xF'F/F2FfoF5-F,6%Q)TURT LE_yF'F/F2-F66-Q\";F'F9F;FioF@FBFDFFFHFJFTFbpF`qF5F5F5F]rF5FOF5F]rF5-F 66-Q\"/F'F9F;F>/FAF1FBFDFFFH/FKQ,0.1666667emF'/FNF^sF5-I#mnGF$6$Q\"2F' F9FfrFbpF`qF5F5F5F`rF5FOF5F`rF5-F66-Q\"+F'F9F;F>F@FBFDFFFH/FKQ,0.22222 22emF'/FNFhsF5F]o-F66-Q\"*F'F9F;F>F@FBFDFFFHF]sF_sF]rFfrFbpF`qF5F5F5Fc rF5FOF5FcrF5FdsF5F\\pFjsF]rFfrFbpF5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJ FMF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFTFbpF`qF_p" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(coarse, proc (`::`(xshift, float), `::`(yshi ft, float)) global stepsize, TURTLE_x, TURTLE_y; `:=`(TURTLE_x, `+`(TU RTLE_x, `*`(xshift, `*`(stepsize)))); `:=`(TURTLE_y, `+`(TURTLE_y, `*` (yshift, `*`(stepsize)))); `:=`(stepsize, `+`(`*`(2, `*`(stepsize)))) \+ end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6cp- I#miGF$6%Q'coarseF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$ 6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/% *symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0 .0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF' /FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFF FHFJFM-I(mfencedGF$6$-F#6*-F,6%Q'xshiftF'F/F2-F66-Q-∷F'F9F; F>F@FBFDFFFHFRFT-F,6%Q&floatF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ ,0.3333333emF'F5-F,6%Q'yshiftF'F/F2F`oFcoF9-F,6#Q!F'-I'mspaceGF$6&/%'h eightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFgp/%*linebreakGQ(newlineF'- Fcp6&FepFhpF[q/F^qQ%autoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q. option~trace;F'F/F2FbpF`qF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJF MF5-F,6%Q)stepsizeF'F/F2FfoF5-F,6%Q)TURTLE_xF'F/F2FfoF5-F,6%Q)TURTLE_y F'F/F2-F66-Q\";F'F9F;FioF@FBFDFFFHFJFTFbpF`qF5F5F5F`rF5FOF5F`rF5-F66-Q \"+F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'/FNF]sF5F]o-F66-Q\"*F'F9F;F>F@F BFDFFFH/FKQ,0.1666667emF'/FNFcsF]rFfrFbpF`qF5F5F5FcrF5FOF5FcrF5FirF5F \\pF_sF]rFfrFbpF`qF5F5F5F]rF5FOF5F]rF5F_sF5-I#mnGF$6$Q\"2F'F9FfrFbpF5- F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRF TFbpF`qF_p" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT 248 56 "Algorithmus zur \+ Umsatzung der adaptiven Sierpinski Kurve" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(S, proc () global SPACETREE, STPTR; `:=`(STPTR, `+ `(STPTR, 1)); if SPACETREE[STPTR] = 0 then mark() else fine(`*`(-1, `* `(1.0)), `*`(-1, `*`(.5))); S(); move_ne(); P(); move_right(); Q(); mo ve_se(); S(); coarse(`*`(-1, `*`(1.0)), .5) end if end proc):" "-I%mro wG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6[w-I#miGF$6%Q\"SF'/%'i talicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/% &fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeop GF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66- Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%% boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F #6#-F,6#Q!F'F9F]o-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/% &depthGFeo/%*linebreakGQ(newlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F 66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F6 6/Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q*SPACETREEF'F/F2-F66-Q\", F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q&STPTRF'F/F2-F66-Q\"; F'F9F;FaqF@FBFDFFFHFJFTF`oF^pF5F`oF^pF5F5F5FdqF5FOF5FdqF5-F66-Q\"+F'F9 F;F>F@FBFDFFFH/FKQ,0.2222222emF'/FNF^rF5-I#mnGF$6$Q\"1F'F9FgqF5F`oF^pF 5F5F5-F66/Q#ifF'FXFZFfnF;F>F@FBFDFFFHFJFMF5F[q-Fin6&-F#6#FdqF9/%%openG Q\"[F'/%&closeGQ\"]F'F5-F66-Q\"=F'F9F;F>F@FBFDFFFHFRFTF5-Far6$Q\"0F'F9 F5F`oF^pF5F5F5-F66/Q%thenF'FXFZFfnF;F>F@FBFDFFFHFJFMF`oF^pF5F5F5F5F5F5 -F,6%Q%markF'F/F2FhnFgqF`oF^pF5F5F5-F66/Q%elseF'FXFZFfnF;F>F@FBFDFFFHF JFMF`oF^pF5F5F5F5F5F5Fbp-F,6%Q8~neun~Kinder~abarbeitenF'F/F2F`oF^pF5F5 F5F5F5F5-F,6%Q%fineF'F/F2-Fin6$-F#6'-F66-Q*&uminus0;F'F9F;F>F@FBFDFFFH F]rF_r-Far6$Q$1.0F'F9F^qFjt-Far6$Q$0.5F'F9F9FgqF5F`oF^pF5F5F5F5F5F5F+F hnFgqF5-F,6%Q(move_neF'F/F2-Fin6%F[oF/F2-F66.FiqF/F2F;FaqF@FBFDFFFHFJF T-F66.F8F/F2F;F>F@FBFDFFFHFJFMF`oF^pF5F5F5F5F5F5-F,6%Q\"PF'F/F2FhnFgqF 5-F,6%Q+move_rightF'F/F2FhnFgqF`oF^pF5F5F5F5F5F5-F,6%Q\"QF'F/F2FhnFgqF 5-F,6%Q(move_seF'F/F2FhnFgqF5F`oF^pF5F5F5F5F5F5F+FhnFgqF`oF^pF5F5F5F5F 5F5-F,6%Q'coarseF'F/F2-Fin6$-F#6&FjtF]uF^qF`uF9FgqF`oF^pF5F5F5-F66/Q$e ndF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FdrFgqF`oF5F_wF5FU-F66-Q\":F'F9F;F>F@FB FDFFFHFRFTF`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(P , proc () global SPACETREE, STPTR; `:=`(STPTR, `+`(STPTR, 1)); if SPAC ETREE[STPTR] = 0 then mark() else fine(.5, `*`(-1, `*`(1.0))); P(); mo ve_nw(); R(); move_up(); S(); move_ne(); P(); coarse(`*`(-1, `*`(.5)), `*`(-1, `*`(1.0))) end if end proc):" "-I%mrowG6#/I+modulenameG6\"I,T ypesettingGI(_syslibGF'6^v-I#miGF$6%Q\"PF'/%'italicGQ%trueF'/%,mathvar iantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separ atorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/% 'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBF DFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fon tweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6#-F,6#Q!F'F9F]o-I'mspa ceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFeo/%*linebreakGQ (newlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFF HFJFM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F66/Q'globalF'FXFZFfnF;F>F @FBFDFFFHFJFMF5-F,6%Q*SPACETREEF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/ FNQ,0.3333333emF'F5-F,6%Q&STPTRF'F/F2-F66-Q\";F'F9F;FaqF@FBFDFFFHFJFTF `oF^pF5F`oF^pF5F5F5FdqF5FOF5FdqF5-F66-Q\"+F'F9F;F>F@FBFDFFFH/FKQ,0.222 2222emF'/FNF^rF5-I#mnGF$6$Q\"1F'F9FgqF5F`oF^pF5F5F5-F66/Q#ifF'FXFZFfnF ;F>F@FBFDFFFHFJFMF5F[q-Fin6&-F#6#FdqF9/%%openGQ\"[F'/%&closeGQ\"]F'F5- F66-Q\"=F'F9F;F>F@FBFDFFFHFRFTF5-Far6$Q\"0F'F9F5F`oF^pF5F5F5-F66/Q%the nF'FXFZFfnF;F>F@FBFDFFFHFJFMF`oF^pF5F5F5F5F5F5-F,6%Q%markF'F/F2FhnFgqF `oF^pF5F5F5-F66/Q%elseF'FXFZFfnF;F>F@FBFDFFFHFJFMF`oF^pF5F5F5F5F5F5-F, 6%Q%fineF'F/F2-Fin6$-F#6&-Far6$Q$0.5F'F9F^q-F66-Q*&uminus0;F'F9F;F>F@F BFDFFFHF]rF_r-Far6$Q$1.0F'F9F9FgqF`oF^pF5F5F5F5F5F5F+FhnFgqF5-F,6%Q(mo ve_nwF'F/F2FhnFgqF`oF^pF5F5F5F5F5F5-F,6%Q\"RF'F/F2FhnFgqF5-F,6%Q(move_ upF'F/F2FhnFgqF`oF^pF5F5F5F5F5F5-F,6%Q\"SF'F/F2FhnFgqF5-F,6%Q(move_neF 'F/F2-Fin6%F[oF/F2-F66.FiqF/F2F;FaqF@FBFDFFFHFJFTF`oF^pF5F5F5F5F5F5F+F