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%Q!6\"F]g\\l-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6#%%NONEG-%%VIEWG6$Fbg\\l Fbg\\l" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r estart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 371 "snow:=proc(n,lx ,ly,rx,ry) local mlx, mly, mrx, mry, kx, ky; mlx:=(2*lx+rx)/3; \nmly:= (2*ly+ry)/3; \nmrx:=(lx+2*rx)/3; \nmry:=(ly+2*ry)/3; \nkx:=(mlx+mrx)/2 +3^(1/2)*(mly-mry)/2; \nky:=(mly+mry)/2+3^(1/2)*(mrx-mlx)/2; \nif n=0 \+ then [[lx,ly],[rx,ry]] else [op(snow(n-1,lx,ly,mlx,mly)),op(snow(n-1,m lx,mly,kx,ky)), \nop(snow(n-1,kx,ky,mrx,mry)),op(snow(n-1,mrx,mry,rx,r y))] fi end;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%snowGf*6'%\"nG%#l xG%#lyG%#rxG%#ryG6(%$mlxG%$mlyG%$mrxG%$mryG%#kxG%#kyG6\"F3C)>8$,&*&#\" \"#\"\"$\"\"\"9%F8%,&*&F9F<9&F8&,&* &F?F8',&*&F?F8(,(*&#F8),(*&FVF " 0 "" {MPLTEXT 1 0 10 "p:=2*Pi/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,$*(\"\"#\"\" \"\"\"$!\"\"%#PiGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "p1 :=plot(snow(1,cos(p),sin(p),1,0),scaling=constrained,axes=none):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "p2:=plot(snow(1,cos(2*p),sin (2*p),cos(p),sin(p)),scaling=constrained,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "p3:=plot(snow(1,cos(3*p),sin(3*p),cos(2*p ),sin(2*p)),scaling=constrained,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warni ng, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "u:=display(p1,p2,p3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "u;" }}{PARA 13 "" 1 "" {GLPLOT2D 291 284 284 {PLOTDATA 2 "6)-%'CURVESG6$7*7$$!3++++++++]!#=$\"3'fQWy.a-m)F*7$$\"\"! F/$\"3Kdi*=p-Nx&F*F-7$$\"3++++++++]F*F+F27$F3$\"3kG\"[fM^n)GF*F57$$\" \"\"F/F.-%'COLOURG6&%$RGBG$\"#5!\"\"F.F.-F$6$7*7$F($!3'fQWy.a-m)F*7$F( $!3kG\"[fM^n)GF*FH7$$FAF/F.FK7$F(F6FMF'F;-F$6$7*F87$F3FIFQ7$F3FFFR7$F. $!3Kdi*=p-Nx&F*FSFEF;-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%,CONSTRAINEDG -%+AXESLABELSG6%Q!6\"F[o-%%FONTG6#%(DEFAULTG-%%VIEWG6$F`oF`o" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C urve 3" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 371 "snow:=proc(n,lx,ly,rx,ry) l ocal mlx, mly, mrx, mry, kx, ky; mlx:=(2*lx+rx)/3; \nmly:=(2*ly+ry)/3; \nmrx:=(lx+2*rx)/3; \nmry:=(ly+2*ry)/3; \nkx:=(mlx+mrx)/2+3^(1/2)*(ml