{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 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 2 0 2 0 2 2 0 1 }{PSTYLE "Hea ding 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 2 0 2 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE " " -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 2 0 2 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 1 0 0 0 0 2 0 2 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 2 0 2 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 2 0 2 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "P\351ano et variantes : W underlich ...etc. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Alain Escul ier - programme \351crit en juillet 2011" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 " utilitaires" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1436 "with(plots):\n#== rotation de centre l'origine\nrotO:= (t,pt) -> [pt[1]*cos(t)-pt[2]*sin(t), pt[1]*sin(t)+pt[2]*cos(t)]:\n#*********** ***transformations de base appliqu\351es \340 une liste*************** ***************\nLrotO:=(t,Liste) -> if type(evalf(Liste[1,1]),numeric ) then map( u ->rotO(t,u),Liste): else map( u->LrotO(t,u),Liste): fi: \nLtrans:=(V,Liste) -> if type(evalf(Liste[1,1]),numeric) then map( u \+ ->expand(u+V),Liste): else map( u->Ltrans(V,u),Liste) fi:\nLhomo:=(k,L iste) -> if type(evalf(Liste[1,1]),numeric) then map( u ->expand(u*k), Liste): else map( u->Lhomo(k,u),Liste) fi:\nLsymY:= Liste -> if type( evalf(Liste[1,1]),numeric) then map( u ->[-u[1],u[2]],Liste): else map ( u->LsymY(u),Liste): fi:\nLplot:= (Liste,coul) -> if type(evalf(List e[1,1]),numeric) then plot(Liste,color=coul): else map( u->Lplot(u,cou l),Liste): fi:\n\nfond:=polygonplot([[-3,-3],[3,-3],[3,3],[-3,3]],colo r=COLOR(RGB,0.98,1,0.9)):\n\nL2pts:=Liste -> if not(type(evalf(Liste[ 1,1]),numeric)) then L2pts(map( op,Liste)): else Liste: fi:\n\nquadril lage:=proc(n,thick) \n local i,pas:\n pas:=2/3^(n-1);\n pl ot([seq([[-3+i*pas,-3],[-3+i*pas,+3]],i=0..3^n),\n seq([[-3, -3+i*pas],[3,-3+i*pas]],i=-0..3^n)],linestyle=3,thickness=thick,color= black):\nend:\nLsymX:= Liste -> if type(evalf(Liste[1,1]),numeric) th en map( u ->[u[1],-u[2]],Liste): else map( u->LsymX(u),Liste): fi:\nre nverse:=proc(L) local n,i: n:=nops(L): [seq(L[n-i+1],i=1..n)]: end:\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "renversetout:=proc(L) local tp ,tp1,i;\n tp:=renverse(L); tp1:=NULL:\n for i to nops(tp) do\n if type(evalf(tp[i,1]),numeric) then tp1:=tp1,tp[i]: else tp1:=t p1,renversetout(tp[i]): fi;\n od;\n [tp1]; \n end:" }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 46 " Principe de construction des courbes de \+ P\351ano" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 349 " \n\nOn partage un ca rr\351 en 9 carr\351s \351l\351mentaires et on joint le coin A au coi n B en suivant les diagonales des carr\351s contigus pris dans l'ordre de num\351rotation. Ce chemin et son sym\351trique par rapport \340 l a diagonale AB sont les seuls permettant de parcourir tous les carr \351s contin\373ment. \n\nLa courbe de P\351ano est obtenu en reportan t le motif de base" }{GLPLOT2D 94 87 87 {PLOTDATA 2 "6--%'CURVESG6$747 $$!