hnFgqF`oF^pF5F5F5F5F5F5-F,6%Q'coarseF'F/F2-Fin6$-F#6'FjtFgtF^qFjtF]uF9 FgqF`oF^pF5F5F5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FdrFgqF`oF5FjvF5 FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFTF`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 " " {XPPEDIT 19 1 "`:=`(Q, proc () global SPACETREE, STPTR; `:=`(STPTR, \+ `+`(STPTR, 1)); if SPACETREE[STPTR] = 0 then mark() else fine(`*`(-1, \+ `*`(.5)), 1.0); Q(); move_se(); S(); move_down(); R(); move_sw(); Q(); coarse(.5, 1.0) end if end proc):" "-I%mrowG6#/I+modulenameG6\"I,Type settingGI(_syslibGF'6]v-I#miGF$6%Q\"QF'/%'italicGQ%trueF'/%,mathvarian tGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separato rGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'ac centGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFF FH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontwe ightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6#-F,6#Q!F'F9F]o-I'mspaceG F$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFeo/%*linebreakGQ(ne wlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJ FM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FB FDFFFHFJFMF5-F,6%Q*SPACETREEF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ ,0.3333333emF'F5-F,6%Q&STPTRF'F/F2-F66-Q\";F'F9F;FaqF@FBFDFFFHFJFTF`oF ^pF5F`oF^pF5F5F5FdqF5FOF5FdqF5-F66-Q\"+F'F9F;F>F@FBFDFFFH/FKQ,0.222222 2emF'/FNF^rF5-I#mnGF$6$Q\"1F'F9FgqF5F`oF^pF5F5F5-F66/Q#ifF'FXFZFfnF;F> F@FBFDFFFHFJFMF5F[q-Fin6&-F#6#FdqF9/%%openGQ\"[F'/%&closeGQ\"]F'F5-F66 -Q\"=F'F9F;F>F@FBFDFFFHFRFTF5-Far6$Q\"0F'F9F5F`oF^pF5F5F5-F66/Q%thenF' FXFZFfnF;F>F@FBFDFFFHFJFMF`oF^pF5F5F5F5F5F5-F,6%Q%markF'F/F2FhnFgqF`oF ^pF5F5F5-F66/Q%elseF'FXFZFfnF;F>F@FBFDFFFHFJFMF`oF^pF5F5F5F5F5F5-F,6%Q %fineF'F/F2-Fin6$-F#6'-F66-Q*&uminus0;F'F9F;F>F@FBFDFFFHF]rF_r-Far6$Q$ 0.5F'F9F^qF5-Far6$Q$1.0F'F9F9FgqF`oF^pF5F5F5F5F5F5F+FhnFgqF5-F,6%Q(mov e_seF'F/F2FhnFgqF`oF^pF5F5F5F5F5F5-F,6%Q\"SF'F/F2FhnFgqF5-F,6%Q*move_d ownF'F/F2FhnFgqF`oF^pF5F5F5F5F5F5-F,6%Q\"RF'F/F2FhnFgqF5-F,6%Q(move_sw F'F/F2FhnFgqF`oF5F5F5F5F5F5F+FhnFgqF`oF^pF5F5F5F5F5F5-F,6%Q'coarseF'F/ F2-Fin6$-F#6&FjtF^qF5F]uF9FgqF`oF^pF5F5F5-F66/Q$endF'FXFZFfnF;F>F@FBFD FFFHFJFMF5FdrFgqF`oF5FfvF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFTF`oF^pF]o" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(R, proc () global SPAC ETREE, STPTR; `:=`(STPTR, `+`(STPTR, 1)); if SPACETREE[STPTR] = 0 then mark() else fine(1.0, .5); R(); move_sw(); Q(); move_left(); P(); mov e_nw(); R(); coarse(1.0, `*`(-1, `*`(.5))) end if end proc):" "-I%mrow G6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6]v-I#miGF$6%Q\"RF'/%'it alicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%& fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopG F=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q *≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%b oldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F# 6#-F,6#Q!F'F9F]o-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%& depthGFeo/%*linebreakGQ(newlineF'-Fao6&FcoFfoFio/F\\pQ%autoF'F5F5F5-F6 6-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q.option~trace;F'F/F2F`oF^pF5F5F5-F66 /Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q*SPACETREEF'F/F2-F66-Q\",F 'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q&STPTRF'F/F2-F66-Q\";F 'F9F;FaqF@FBFDFFFHFJFTF`oF^pF5F`oF^pF5F5F5FdqF5FOF5FdqF5-F66-Q\"+F'F9F ;F>F@FBFDFFFH/FKQ,0.2222222emF'/FNF^rF5-I#mnGF$6$Q\"1F'F9FgqF5F`oF^pF5 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(points) end proc):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sysl ibGF'6[p-I#miGF$6%Q+SierpinskiF'/%'italicGQ%trueF'/%,mathvariantGQ'ita licF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%) stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF= /%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ, 0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFe nF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6%-F,6%Q#stF'F/F2-F66-Q-&Proporti on;F'F9F;F>F@FBFDFFFHFRFT-F,6%Q%listF'F/F2F9-F,6#Q!F'-I'mspaceGF$6&/%' heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGF^p/%*linebreakGQ(newlineF' -Fjo6&F\\pF_pFbp/FepQ%autoF'F5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFFH FJFMF5-F,6%Q'pointsF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.333333 3emF'F5-F,6%Q*SPACETREEF'F/F2FaqF5-F,6%Q&STPTRF'F/F2-F66-Q\";F'F9F;Fdq F@FBFDFFFHFJFTFioFgpF5F5F5FgqF5FOF5F]oF]rFioFgpF5F5F5FjqF5FOF5-I#mnGF$ 6$Q\"0F'F9F]rFioFgpF5F5F5-F,6%Q,init_turtleF'F/F2-Fin6$-F#6#FfoF9F]rFi 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8emF'/FSF_q-F,6%Q,CONSTRAINEDF'F/F2F`oF:-F,6%Q*thicknessF'F/F2F[q-F]o6 $Q\"3F'F>F`oF:-F,6%Q%viewF'F/F2F[q-F66&-F#6*-F]o6$Q\"0F'F>-F;6-Q#..F'F >F@FCFEFGFIFKFM/FPQ,0.2222222emF'FRF\\oF`oF:FarFdr-F]o6$Q$0.5F'F>F>/%% openGQ\"[F'/%&closeGQ\"]F'F>-F;6-Q\";F'F>F@FcoFEFGFIFKFMFOF`qFfoFdp-F, 6#Q!F'" }}{PARA 13 "" 1 "" {TEXT 249 0 "" }{GLPLOT2D 856 417 417 {PLOTDATA 2 "6'-%'CURVESG6$7&7$$\"#D!\"#$\"$D\"!\"$7$$\"$v$!\"$$\"#D! \"#7$$\"$D'!\"$$\"#D!\"#7$$\"#v!\"#$\"$D\"!\"$-%&COLORG6&%$RGBG$\"#5! \"\"$\"\"!!\"\"$\"\"!!\"\"-%%VIEWG6$;$\"\"!!\"\"$\"#5!\"\";$\"\"!!\"\" $\"\"&!\"\"-%*THICKNESSG6#\"\"$-%*AXESSTYLEG6#%'NORMALG-%(SCALINGG6#%, CONSTRAINEDG" 1 2 2 1 10 3 2 6 0 4 1 1.0 45.0 45.0 0 0 "Curve 1" }} {TEXT 249 0 "" }}}}{SECT 0 {PARA 211 "" 0 "" {TEXT 203 33 "Partitionin g the Sierpinski-Curve" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=` (colours, [black, blue, green, red, brown, magenta, cyan, navy, pink, \+ grey, yellow, coral]):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_s yslibGF'6(-I#miGF$6%Q(coloursF'/%'italicGQ%trueF'/%,mathvariantGQ'ital icF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)s tretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/ %'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0 .2777778emF'/FNFSF5-I(mfencedGF$6&-F#6C-F,6%Q&blackF'F/F2-F66-Q\",F'F9 F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'-F,6%Q%blueF'F/F2FgnF5-F,6%Q&gree nF'F/F2FgnF5-F,6%Q$redF'F/F2FgnF5-F,6%Q&brownF'F/F2FgnF5-F,6%Q(magenta F'F/F2FgnF5-F,6%Q%cyanF'F/F2FgnF5-F,6%Q%navyF'F/F2FgnF5-F,6%Q%pinkF'F/ F2FgnF5-F,6%Q%greyF'F/F2FgnF5-F,6%Q'yellowF'F/F2FgnF5-F,6%Q&coralF'F/F 