y-mry)/2; \nky:=(mly+mry)/2+3^(1/2)*(mrx-mlx)/2; \nif n=0 then [[lx,ly ],[rx,ry]] else [op(snow(n-1,lx,ly,mlx,mly)),op(snow(n-1,mlx,mly,kx,ky )), \nop(snow(n-1,kx,ky,mrx,mry)),op(snow(n-1,mrx,mry,rx,ry))] fi end; \n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%snowGf*6'%\"nG%#lxG%#lyG%#rxG %#ryG6(%$mlxG%$mlyG%$mrxG%$mryG%#kxG%#kyG6\"F3C)>8$,&*&#\"\"#\"\"$\"\" \"9%F8%,&*&F9F<9&F8&,&*&F?F8',&*&F?F8(,(*&#F8),(*&FVF " 0 "" {MPLTEXT 1 0 10 "p:=2*Pi/3 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG,$*(\"\"#\"\"\"\"\"$!\"\"%# PiGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "p1:=plot(snow(2, cos(p),sin(p),1,0),scaling=constrained,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "p2:=plot(snow(2,cos(2*p),sin(2*p),cos(p),si n(p)),scaling=constrained,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "p3:=plot(snow(2,cos(3*p),sin(3*p),cos(2*p),sin(2*p)), scaling=constrained,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "u:=display(p1,p2,p3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "u;" }}{PARA 13 "" 1 "" {GLPLOT2D 314 302 302 {PLOTDATA 2 "6)-%'CURVESG6$7B7$$!3++++++++]!#=$\"3'fQWy.a-m)F*7$$!3:LL LLLLLLF*$\"3O4]>*e.!)p(F*F-7$$!3emmmmmmm;F*F+F27$F3$\"3!RjX09`dt'F*F57 $$\"\"!F:$\"3Kdi*=p-Nx&F*F87$$\"3emmmmmmm;F*F6F=7$F>F+F@7$$\"3:LLLLLLL LF*F0FA7$$\"3++++++++]F*F+FD7$FEF6FG7$$\"3ImmmmmmmmF*F;FH7$FE$\"3G\")o CVAD6[F*FK7$FE$\"3kG\"[fM^n)GF*FN7$FI$\"3M_()H(*3]C>F*FQ7$$\"3qLLLLLLL $)F*FOFT7$FU$\"3shP\\'[/Di*!#>FW7$$\"\"\"F:F9-%'COLOURG6&%$RGBG$\"#5! \"\"F9F9-F$6$7B7$F($!3'fQWy.a-m)F*7$F($!3!RjX09`dt'F*Feo7$$!3Immmmmmmm F*$!3Kdi*=p-Nx&F*Fho7$F($!3G\")oCVAD6[F*F]p7$F($!3kG\"[fM^n)GF*F`p7$Fi o$!3M_()H(*3]C>F*Fcp7$$!3qLLLLLLL$)F*FapFfp7$Fgp$!3shP\\'[/Di*FZFip7$$ F^oF:F9F\\q7$FgpFXF^q7$FgpFOF_q7$FioFRF`q7$F(FOFaq7$F(FLFbq7$FioF;Fcq7 $F(F6FdqF'Fhn-F$6$7BFen7$FUFjpFhq7$FUFapFiq7$FIFdpFjq7$FEFapF[r7$FEF^p F\\r7$FIF[pF]r7$FEFfoF^r7$FEFcoF_r7$FB$!3O4]>*e.!)p(F*F`r7$F>FcoFcr7$F >FfoFdr7$F9F[pFer7$F3FfoFfr7$F3FcoFgr7$F.FarFhrFboFhn-%+AXESLABELSG6%Q !6\"F\\s-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6#%%NONEG-%(SCALINGG6#%,CONST RAINEDG-%%VIEWG6$FasFas" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 371 "snow:=proc(n,lx,ly,rx,ry) local mlx, mly, mrx, mry, kx, ky; mlx:= (2*lx+rx)/3; \nmly:=(2*ly+ry)/3; \nmrx:=(lx+2*rx)/3; \nmry:=(ly+2*ry)/ 3; \nkx:=(mlx+mrx)/2+3^(1/2)*(mly-mry)/2; \nky:=(mly+mry)/2+3^(1/2)*(m