\"#\"\"!F(F'7$F($F*F*F+7$F($\"\"#F*F-7$F,F.F07$F,F,F17$F,F(F27$F.F( F37$F.F,F47$F.F.F5-%'COLOURG6&%$RGBG$\"#5!\"\"F,F,-F$6&7$7$$!\"$F*FA7$ FA$\"\"$F*-F76&F9F*F*F*-%*LINESTYLEG6#FE-%*THICKNESSG6#\"\"\"-F$6&7$7$ FDFA7$FDFDFFFHFK-F$6&7$F@FRFFFHFK-F$6&7$FCFSFFFHFK-%)POLYGONSG6$7&F@FR FSFC-%&COLORG6&F9$\"#)*F)FN$\"\"*F<-%(SCALINGG6#%,CONSTRAINEDG-%+AXESL ABELSG6%Q!6\"Ffo-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6#%%NONEG-FL6#F/-%%VI EWG6$F[pF[p" 1 2 0 1 10 2 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 " Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" }}{TEXT -1 46 " ou son sym\351trique par rapport \340 la verticale" }{GLPLOT2D 104 97 97 {PLOTDATA 2 "6--%'CURVESG6$747$$!\"#\"\"!$\"\"#F*F'7$F($F*F* F-7$F(F(F/7$F.F(F07$F.F.F17$F.F+F27$F+F+F37$F+F.F47$F+F(F5-%'COLOURG6& %$RGBG$\"#5!\"\"F.F.-F$6&7$7$$!\"$F*FA7$FA$\"\"$F*-F76&F9F*F*F*-%*LINE STYLEG6#FE-%*THICKNESSG6#\"\"\"-F$6&7$7$FDFA7$FDFDFFFHFK-F$6&7$F@FRFFF HFK-F$6&7$FCFSFFFHFK-%)POLYGONSG6$7&F@FRFSFC-%&COLORG6&F9$\"#)*F)FN$\" \"*F<-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6%Q!6\"Ffo-%%FONTG6#%(DE FAULTG-%*AXESSTYLEG6#%%NONEG-FL6#F,-%%VIEWG6$F[pF[p" 1 2 0 1 10 2 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" " Curve 4" "Curve 5" "Curve 6" }}{TEXT -1 339 " , ramen\351s \340 la tai lle d'un petit carr\351, dans les 9 carr\351s de fa\347on que les diag onales trac\351es correspondent \340 la droite point d'entr\351e-point de sortie du motif ad\351quat. \nLe motif de base est donc report\351 dans les carr\351s 1,3,5,7,9 et son sym\351trique dans les carr\351s \+ 2,4,6,8. \n\nOn joint les motifs dans l'ordre 1,2,..., 9 ; on obtient \+ ainsi " }{GLPLOT2D 122 113 113 {PLOTDATA 2 "61-%'CURVESG6$7^u7$$!3_mmm mmmmE!#7$F,F?FA7$F,F=FB7$F,F9FC7$F(F9FD7$F(F=FE7$F(F?FF7$F($\"3ELLLL LLL8F*FG7$F($\"\"#F.FJ7$F($\"3_mmmmmmmEF*FM7$F,FNFP7$F,FKFQ7$F,FHFR7$F 0FHFS7$F0FKFT7$F0FNFU7$F9FNFV7$F9FKFW7$F9FHFX7$F=FHFY7$F=FKFZ7$F=FNFen 7$F?FNFfn7$F?FKFgn7$F?FHFhn7$F?F?Fin7$F?F=Fjn7$F?F9F[o7$F=F9F\\o7$F=F= F]o7$F=F?F^o7$F9F?F_o7$F9F=F`o7$F9F9Fao7$F9F0Fbo7$F9F,Fco7$F9F(Fdo7$F= F(Feo7$F=F,Ffo7$F=F0Fgo7$F?F0Fho7$F?F,Fio7$F?F(Fjo7$FHF(F[p7$FHF,F\\p7 $FHF0F]p7$FKF0F^p7$FKF,F_p7$FKF(F`p7$FNF(Fap7$FNF,Fbp7$FNF0Fcp7$FNF9Fd p7$FNF=Fep7$FNF?Ffp7$FKF?Fgp7$FKF=Fhp7$FKF9Fip7$FHF9Fjp7$FHF=F[q7$FHF? F\\q7$FHFHF]q7$FHFKF^q7$FHFNF_q7$FKFNF`q7$FKFKFaq7$FKFHFbq7$FNFHFcq7$F NFKFdq7$FNFNFeq-%'COLOURG6&%$RGBG$\"#5!\"\"F=F=-F$6&7$7$$!\"$F.Far7$Fa r$\"\"$F.-Fgq6&FiqF.F.F.-%*LINESTYLEG6#Fer-%*THICKNESSG6#\"\"\"-F$6&7$ 7$$F\\rF.Far7$FcsFdrFfrFhrF[s-F$6&7$7$$F^sF.Far7$FisFdrFfrFhrF[s-F$6&7 $7$FdrFar7$FdrFdrFfrFhrF[s-F$6&7$F`rF^tFfrFhrF[s-F$6&7$7$FarFcs7$FdrFc sFfrFhrF[s-F$6&7$7$FarFis7$FdrFisFfrFhrF[s-F$6&7$FcrF_tFfrFhrF[s-%)POL YGONSG6$7&F`rF^tF_tFcr-%&COLORG6&Fiq$\"#)*F-F^s$\"\"*F\\r-%(SCALINGG6# %,CONSTRAINEDG-%+AXESLABELSG6%Q!6\"Fbv-%%FONTG6#%(DEFAULTG-%*AXESSTYLE G6#%%NONEG-F\\s6#FL-%%VIEWG6$FgvFgv" 1 2 0 1 10 2 2 9 1 1 1 1.000000 144.000000 137.