2F9/%%openGQ\"[F'/%&closeGQ\"]F'-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 203 33 "Divide the list into pts sublists " }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(partition, proc (`::`(pts, l ist), `::`(number, posint)) local parts, i; `:=`(parts, [pts[`*`(`+`(n umber, `-`(1)), `*`(floor(`/`(`*`(nops(pts)), `*`(number))))) .. -1]]) ; for i from `+`(number, `-`(1)) by -1 to 2 do `:=`(parts, [pts[`*`(`+ `(i, `-`(1)), `*`(floor(`/`(`*`(nops(pts)), `*`(number))))) .. `*`(i, \+ `*`(floor(`/`(`*`(nops(pts)), `*`(number)))))], op(parts)]) end do; `: =`(parts, [pts[1 .. floor(`/`(`*`(nops(pts)), `*`(number)))], op(parts )]); return parts end proc):" "-I%mrowG6#/I+modulenameG6\"I,Typesettin gGI(_syslibGF'6gq-I#miGF$6%Q*partitionF'/%'italicGQ%trueF'/%,mathvaria ntGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separat orGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'a ccentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDF FFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontw eightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6*-F,6%Q$ptsF'F/F2-F66-Q- ∷F'F9F;F>F@FBFDFFFHFRFT-F,6%Q%listF'F/F2-F66-Q\",F'F9F;/F?F 1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q'numberF'F/F2F`o-F,6%Q'posintF' F/F2F9-F,6#Q!F'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&d epthGFjp/%*linebreakGQ(newlineF'-Ffp6&FhpF[qF^q/FaqQ%autoF'F5F5F5-F66/ Q&localF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q&partsF'F/F2Ffo-F,6%Q\"iF'F/ F2-F66-Q\";F'F9F;FioF@FBFDFFFHFJFTFepFcqF5F5F5FjqF5FOF5-Fin6&-F#6&F5F] o-Fin6&-F#6+F5-Fin6$-F#6%F\\p-F66-Q*&uminus0;F'F9F;F>F@FBFDFFFH/FKQ,0. 2222222emF'/FNFcs-I#mnGF$6$Q\"1F'F9F9-F66-Q\"*F'F9F;F>F@FBFDFFFH/FKQ,0 .1666667emF'/FNF]t-F,6%Q&floorF'/F0F=F9-Fin6$-F#6&-F,6%Q%nopsF'F/F2-Fi n6$-F#6#F]oF9-F66-Q\"/F'F9F;F>/FAF1FBFDFFFHF\\tF^tF\\pF9-F66-Q#..F'F9F ;F>F@FBFDFFFHFbsFMF_sFesF5F9/%%openGQ\"[F'/%&closeGQ\"]F'F5F9FeuFhuF`r FepFcqF5F5F5-F66/Q$forF'FXFZFfnF;F>F@FBFDFFFHFJFMF5F]rF5-F66/Q%fromF'F XFZFfnF;F>F@FBFDFFFHFJFMF5F\\pF_sFesF5-F66/Q#byF'FXFZFfnF;F>F@FBFDFFFH FJFMF5F_sFesF5-F66/Q#toF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-Ffs6$Q\"2F'F9F5-F 66/Q#doF'FXFZFfnF;F>F@FBFDFFFHFJFMFepFcqF5F5F5F5F5F5FjqF5FOF5-Fin6&-F# 6F@FBFDFFFH FJFMF5FjvF`rFepFcqF5F5F5FjqF5FOF5-Fin6&-F#6*F5F]o-Fin6&-F#6(F5FesFbuF_ 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)7$$\")Dc,m!\")$\"(Dc,\"!\"(7$$\"(vV['!\"($\"'v$4\"!\"'7$$\"'D1k!\"'$ \"(v=<\"!\"(7$$\"(D\"Gj!\"($\")D1*G\"!\")7$$\")v=nj!\")$\"(D\"G8!\"(7$ $\")DJXk!\")$\"(D\"G8!\"(7$$\"(vV['!\"($\")D1*G\"!\")7$$\")vVBl!\")$\" (D\"G8!\"(7$$\"(vV['!\"($\")v=n8!\")7$$\"(vV['!\"($\")DJX9!\")7$$\")vV Bl!\")$\"(vV[\"!\"(7$$\"(D1k'!\"($\"'D19!\"'7$$\"'v=n!\"'$\"(D\"G8!\"( 7$$\")v$f$o!\")$\"(D\"G8!\"(7$$\"(voz'!\"($\")v=n8!\")7$$\"(voz'!\"($ \")DJX9!\")7$$\")v$f$o!\")$\"(vV[\"!\"(7$$\"(voz'!\"($\")vVB:!\")7$$\" )D\"yv'!\")$\"(vV[\"!\"(7$$\")vozm!\")$\"(vV[\"!\"(7$$\"(D1k'!\"($\")v VB:!\")7$$\"'v=n!\"'$\"(D1k\"!\"(7$$\"(voz'!\"($\"'v=!\"(7$$\"(v$4r!\" ($\"'DJ?!\"'7$$\"(DcE(!\"($\"'DJ?!\"'7$$\"'vVt!\"'$\"(DJ&>!\"(7$$\"(v= U(!\"($\"'DJ?!\"'7$$\"'vVt!\"'$\"(v$4@!\"(7$$\"'vVt!\"'$\"(DcE#!\"(7$$ \"(v=U(!\"($\"'vVB!\"'7$$\")D1Rv!\")$\"(v=U#!\"(7$$\"(D\"yv!\"($\")D\" GQ#!\")7$$\"(D\"yv!\"($\")vo/B!\")7$$\")D1Rv!\")$\"(DcE#!\"(7$$\"(D\"y v!\"($\")DcEA!\")7$$\")v=!\")7$$\")v=!\"(7$$\")DJ&p (!\")$\"(DJ&>!\"(7$$\"(vVt(!\"($\")D19>!\")7$$\")vVtx!\")$\"(DJ&>!\"(7 $$\"(vVt(!\"($\")v=#*>!\")7$$\"(vVt(!\"($\")DJq?!\")7$$\")vVtx!\")$\"( v$4@!\"(7$$\"(D1*y!\"($\"'DJ?!\"'7$$\"'voz!\"'$\"(DJ&>!\"(7$$\"'voz!\" '$\"(voz\"!\"(7$$\"(D1*y!\"($\"'v=!\")7$$\")vVtx!\")$\"'vVB!\"(7$$ \"(D1*y!\"($\"&Dc\"!\"'7$$\"'voz!\"'$\"&D\"y!\"(7$$\")v$f3)!\")$\"&D\" y!\"(7$$\"(vo/)!\"($\"(v=<\"!\")7$$\"(vo/)!\"($\"(DJ&>!\")7$$\")v$f3)! \")$\"'vVB!\"(7$$\"(vo/)!\"($\"(vVt#!\")7$$\")D\"y+)!\")$\"'vVB!\"(7$$ \")voHz!\")$\"'vVB!\"(7$$\"(D1*y!\"($\"(vVt#!\")7$$\"'voz!\"'$\"'D1R! \"(7$$\"(vo/)!\"($\"&vo%!\"'7$$\"(DJ?)!\"($\"&vo%!\"'7$$\"'D\"G)!\"'$ \"'D1R!\"(7$$\"'D\"G)!\"'$\"'vVB!\"(7$$\"(DJ?)!\"($\"&Dc\"!\"'7$$\"'D \"G)!\"'$\"&D\"y!\"(7$$\"(v$f$)!\"($\"&Dc\"!\"'7$$\"(Dc^)!\"($\"&Dc\"! \"'7$$\"'v$f)!\"'$\"&D\"y!\"(7$$\")v$4r)!\")$\"&D\"y!\"(7$$\"(v=n)!\"( $\"(v=<\"!\")7$$\"(v=n)!\"($\"(DJ&>!\")7$$\")v$4r)!\")$\"'vVB!\"(7$$\" (v=n)!\"($\"(vVt#!\")7$$\")D\"Gj)!\")$\"'vVB!\"(7$$\")voa&)!\")$\"'vVB !\"(7$$\"(Dc^)!\"($\"(vVt#!\")7$$\"'v$f)!\"'$\"'D1R!\"(7$$\"(v=n)!\"($ \"&vo%!\"'7$$\"(v=n)!\"($\"(v$fe!\")7$$\")D\"Gj)!\")$\"'voa!\"(7$$\")v oa&)!\")$\"'voa!\"(7$$\"(Dc^)!\"($\"(v$fe!\")7$$\")Dcw%)!\")$\"'voa!\" (7$$\"(Dc^)!\"($\"(D\"y]!\")7$$\"(Dc^)!\"($\"(voH%!\")7$$\")Dcw%)!\")$ \"'D1R!\"(7$$\"(v$f$)!\"($\"&vo%!\"'7$$\"'D\"G)!\"'$\"'voa!\"(7$$\"'D \"G)!\"'$\"'DJq!\"(7$$\"(v$f$)!\"($\"&D\"y!\"'7$$\"(Dc^)!\"($\"&D\"y! \"'7$$\"'v$f)!\"'$\"'DJq!\"(7$$\"(v=n)!\"($\"&D\"y!\"'7$$\"'v$f)!\"'$ \"'v$f)!\"(7$$\"'v$f)!\"'$\"(Dc,\"!\"(7$$\"(v=n)!\"($\"'v$4\"!\"'7$$\" (D\"G))!\"($\"'v$4\"!\"'7$$\"'D1*)!\"'$\"(Dc,\"!\"(7$$\"'D1*)!\"'$\"'v $f)!\"(7$$\"(D\"G))!\"($\"&D\"y!\"'7$$\"'D1*)!\"'$\"'DJq!\"(7$$\"(vV)* )!\"($\"&D\"y!\"'7$$\"(D19*!\"($\"&D\"y!\"'7$$\"'v=#*!\"'$\"'DJq!\"(7$ $\"&D1*!\"&$\"&vo%!\"'7$$\"'D1*)!\"'$\"%DJ!\"&7$$\"'D1*)!\"'$\"&D\"y! \"(7$$\"(vV)*)!\"($\"&Dc\"!\"'7$$\"(D19*!\"($\"&Dc\"!\"'7$$\"'v=#*!\"' $\"&D\"y!\"(7$$\"(voH*!\"($\"&Dc\"!\"'7$$\"'v=#*!\"'$\"'vVB!\"(7$$\"'v =#*!\"'$\"'D1R!\"(7$$\"(voH*!\"($\"&vo%!\"'7$$\"'DJ&*!\"'$\"%DJ!\"&7$$ \"&vo*!\"&$\"&Dc\"!\"'-%&COLORG6&%$RGBG$\"#5!\"\"$\"2OYJ!e@R!)\\!#<$\" \"!!