rx-mlx)/2; \nif n=0 then [[lx,ly],[rx,ry]] else [op(snow(n-1,lx,ly,mlx ,mly)),op(snow(n-1,mlx,mly,kx,ky)), \nop(snow(n-1,kx,ky,mrx,mry)),op(s now(n-1,mrx,mry,rx,ry))] fi end;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%%snowGf*6'%\"nG%#lxG%#lyG%#rxG%#ryG6(%$mlxG%$mlyG%$mrxG%$mryG%#kxG%# kyG6\"F3C)>8$,&*&#\"\"#\"\"$\"\"\"9%F8%,&*&F9F<9&F< F<*&F?F<9(F8&,&*&F?F8',&*&F?F8(,(*&#F8),( *&FVF \+ " 0 "" {MPLTEXT 1 0 10 "p:=2*Pi/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"pG,$*(\"\"#\"\"\"\"\"$!\"\"%#PiGF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "p1:=plot(snow(0,cos(p),sin(p),1,0),scaling=constraine d,axes=none):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "p2:=plot(s now(0,cos(2*p),sin(2*p),cos(p),sin(p)),scaling=constrained,axes=none): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "p3:=plot(snow(0,cos(3*p ),sin(3*p),cos(2*p),sin(2*p)),scaling=constrained,axes=none):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "u:=display(p1,p2,p3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "u;" }}{PARA 13 "" 1 "" {GLPLOT2D 300 293 293 {PLOTDATA 2 "6)-%'CURVESG6$7$7$$!3++++++++]!#=$ \"3'fQWy.a-m)F*7$$\"\"\"\"\"!$F0F0-%'COLOURG6&%$RGBG$\"#5!\"\"F1F1-F$6 $7$7$F($!3'fQWy.a-m)F*F'F2-F$6$7$F-F " 0 "" {MPLTEXT 1 0 8 "re start;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1441 "Z:=proc(n) 2^(n +1) end; \nU:=proc(x,y,n) if n=0 then [[x,y+1]] else [op(U(x,y,n-1)),o p(R(x,y+Z(n)-3,0)),op(U(x+1,y+Z(n)-3,0)), \nop(R(x+1,y+Z(n)-2,n-1)),op (U(x+Z(n)-2,y+Z(n)-2,0)), \nop(L(x+Z(n)-2,y+Z(n)-1,n-1)),op(U(x+1,y+Z( n)-1,0)), \nop(L(x+1,y+Z(n),0)),op(U(x,y+Z(n),n-1))]; \nfi; \nend; \nD n:=proc(x,y,n) if n=0 then [[x,y-1]] else [op(Dn(x,y,n-1)),op(L(x,y-Z( n)+3,0)), \nop(Dn(x-1,y-Z(n)+3,0)),op(L(x-1,y-Z(n)+2,n-1)), \nop(Dn(x- Z(n)+2,y-Z(n)+2,0)),op(R(x-Z(n)+2,y-Z(n)+1,n-1)), \nop(Dn(x-1,y-Z(n)+1 ,0)),op(R(x-1,y-Z(n),0)),op(Dn(x,y-Z(n),n-1))]; \nfi; \nend; \nR:=proc (x,y,n) if n=0 then [[x+1,y]] else [op(R(x,y,n-1)),op(Dn(x+Z(n)-3,y,0) ), \nop(R(x+Z(n)-3,y-1,0)),op(Dn(x+Z(n)-2,y-1,n-1)),op(R(x+Z(n)-2,y-Z( n)+2,0)), \nop(U(x+Z(n)-1,y-Z(n)+2,n-1)),op(R(x+Z(n)-1,y-1,0)),op(U(x+ Z(n),y-1,0)), \nop(R(x+Z(n),y,n-1))]; \nfi; \nend; \nL:=proc(x,y,n) if n=0 then [[x-1,y]] else [op(L(x,y,n-1)),op(U(x-Z(n)+3,y,0)), \nop(L(x -Z(n)+3,y+1,0)),op(U(x-Z(n)+2,y+1,n-1)),op(L(x-Z(n)+2,y+Z(n)-2,0)), \n op(Dn(x-Z(n)+1,y+Z(n)-2,n-1)),op(L(x-Z(n)+1,y+1,0)),op(Dn(x-Z(n),y+1,0 )), \nop(L(x-Z(n),y,n-1))]; \nfi; \nend; \nP:=proc(n) 2^(n+2) end; \nW :=proc(x,y,n) [[x,y],op(U(x,y,n)),op(R(x,y+P(n)-3,0)),op(U(x+1,y+P(n)- 3,0)), \nop(R(x+1,y+P(n)-2,n)),op(Dn(x+P(n)-2,y+P(n)-2,0)), \nop(R(x+P (n)-2,y+P(n)-3,0)),op(Dn(x+P(n)-1,y+P(n)-3,n)), \nop(L(x+P(n)-1,y,0)), op(Dn(x+P(n)-2,y,0)),op(L(x+P(n)-2,y-1,n)), \nop(U(x+1,y-1,0)),op(L(x+ 1,y,0))] \nend; \nu:=plot(W(0,0,4),color=cyan,axes=none):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"ZGf*6#%\"nG6\"F(F()\"\"#,&9$\"\"\"F-F-F( F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"UGf*6%%\"xG%\"yG%\"nG6\"F* F*@%/9&\"\"!7#7$9$,&9%\"\"\"F4F47+-%#opG6#-F$6%F1F3,&F-F4F4!\"\"-F76#- %\"RG6%F1,(F3F4-%\"ZG6#F-F4\"\"$F%#DnGf*6%%\"xG%\"yG%\"nG6\"F* F*@%/9&\"\"!7#7$9$,&9%\"\"\"F4!\"\"7+-%#opG6#-F$6%F1F3,&F-F4F4F5-F86#- %\"LG6%F1,(F3F4-%\"ZG6#F-F5\"\"$F4F.-F86#-F$6%,&F1F4F4F5FBF.-F86#-F@6% FK,(F3F4FCF5\"\"#F4F<-F86#-F$6%,(F1F4FCF5FQF4FPF.-F86#-%\"RG6%FV,(F3F4 FCF5F4F4F<-F86#-F$6%FKFfnF.-F86#-FZ6%FK,&F3F4FCF5F.-F86#-F$6%F1F_oF%\"RGf*6%%\"xG%\"yG%\"nG6\"F* F*@%/9&\"\"!7#7$,&9$\"\"\"F3F39%7+-%#opG6#-F$6%F2F4,&F-F3F3!\"\"-F76#- %#DnG6%,(F2F3-%\"ZG6#F-F3\"\"$F%\"LGf*6%%\"xG%\"yG%\"nG6\"F* F*@%/9&\"\"!7#7$,&9$\"\"\"F3!\"\"9%7+-%#opG6#-F$6%F2F5,&F-F3F3F4-F86#- %\"UG6%,(F2F3-%\"ZG6#F-F4\"\"$F3F5F.-F86#-F$6%FB,&F5F3F3F3F.-F86#-F@6% ,(F2F3FCF4\"\"#F3FKF<-F86#-F$6%FP,(F5F3FCF3FQF4F.-F86#-%#DnG6%,(F2F3FC F4F3F3FVF<-F86#-F$6%FfnFKF.-F86#-FZ6%,&F2F3FCF4FKF.-F86#-F$6%F_oF5F%\"PGf*6#%\"nG6\"F(F()\"\"#,& 9$\"\"\"F*F-F(F(F(" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"WGf*6%%\"xG% \"yG%\"nG6\"F*F*7/7$9$9%-%#opG6#-%\"UG6%F-F.9&-F06#-%\"RG6%F-,(F.\"\" \"-%\"PG6#F5F<\"\"$!\"\"\"\"!-F06#-F36%,&F-F " 0 "" {MPLTEXT 1 0 2 "u;" }}{PARA 13 "" 1 "" {GLPLOT2D 290 266 266 {PLOTDATA 2 "6'-%'CURVESG6#7ieu7$$\"\"!F)F(7$F($\"\"\"F)7$F+F+7$F+ $\"\"#F)7$F/F/7$F/$\"\"$F)7$F+F37$F+$\"\"%F)7$F(F77$F($\"\"&F)7$F+F;7$ F+$\"\"'F)7$F/F?7$F/F;7$F3F;7$F3F77$F7F77$F7F;7$F;F;7$F;F?7$F?F?7$F?$ \"\"(F)7$F;FK7$F;$\"\")F)7$F7FO7$F7$\"\"*F)7$F3FS7$F3FO7$F/FO7$F/FK7$F +FK7$F+FO7$F(FO7$F(FS7$F+FS7$F+$\"#5F)7$F/Fin7$F/$\"#6F)7$F+F]o7$F+$\" #7F)7$F(Fao7$F($\"#8F)7$F+Feo7$F+$\"#9F)7$F/Fio7$F/Feo7$F3Feo7$F3Fao7$ 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