\"\"-%*THICKNESSG6#\"\"\"-%*AXESSTYLEG6#%$BOXG-%(SCALINGG6#%,CONST RAINEDG" 1 2 2 1 10 1 2 6 0 2 1 1.0 45.0 45.0 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" }}{TEXT 249 0 "" }}}}}{SECT 0 {PARA 212 "" 0 "" {TEXT 203 16 "Refinement Trees" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, fibTree(2)):" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q*SPACETREEF'/%'italicGQ%tru eF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&fa lseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movab lelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔ F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q(fibTreeF'F/F2-I(mfen cedGF$6$-F#6#-I#mnGF$6$Q\"2F'F9F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 203 70 "Most of the algorithms are also s uitable for bisection (use BASE := 2)" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(BASE, 4):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sysli bGF'6(-I#miGF$6%Q%BASEF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I# moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchy GF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspac eGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.277777 8emF'/FNFSF5-I#mnGF$6$Q\"4F'F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 203 34 "Sum up the weights of all subtree s" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(sumWeightsRec, proc (`::`(i ndex, posint), `::`(stream, list), `::`(countInner, integer)) local i, val, retval; global BASE, SPACETREE; `:=`(val, 0); `:=`(retval, [inde x, stream]); if SPACETREE[retval[1]] = 0 then `:=`(retval[2], [1, op(r etval[2])]); return retval else for i to BASE do `:=`(retval[1], `+`(r etval[1], 1)); `:=`(retval, sumWeightsRec(retval[1], retval[2], countI nner)); `:=`(val, `+`(val, retval[2][1])) end do; `:=`(retval[2], [`+` (val, countInner), op(retval[2])]); return retval end if end proc):" " -I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6c_l-I#miGF$6%Q.s umWeightsRecF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\" ~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symm etricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF '/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFS F5-F66/Q%procF'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJF M-I(mfencedGF$6$-F#6/-F,6%Q&indexF'F/F2-F66-Q-∷F'F9F;F>F@FB FDFFFHFRFT-F,6%Q'posintF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.33 33333emF'F5-F,6%Q'streamF'F/F2F`o-F,6%Q%listF'F/F2FfoF5-F,6%Q+countInn erF'F/F2F`o-F,6%Q(integerF'F/F2F9-F,6#Q!F'-I'mspaceGF$6&/%'heightGQ&0. 0exF'/%&widthGQ&0.0emF'/%&depthGF`q/%*linebreakGQ(newlineF'-F\\q6&F^qF aqFdq/FgqQ%autoF'F5F5-F66/Q&localF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q\" iF'F/F2FfoF5-F,6%Q$valF'F/F2FfoF5-F,6%Q'retvalF'F/F2-F66-Q\";F'F9F;Fio F@FBFDFFFHFJFTF[qF5F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6% Q%BASEF'F/F2FfoF5-F,6%Q*SPACETREEF'F/F2FirF[qFiqF5F5FcrF5FOF5-I#mnGF$6 $Q\"0F'F9FirF[qFiqF5F5FfrF5FOF5-Fin6&-F#6&F]oFfoF5F\\pF9/%%openGQ\"[F' /%&closeGQ\"]F'FirF[qFiqF5F5F[qF5F5F5-F66/Q#ifF'FXFZFfnF;F>F@FBFDFFFHF JFMF5Fbs-Fin6&-F#6$Ffr-Fin6&-F#6#-Ffs6$Q\"1F'F9F9F]tF`tF9F]tF`tF5-F66- Q\"=F'F9F;F>F@FBFDFFFHFRFTF5FesF5-F66/Q%thenF'FXFZFfnF;F>F@FBFDFFFHFJF MF[qFiqF5F5F5F5Ffr-Fin6&-F#6#-Ffs6$Q\"2F'F9F9F]tF`tF5FOF5-Fin6&-F#6'F^ uFfoF5-F,6%Q#opF'F/F2-Fin6$-F#6$FfrFguF9F9F]tF`tFirF[qFiqF5F5F5F5-F66/ Q'returnF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FfrF[qFiqF5F5-F66/Q%elseF'FXFZFfn F;F>F@FBFDFFFHFJFMF[qFiqF5F5F5F5-F66/Q$forF'FXFZFfnF;F>F@FBFDFFFHFJFMF 5F`rF5-F66/Q%fromF'FXFZFfnF;F>F@FBFDFFFHFJFMF5F^uF5-F66/Q#toF'FXFZFfnF ;F>F@FBFDFFFHFJFMF5F_sF5-F66/Q#doF'FXFZFfnF;F>F@FBFDFFFHFJFMF[qFiqF5F5 F5F5F5F5FfrFjtF5FOF5FfrFjt-F66-Q\"+F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF '/FNF_xF^uFirF[qFiqF5F5F5F5F5F5FfrF5FOF5F+-Fin6$-F#6+FfrFjtFfoF5FfrFgu FfoF5FbpF9FirF[qFiqF5F5F5F5F5F5FcrF5FOF5FcrF[xFfrFguFjtFhpF[qFiqF5F5F5 F5-F66/Q$endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FhwFirF[qFiqF5F5F5F5FfrFguF5F OF5-Fin6&-F#6)FcrF[xFbpFfoF5FbvFevF9F]tF`tFirF[qFiqF5F5F5F5FivF5FfrF[q FiqF5F5FexF5FctFirF[qF5FexF5FU-F66-Q\":F'F9F;F>F@FBFDFFFHFRFTF[qFiqF[q Fiq-F,6%Q+sumWeightsF'F/F2F5FOF5FU-Fin6$-F#6#FhpF9FhpF[qF5F5F5F]rF5-F, 6%Q%lst1F'F/F2FfoF5-F,6%Q%lst2F'F/F2FfoF5FfrFfoF`rFirF[qFiqF5F5FfrF5FO F5-Fin6&FdyF9F]tF`tFirF[qFiqF5F5FfyF5FOF5F+-Fin6$-F#6)F^uFfoF5F\\zFfoF 5FesF9FirF[qFiqF5F5FiyF5FOF5F+-Fin6$-F#6)F^uFfoF5F\\zFfoF5F^uF9FirF[qF 5F5F5F_wF5F`rF5FbwF5F^uF5FewF5-F,6%Q%nopsF'F/F2-Fin6$-F#6$FfyFguF9F5Fh wF[qFiqF5F5F5F5FfrF5FOF5-Fin6&-F#6'Fbv-Fin6$-F#6#FfrF9FfoF5-Fin6&-F#6* FfyFgu-Fin6&-F#6#F`rF9F]tF`tFfoF5FiyFguFi[lF9F]tF`tF9F]tF`tFhpF[qFiqF5 F5FexF5FhwFirF[qFiqF5F5FivF5FfrFirF[qF5FexF5FUF\\yF[qFiqFhp" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 203 68 "Effectively convert the SPACETREE into a REFTREE with summed weights" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(REFTREE, sumWeights()):" "-I%mrowG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6)-I#miGF$6%Q(REFTREEF'/%'italicGQ%trueF'/%,mathvarian tGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separato rGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'ac centGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFF FH/FKQ,0.2777778emF'/FNFSF5-F,6%Q+sumWeightsF'F/F2-I(mfencedGF$6$-F#6# -F,6#Q!F'F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 47 "Create \"count\" partitions of the given REFTREE;" }} {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(createPartitions, proc (`::`(cou nt, posint)) local pos, treesize, partsize, parts, p, size, i; global \+ REFTREE, BASE; `:=`(pos, 1); `:=`(parts, []); `:=`(treesize, REFTREE[1 ][1]); `:=`(partsize, floor(`/`(`*`(treesize), `*`(count)))); for p to count do `:=`(size, 0); `:=`(parts, [op(parts), []]); while `<`(size, partsize) do if `<=`(`+`(size, REFTREE[pos][1]), partsize) then `:=`( size, `+`(size, REFTREE[pos][1])); for i to REFTREE[pos][2] do if REFT REE[pos][1] = 1 then `:=`(parts[p], [op(parts[p]), pos]) end if; `:=`( pos, `+`(pos, 1)) end do else `:=`(pos, `+`(pos, 1)) end if end do end do; if `<`(pos, nops(REFTREE)) then for pos from pos to nops(REFTREE) do if REFTREE[pos][1] = 1 then `:=`(parts[count], [op(parts[count]), \+ pos]) end if end do end if; return parts end proc):" "-I%mrowG6#/I+mod ulenameG6\"I,TypesettingGI(_syslibGF'6_jl-I#miGF$6%Q1createPartitionsF '/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'norma lF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(la rgeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL -F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%proc F'/%%boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF $6$-F#6%-F,6%Q&countF'F/F2-F66-Q-∷F'F9F;F>F@FBFDFFFHFRFT-F, 6%Q'posintF'F/F2F9-F,6#Q!F'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ &0.0emF'/%&depthGF^p/%*linebreakGQ(newlineF'F5F5-F66/Q'globalF'FXFZFfn F;F>F@FBFDFFFHFJFMF5-F,6%Q(REFTREEF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFH FJ/FNQ,0.3333333emF'F5-F,6%Q%BASEF'F/F2-F66-Q\";F'F9F;F`qF@FBFDFFFHFJF TFio-Fjo6&F\\pF_pFbp/FepQ%autoF'F5F5-F66/Q&localF'FXFZFfnF;F>F@FBFDFFF HFJFMF5-F,6%Q$posF'F/F2F]qF5-F,6%Q)treesizeF'F/F2F]qF5-F,6%Q)partsizeF 'F/F2F]qF5-F,6%Q&partsF'F/F2F]qF5-F,6%Q\"pF'F/F2F]qF5-F,6%Q%sizeF'F/F2 F]qF5-F,6%Q\"iF'F/F2FfqFioFiqF5F5FioFiqF5F5F`rF5FOF5-I#mnGF$6$Q\"1F'F9 FfqFioFiqF5F5FirF5FOF5-Fin6&-F#6#FfoF9/%%openGQ\"[F'/%&closeGQ\"]F'Ffq FioF5F5FcrF5FOF5Fjp-Fin6&-F#6#FesF9F]tF`tFctFfqFioFiqF5F5FfrF5FOF5-F,6 %Q&floorF'/F0F=F9-Fin6$-F#6%Fcr-F66-Q\"/F'F9F;F>/FAF1FBFDFFFH/FKQ,0.16 66667emF'/FNFduF]oF9FfqFioFioFiqF5F5-F66/Q$forF'FXFZFfnF;F>F@FBFDFFFHF JFMF5F\\sF5-F66/Q%fromF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FesF5-F66/Q#toF'FXF 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FioFiqF5F5F5F5F5F5F5F5F_zF5F_vFfqFioF5F5F5F5F5F5F5-F66/Q%elseF'FXFZFfn F;F>F@FBFDFFFHFJFMFioFiqF5F5F5F5F5F5F5F5F`rF5FOF5F`rF5FiwF5FesFfqFioFi qF5F5F5F5F5F5F_zF5FfwFfqFioFiqF5F5F5F5F_zF5F_vFfqFioFiqF5F5F_zF5F_vFfq FioFiqF5F5FioF5F5-F66-Q\"#F'F9F;F>F@FBFDFFFHFJFM-F,6%Q1if~pos~<~REFTRE EF'F/F2FctFixF5FfxFioF5F5FfwF5F`rF5FcwF5-F,6%Q%nopsF'F/F2-Fin6$-F#6#Fj pF9F5FfxFioF5F5F5F5FfuF5F`rF5FiuF5F`rF5F\\vF5F[[lF^[lF5F_vFioF5F5F5F5F fwF5FjpF_xFctF5F`yF5FesF5FfxFioF5F5F5F5F5F5F5F5Fir-Fin6&-F#6#F]oF9F]tF `tF5FOF5-Fin6&-F#6'Fiv-Fin6$-F#6$FirFb[lF9F]qF5F`rF9F]tF`tFfqFioF5F5F5 F5F5F5F_zF5FfwFfqFioF5F5F5F5F_zF5F_vFfqFioF5F5F_zF5FfwFfqFioFiqF5F5Fio FiqF5F5-F66/Q'returnF'FXFZFfnF;F>F@FBFDFFFHFJFMF5FirFfqFioF5F_zF5FU-F6 6-Q\":F'F9F;F>F@FBFDFFFHFRFTFioFiqFfo" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(PARTS, createPartitions(3)):" "-I%mrowG6#/I+module nameG6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q&PARTSF'/%'italicGQ%tru eF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&fa lseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movab lelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔ F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q1createPartitionsF'F/ F2-I(mfencedGF$6$-F#6#-I#mnGF$6$Q\"3F'F9F9-F66-Q\":F'F9F;F>F@FBFDFFFHF RFT" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 70 "Calculate the points whic h represent the vertices of the grid elements" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(createPointsRec, proc (`::`(tri, list), `::`(pos, \+ posint), `::`(pts, list)) local m, tmp1, tmp2, tmp11, tmp12, tmp21, tm p22, retval; global REFTREE; `:=`(retval, [0, []]); if `<`(1, REFTREE[ pos][1]) then `:=`(m, `+`(`*`(`/`(1, 2), `*`(tri[2])), `*`(`/`(1, 2), \+ `*`(tri[3])))); `:=`(tmp1, [m, tri[1], tri[2], m]); `:=`(tmp2, [m, tri [3], tri[1], m]); `:=`(m, `+`(`*`(`/`(1, 2), `*`(tmp1[2])), `*`(`/`(1, 2), `*`(tmp1[3])))); `:=`(tmp11, [m, tmp1[3], tmp1[1], m]); `:=`(tmp1 2, [m, tmp1[1], tmp1[2], m]); `:=`(m, `+`(`*`(`/`(1, 2), `*`(tmp2[2])) , `*`(`/`(1, 2), `*`(tmp2[3])))); `:=`(tmp21, [m, tmp2[3], tmp2[1], m] ); `:=`(tmp22, [m, tmp2[1], tmp2[2], m]); `:=`(retval, createPointsRec (tmp22, `+`(pos, 1), pts)); `:=`(retval, createPointsRec(tmp21, `+`(re tval[1], 1), retval[2])); `:=`(retval, createPointsRec(tmp12, `+`(retv al[1], 1), retval[2])); `:=`(retval, createPointsRec(tmp11, `+`(retval [1], 1), retval[2])) else `:=`(retval[1], pos); `:=`(retval[2], [op(pt s), tri]) end if; return retval end proc):" "-I%mrowG6#/I+modulenameG6 \"I,TypesettingGI(_syslibGF'6^cl-I#miGF$6%Q0createPointsRecF'/%'italic GQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenc eGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/% .movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*&co loneq;F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%%boldG F1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F#6/-F ,6%Q$triF'F/F2-F66-Q-∷F'F9F;F>F@FBFDFFFHFRFT-F,6%Q%listF'F/ F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q$posF'F/F2 F`o-F,6%Q'posintF'F/F2FfoF5-F,6%Q$ptsF'F/F2F`oFcoF9-F,6#Q!F'-I'mspaceG F$6&/%'heightGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGF]q/%*linebreakGQ(ne wlineF'F5F5-F66/Q'globalF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q(REFTREEF'F /F2-F66-Q\";F'F9F;FioF@FBFDFFFHFJFTFhp-Fip6&F[qF^qFaq/FdqQ%autoF'F5F5- F66/Q&localF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q\"mF'F/F2FfoF5-F,6%Q%tmp 1F'F/F2FfoF5-F,6%Q%tmp2F'F/F2FfoF5-F,6%Q&tmp11F'F/F2FfoF5-F,6%Q&tmp12F 'F/F2FfoF5-F,6%Q&tmp21F'F/F2FfoF5-F,6%Q&tmp22F'F/F2FfoF5-F,6%Q'retvalF 'F/F2F\\rFhpF_rF5F5FhpF_rF5F5F[tF5FOF5-Fin6&-F#6%-I#mnGF$6$Q\"0F'F9Ffo -Fin6&-F#6#FepF9/%%openGQ\"[F'/%&closeGQ\"]F'F9FjtF]uF\\rFhpF_rF5F5Fhp F5F5-F66/Q#ifF'FXFZFfnF;F>F@FBFDFFFHFJFMF5Fiq-Fin6&-F#6#F\\pF9FjtF]u-F in6&-F#6#-Fct6$Q\"1F'F9F9FjtF]uF5-F66-Q\">F'F9F;F>F@FBFDFFFHFRFTF5F[vF hpF_rF5F5-F66/Q%thenF'FXFZFfnF;F>F@FBFDFFFHFJFMFhpF5F5-F66-Q\"#F'F9F;F >F@FBFDFFFHFJFM-F,6%Q(~RefineF'F/F2FhpF_rF5F5FfrF5FOF5-Fin6$-F#6'F]o-F 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Fin6$-F#6-FesFfoF5F[tFguFewF[vFfoF5F[tF^wF9F\\rFhpF_rF5F5F5F5F[tF5FOF5 F+-Fin6$-F#6-FbsFfoF5F[tFguFewF[vFfoF5F[tF^wF9F\\rFhpF_rF5F5F5F5F[tF5F OF5F+-Fin6$-F#6-F_sFfoF5F[tFguFewF[vFfoF5F[tF^wF9F\\rFhpF_rF5F5-F66/Q% elseF'FXFZFfnF;F>F@FBFDFFFHFJFMFhpF5F5F5F5Fdv-F,6%Q.Add~triangelsF'F/F 2FhpF_rF5F5F5F5F[tFguF5FOF5F\\pF\\rFhpF_rF5F5F5F5F[tF^wF5FOF5-Fin6&-F# 6'-F,6%Q#opF'F/F2-Fin6$-F#6#FbpF9FfoF5F]oF9FjtF]uF\\rFhpF_rF5F5-F66/Q$ endF'FXFZFfnF;F>F@FBFDFFFHFJFMF5F`uF\\rFhpF_rF5F5FhpF_rF5F5-F66/Q'retu rnF'FXFZFfnF;F>F@FBFDFFFHFJFMF5F[tF\\rFhpF5F]]lF5FU-F66-Q\":F'F9F;F>F@ FBFDFFFHFRFTFhpF_rFhpF_r-F,6%Q-createPointsF'F/F2F5FOF5FU-Fin6$FhtF9Fe pFhpF_rF5F5FcrF5F[tF\\rFhpF_rF5F5F[tF5FOF5F+-Fin6$-F#6)-Fin6&-F#6,-Fin 6&-F#6*F[vFhxFbwFfoF5F[vFhxFbwF9FjtF]uFfoF5-Fin6&-F#6&FbtFfoF5FbtF9Fjt F]uFfoF5-Fin6&-F#6&F[vFfoF5FbtF9FjtF]uFfoF5Fc^lF9FjtF]uFfoF5F[vFfoF5Ff tF9F\\rFhpF_rF5F5F`]lF5F[tF^wF\\rFhpF5F]]lF5FUFc]l" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(PTS, createPoints()):" "-I%mrowG6#/I+mod ulenameG6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q$PTSF'/%'italicGQ%tr ueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&f alseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.mova blelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*&coloneq ;F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q-createPointsF'F/F2- I(mfencedGF$6$-F#6#-F,6#Q!F'F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 203 66 "Partitionize the points according to the partitions created before" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 " `:=`(partitionizePoints, proc (`::`(parts, list), `::`(pts, list)) loc al i, j, ppos, ppts, pos; `:=`(ppts, []); `:=`(ppos, 1); `:=`(pos, 1); for i to nops(parts) do `:=`(ppts, [op(ppts), []]); for j to nops(par ts[ppos]) do `:=`(ppts[ppos], [op(ppts[ppos]), pts[pos]]); `:=`(pos, ` +`(pos, 1)) end do; `:=`(ppos, `+`(ppos, 1)) end do; for i from pos to nops(pts) do `:=`(ppts[`+`(ppos, `-`(1))], [op(ppts[`+`(ppos, `-`(1)) ]), pts[pos]]) end do; return ppts end proc):" "-I%mrowG6#/I+modulenam eG6\"I,TypesettingGI(_syslibGF'6fy-I#miGF$6%Q3partitionizePointsF'/%'i talicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/% &fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeop GF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66- Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F66/Q%procF'/%% boldGF1/F3Q%boldF'/%+fontweightGFenF;F>F@FBFDFFFHFJFM-I(mfencedGF$6$-F #6*-F,6%Q&partsF'F/F2-F66-Q-∷F'F9F;F>F@FBFDFFFHFRFT-F,6%Q%l istF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'F5-F,6%Q$pt sF'F/F2F`oFcoF9-F,6#Q!F'-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGQ&0. 0emF'/%&depthGFgp/%*linebreakGQ(newlineF'-Fcp6&FepFhpF[q/F^qQ%autoF'F5 F5-F66/Q&localF'FXFZFfnF;F>F@FBFDFFFHFJFMF5-F,6%Q\"iF'F/F2FfoF5-F,6%Q \"jF'F/F2FfoF5-F,6%Q%pposF'F/F2FfoF5-F,6%Q%pptsF'F/F2FfoF5-F,6%Q$posF' F/F2-F66-Q\";F'F9F;FioF@FBFDFFFHFJFTFbpF5F5F`rF5FOF5-Fin6&-F#6#F_pF9/% 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\"($\"(Dcw*!\")7$$\"'DJX!\"'$\"'v$f)!\"(7$$\"(DJX%!\"($\"&D\"y!\"'7$$ \"(voH%!\"($\"&D\"y!\"'7$$\"'v=U!\"'$\"'v$f)!\"(7$$\"'v=U!\"'$\"(Dc,\" !\"(7$$\"(voH%!\"($\"'v$4\"!\"'7$$\"'v=U!\"'$\"(v=<\"!\"(7$$\"(D19%!\" ($\"'v$4\"!\"'7$$\"(vV)R!\"($\"'v$4\"!\"'7$$\"'D1R!\"'$\"(v=<\"!\"(7$$ \"'D1R!\"'$\"(D\"G8!\"(7$$\"(vV)R!\"($\"'D19!\"'7$$\"(D19%!\"($\"'D19! \"'7$$\"'v=U!\"'$\"(D\"G8!\"(7$$\"(voH%!\"($\"'D19!\"'7$$\"'v=U!\"'$\" (vV[\"!\"(7$$\"'v=U!\"'$\"(D1k\"!\"(7$$\"(voH%!\"($\"'v=!\")7$$\")v=nQ! \")$\"(DJ&>!\"(7$$\")DJXR!\")$\"(DJ&>!\"(7$$\"(vV)R!\"($\")D19>!\")7$$ \")vVBS!\")$\"(DJ&>!\"(7$$\"(vV)R!\"($\")v=#*>!\")7$$\"(vV)R!\"($\")DJ q?!\")7$$\")vVBS!\")$\"(v$4@!\"(7$$\"(D19%!\"($\"'DJ?!\"'7$$\"'v=U!\"' $\"(DJ&>!\"(7$$\"'v=U!\"'$\"(voz\"!\"(7$$\"(D19%!\"($\"'v= " 0 "" {XPPEDIT 19 1 "`:=`(PARTITIONS, 8);" "-I%mrowG6#/I+modulenameG6\"I,Typ esettingGI(_syslibGF'6'-I#miGF$6%Q+PARTITIONSF'/%'italicGQ%trueF'/%,ma thvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%* separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimits GF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F> F@FBFDFFFH/FKQ,0.2777778emF'/FNFS-I#mnGF$6$Q\"8F'F9-F66-Q\";F'F9F;/F?F 1F@FBFDFFFHFJFT" }}{PARA 11 "" 1 "" {XPPMATH 20 "\"\")" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, fibTree(5)):" "-I%mro wG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q*SPACETREE F'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'norm alF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(l argeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGF L-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q(fib TreeF'F/F2-I(mfencedGF$6$-F#6#-I#mnGF$6$Q\"5F'F9F9-F66-Q\":F'F9F;F>F@F BFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(pts, Sier pinski(SPACETREE)):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sysl ibGF'6)-I#miGF$6%Q$ptsF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I# moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchy GF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspac eGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.277777 8emF'/FNFSF5-F,6%Q+SierpinskiF'F/F2-I(mfencedGF$6$-F#6#-F,6%Q*SPACETRE EF'F/F2F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(curve, plot(pts, 0 .. 1, 0 .. .5, color = blue, sc aling = CONSTRAINED, thickness = 3)):" "-I%mrowG6#/I+modulenameG6\"I,T ypesettingGI(_syslibGF'6)-I#miGF$6%Q&curveF'/%'italicGQ%trueF'/%,mathv ariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*sep aratorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF= /%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@F BFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q%plotF'F/F2-I(mfencedGF$6$-F#68- F,6%Q$ptsF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'-I#mn GF$6$Q\"0F'F9-F66-Q#..F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'FM-Fao6$Q\"1 F'F9FjnF`oFdo-Fao6$Q$0.5F'F9FjnF5-F,6%Q&colorF'F/F2-F66-Q\"=F'F9F;F>F@ FBFDFFFHFRFT-F,6%Q%blueF'F/F2Fjn-F,6%Q(scalingF'F/F2Fbp-F,6%Q,CONSTRAI NEDF'F/F2Fjn-F,6%Q*thicknessF'F/F2Fbp-Fao6$Q\"3F'F9F9-F66-Q\":F'F9F;F> F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(parts, partition(pts, PARTITIONS)):" "-I%mrowG6#/I+modulenameG6\"I,Typesetti ngGI(_syslibGF'6)-I#miGF$6%Q&partsF'/%'italicGQ%trueF'/%,mathvariantGQ 'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF =/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accen tGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/ FKQ,0.2777778emF'/FNFSF5-F,6%Q*partitionF'F/F2-I(mfencedGF$6$-F#6%-F,6 %Q$ptsF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'-F,6%Q+P ARTITIONSF'F/F2F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(partcurve, plot(parts, axes = BOXED, scali ng = CONSTRAINED, thickness = 2, color = colours, view = [0 .. 1, 0 .. .5])):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6)-I#mi GF$6%Q*partcurveF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6 -Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%* symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0. 0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/ FNFSF5-F,6%Q%plotF'F/F2-I(mfencedGF$6$-F#6:-F,6%Q&partsF'F/F2-F66-Q\", F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'-F,6%Q%axesF'F/F2-F66-Q\"=F'F 9F;F>F@FBFDFFFHFRFT-F,6%Q&BOXEDF'F/F2FjnF5-F,6%Q(scalingF'F/F2Fco-F,6% Q,CONSTRAINEDF'F/F2FjnF5-F,6%Q*thicknessF'F/F2Fco-I#mnGF$6$Q\"2F'F9Fjn F5-F,6%Q&colorF'F/F2Fco-F,6%Q(coloursF'F/F2Fjn-F,6%Q%viewF'F/F2Fco-FY6 &-F#6)-Fcp6$Q\"0F'F9-F66-Q#..F'F9F;F>F@FBFDFFFH/FKQ,0.2222222emF'FM-Fc p6$Q\"1F'F9FjnFcqFfq-Fcp6$Q$0.5F'F9F9/%%openGQ\"[F'/%&closeGQ\"]F'F9-F 66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(REFTREE, sumWeights()):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF '6)-I#miGF$6%Q(REFTREEF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I# moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchy GF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspac eGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.277777 8emF'/FNFSF5-F,6%Q+sumWeightsF'F/F2-I(mfencedGF$6$-F#6#-F,6#Q!F'F9-F66 -Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(PARTS, createPartitions(PARTITIONS)):" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q&PARTSF'/%'italicGQ%trueF'/ %,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF '/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movableli mitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9 F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q1createPartitionsF'F/F2-I (mfencedGF$6$-F#6#-F,6%Q+PARTITIONSF'F/F2F9-F66-Q\":F'F9F;F>F@FBFDFFFH FRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(PTS, createPoint s()):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6)-I#miGF $6%Q$PTSF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/ F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetri cGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%' rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F ,6%Q-createPointsF'F/F2-I(mfencedGF$6$-F#6#-F,6#Q!F'F9-F66-Q\":F'F9F;F >F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(PPTS, partitionizePoints(PARTS, PTS)):" "-I%mrowG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6)-I#miGF$6%Q%PPTSF'/%'italicGQ%trueF'/%,mathvarian tGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separato rGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'ac centGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFF FH/FKQ,0.2777778emF'/FNFSF5-F,6%Q3partitionizePointsF'F/F2-I(mfencedGF $6$-F#6%-F,6%Q&PARTSF'F/F2-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.33333 33emF'-F,6%Q$PTSF'F/F2F9-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(grid, plotTriangles(PPTS, 1)):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6)-I#miGF$6%Q%gr idF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'no rmalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF=/% (largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspace GFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-F,6%Q.p lotTrianglesF'F/F2-I(mfencedGF$6$-F#6%-F,6%Q%PPTSF'F/F2-F66-Q\",F'F9F; /F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'-I#mnGF$6$Q\"1F'F9F9-F66-Q\":F'F9F; F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "plots[dis play](partcurve, grid);" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_ syslibGF'6&-I#miGF$6%Q&plotsF'/%'italicGQ%trueF'/%,mathvariantGQ'itali cF'-I(mfencedGF$6&-F#6#-F,6%Q(displayF'F/F2/F3Q'normalF'/%%openGQ\"[F' /%&closeGQ\"]F'-F66$-F#6%-F,6%Q*partcurveF'/F0Q&falseF'F=-I#moGF$6-Q\" ,F'F=/%&fenceGFM/%*separatorGF1/%)stretchyGFM/%*symmetricGFM/%(largeop GFM/%.movablelimitsGFM/%'accentGFM/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.333 3333emF'-F,6%Q%gridF'FLF=F=-FO6-Q\";F'F=FRFTFVFXFZFfnFhnFjn/F^oQ,0.277 7778emF'" }}{PARA 13 "" 1 "" {TEXT 249 0 "" }{GLPLOT2D 710 376 376 {PLOTDATA 2 "6_w-%'CURVESG6%797$$\"$D\"!\"$$\"$D'!\"%7$$\"%v=!\"%$\"$D \"!\"$7$$\"%DJ!\"%$\"$D\"!\"$7$$\"$v$!\"$$\"$D'!\"%7$$\"&vo%!\"&$\"$D' !\"%7$$\"%vV!\"%$\"%v$*!\"&7$$\"&D1%!\"&$\"'D19!\"'7$$\"'v=U!\"'$\"&Dc \"!\"&7$$\"'DJX!\"'$\"&Dc\"!\"&7$$\"&vo%!\"&$\"'D19!\"'7$$\"'vV[!\"'$ \"&Dc\"!\"&7$$\"&vo%!\"&$\"'v=!\"(7$$\"(v$4Y !\"($\"'DJ?!\"'7$$\"(Dcw%!\"($\"'DJ?!\"'7$$\"'vV[!\"'$\"(DJ&>!\"(7$$\" (v=#\\!\"($\"'DJ?!\"'7$$\"'vV[!\"'$\"(v$4@!\"(7$$\"(Dcw%!\"($\")DcEA! \")7$$\")vo/[!\")$\"(DcE#!\"(7$$\")D\"G)[!\")$\"(DcE#!\"(7$$\"(v=#\\! \"($\")DcEA!\")7$$\")v$4'\\!\")$\"(DcE#!\"(-%&COLORG6&%$RGBG$\"\"!!\" \"$\"\"!!\"\"$\"\"!!\"\"-%*THICKNESSG6#\"\"#-%'CURVESG6%7:7$$\")v$4' \\!\")$\"(DcE#!\"(7$$\"(v=#\\!\"($\")vo/B!\")7$$\"(v=#\\!\"($\")D\"GQ# !\")7$$\")v$4'\\!\")$\"(v=U#!\"(7$$\"(v=#\\!\"($\")v$4Y#!\")7$$\")D\"G )[!\")$\"(v=U#!\"(7$$\")vo/[!\")$\"(v=U#!\"(7$$\"(Dcw%!\"($\")v$4Y#!\" )7$$\")DcEZ!\")$\"(v=U#!\"(7$$\"(Dcw%!\"($\")D\"GQ#!\")7$$\"(Dcw%!\"($ \")vo/B!\")7$$\")DcEZ!\")$\"(DcE#!\"(7$$\"(v$4Y!\"($\"'vVB!\"'7$$\"'DJ X!\"'$\"(v=U#!\"(7$$\"(DJX%!\"($\"'vVB!\"'7$$\"'DJX!\"'$\"(DcE#!\"(7$$ \"'DJX!\"'$\"(v$4@!\"(7$$\"(DJX%!\"($\"'DJ?!\"'7$$\"'v=U!\"'$\"&v=#!\" &7$$\"&D1%!\"&$\"'vVB!\"'7$$\"'D1R!\"'$\"&v=#!\"&7$$\"&D1%!\"&$\"'DJ?! \"'7$$\"&D1%!\"&$\"'v=&!\")$\"(vVt#!\"(7$$\") v=<^!\")$\"(vVt#!\"(7$$\"(D\"y]!\"($\")vVtF!\")7$$\")D1R]!\")$\"(vVt#! \"(7$$\"(D\"y]!\"($\")DJ&p#!\")7$$\"(D\"y]!\"($\")v= &!\")$\"(D\"yD!\"(7$$\"(vVB&!\"($\")D1RD!\")7$$\")vVt_!\")$\"(D\"yD!\" (7$$\"(vVB&!\"($\")v=&!\")$\"(v=U#!\"(7$$\")v= <^!\")$\"(v=U#!\"(7$$\"(D\"y]!\"($\")v$4Y#!\")7$$\")D1R]!\")$\"(v=U#! \"(7$$\"(D\"y]!\"($\")D\"GQ#!\")7$$\"(D\"y]!\"($\")vo/B!\")-%&COLORG6& %$RGBG$\"\"!!\"\"$\"#5!\"\"$\"#5!\"\"-%*THICKNESSG6#\"\"#-%'CURVESG6%7 :7$$\"(D\"y]!\"($\")vo/B!\")7$$\")D1R]!\")$\"(DcE#!\"(7$$\"(D\"y]!\"($ \")DcEA!\")7$$\")v=<^!\")$\"(DcE#!\"(7$$\")DJ&>&!\")$\"(DcE#!\"(7$$\"( vVB&!\"($\")DcEA!\")7$$\"'Dc^!\"'$\"(v$4@!\"(7$$\"(D\"y]!\"($\"'DJ?!\" '7$$\"'Dc^!\"'$\"(DJ&>!\"(7$$\"(vVB&!\"($\"'DJ?!\"'7$$\"(D1R&!\"($\"'D J?!\"'7$$\"'voa!\"'$\"(DJ&>!\"(7$$\"&DJ&!\"&$\"'v= " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 203 53 "Here are some other nice manually defined SPACETRE ES:" }}{PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, [1, 0, 1, 0, 0 , 0, 0, 1, 0, 0, 0, 0, 0, 0]):" "-I%mrowG6#/I+modulenameG6\"I,Typesett ingGI(_syslibGF'6(-I#miGF$6%Q*SPACETREEF'/%'italicGQ%trueF'/%,mathvari antGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separa torGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%' accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFD FFFH/FKQ,0.2777778emF'/FNFSF5-I(mfencedGF$6&-F#6=-I#mnGF$6$Q\"1F'F9-F6 6-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'-Fen6$Q\"0F'F9FhnFZFhnF ^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oF9/%%open GQ\"[F'/%&closeGQ\"]F'-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, \+ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0]): " "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6(-I#miGF$6%Q* SPACETREEF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F' /F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetr icGF=/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/% 'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5- I(mfencedGF$6&-F#6eq-I#mnGF$6$Q\"1F'F9-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ /FNQ,0.3333333emF'FZFhn-Fen6$Q\"0F'F9FhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^ oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^ oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhnF^oFhnF^oFhnF^o FhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oF hnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oF9/%%openGQ\"[F'/%&close GQ\"]F'-F66-Q\":F'F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, \+ 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 , 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, \+ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]):" "-I%mrowG6#/I+modulenameG6\"I,Type settingGI(_syslibGF'6(-I#miGF$6%Q*SPACETREEF'/%'italicGQ%trueF'/%,math variantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*se paratorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF =/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@ FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-I(mfencedGF$6&-F#6ey-I#mnGF$6$Q\"1F' F9-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'FZFhn-Fen6$Q\"0F'F 9FhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^o FhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFh nF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFh nF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhnF^oFhnF^oFhn F^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhnF^oFhnF ZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^o FhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^o FhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZF hnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oF hnFZFhnF^oFhnF^oFhnF^oFhnF^oF9/%%openGQ\"[F'/%&closeGQ\"]F'-F66-Q\":F' F9F;F>F@FBFDFFFHFRFT" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`( SPACETREE, [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0 , 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, \+ 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 , 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, \+ 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0 , 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]):" "- I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6(-I#miGF$6%Q*SPAC ETREEF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q\"~F'/F3Q 'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF=/%*symmetricGF =/%(largeopGF=/%.movablelimitsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rsp aceGFL-F66-Q*≔F'F9F;F>F@FBFDFFFH/FKQ,0.2777778emF'/FNFSF5-I(mf encedGF$6&-F#6eal-I#mnGF$6$Q\"1F'F9-F66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FN Q,0.3333333emF'FZFhn-Fen6$Q\"0F'F9FhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFh nF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhn F^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnFZFhnF^oFhnF^oFhnF^ oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^ oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZ FhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^o FhnFZFhnFZFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFh nF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhn F^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF ^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnFZFhnF^oFhnF^oFhnF^o FhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^o FhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZF hnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oF hnFZFhnFZFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhn F^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhn F^oFhnF^oF9/%%openGQ\"[F'/%&closeGQ\"]F'-F66-Q\":F'F9F;F>F@FBFDFFFHFRF T" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, [1, 1, 0 , 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, \+ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 , 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, \+ 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0 , 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, \+ 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1 , 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]):" "-I%mrowG6#/I+modulenameG6\"I,Typesetti ngGI(_syslibGF'6(-I#miGF$6%Q*SPACETREEF'/%'italicGQ%trueF'/%,mathvaria ntGQ'italicF'-I#moGF$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separat orGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelimitsGF=/%'a ccentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-F66-Q*≔F'F9F;F>F@FBFDF FFH/FKQ,0.2777778emF'/FNFSF5-I(mfencedGF$6&-F#6eil-I#mnGF$6$Q\"1F'F9-F 66-Q\",F'F9F;/F?F1F@FBFDFFFHFJ/FNQ,0.3333333emF'FZFhn-Fen6$Q\"0F'F9Fhn F^oFhnF^oFhnF^oFhnFZFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF ZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^o FhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnFZFhnFZFhnFZFhn F^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhn F^oFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnF^oFh nF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhn FZFhnF^oFhnF^oFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnFZFhnF^oFhnF^oFhnF^oFhnF 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0 "" {XPPEDIT 19 1 "`:=`(SPACETREE, [1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, \+ 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 , 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, \+ 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0 , 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, \+ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0 , 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, \+ 0, 0, 0]):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6(-I #miGF$6%Q*SPACETREEF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moG F$6-Q\"~F'/F3Q'normalF'/%&fenceGQ&falseF'/%*separatorGF=/%)stretchyGF= 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