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Cur ve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" }}{TEXT -1 250 " , nouveau motif avec lequel on recommence le processus pr\351c \351dent ... et ...etc. \nOn obtient ainsi des courbes qui \"remplisse nt\" de plus en plus le carr\351 initial. \nOn peut g\351n\351raliser \+ avec les transform\351es par rotation de Pi/2 des motifs pr\351c\351d ents " }{GLPLOT2D 103 83 83 {PLOTDATA 2 "6--%'CURVESG6$747$$\"\"#\"\"! F(F'7$$F*F*F(F+7$$!\"#F*F(F-7$F.F,F07$F,F,F17$F(F,F27$F(F.F37$F,F.F47$ F.F.F5-%'COLOURG6&%$RGBG$\"#5!\"\"F,F,-F$6&7$7$$!\"$F*FA7$FA$\"\"$F*-F 76&F9F*F*F*-%*LINESTYLEG6#FE-%*THICKNESSG6#\"\"\"-F$6&7$7$FDFA7$FDFDFF FHFK-F$6&7$F@FRFFFHFK-F$6&7$FCFSFFFHFK-%)POLYGONSG6$7&F@FRFSFC-%&COLOR G6&F9$\"#)*F/FN$\"\"*F<-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6%Q!6 \"Ffo-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6#%%NONEG-FL6#F)-%%VIEWG6$F[pF[p " 1 2 0 1 10 2 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "C urve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" }}{TEXT -1 2 ", " } {GLPLOT2D 91 77 77 {PLOTDATA 2 "6--%'CURVESG6$747$$\"\"#\"\"!$!\"#F*F' 7$$F*F*F+F-7$F+F+F/7$F+F.F07$F.F.F17$F(F.F27$F(F(F37$F.F(F47$F+F(F5-%' COLOURG6&%$RGBG$\"#5!\"\"F.F.-F$6&7$7$$!\"$F*FA7$FA$\"\"$F*-F76&F9F*F* F*-%*LINESTYLEG6#FE-%*THICKNESSG6#\"\"\"-F$6&7$7$FDFA7$FDFDFFFHFK-F$6& 7$F@FRFFFHFK-F$6&7$FCFSFFFHFK-%)POLYGONSG6$7&F@FRFSFC-%&COLORG6&F9$\"# )*F,FN$\"\"*F<-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLABELSG6%Q!6\"Ffo-%%FO NTG6#%(DEFAULTG-%*AXESSTYLEG6#%%NONEG-FL6#F)-%%VIEWG6$F[pF[p" 1 2 0 1 10 2 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C urve 3" "Curve 4" "Curve 5" "Curve 6" }}{TEXT -1 172 "\ndonc 2 possibi lit\351s pour chacun des 9 carr\351s soit 2^9 = 512 courbes diff\351re ntes ( 2 \340 2 sym\351triques par rapport \340 la diagonale et 2 \340 2 sym\351triques par rapport au centre )" }}}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 122 "motif ver tical ayant ses extr\351mit\351s sur la diagonale du carr\351 : dive rses courbes ( p\351ano, wunderlich, colonnes ... etc.)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 799 "#=========================au sens \+ pr\350s ==========================================\n#==== type Dm diag onale montante :ID=motif SXR=symOX(rot(Pi/2,ID)) ( IDr,SXRr sens inver se) \n#==== type Dd diagonale descendante :IDR=rot(Pi/2,motif) SX=symO X(ID) ( IDRr,SXr sens inverse)\n#==== forme des suites : [Dm,Dd,Dm, Dd ,Dm,Dd, Dm,Dd,Dm] ==> 2^9 courbes possibles\nsuitesV:=proc() local fo rme,i,j,k,l,m,n,o,p,q,tp,rg: global ID, IDr, SXr, SXR, IDR, SXRr:\n \+ rg:=1..2:\n forme:=[ [ID,SXR],[SXr,IDR],[ID,SXR], [SX,IDRr],[IDr,S XRr],[SX,IDRr], [ID,SXR],[SXr,IDR],[ID,SXR]]:\n [seq(seq(seq( seq(s eq(seq( seq(seq(seq([forme[1,i],forme[2,j],forme[3,k], forme[4,l],form e[5,m],forme[6,n],\n forme[7,o],forme[8,p],forme[9,q]],i=rg), j=rg),k=rg),l=rg),m=rg),n=rg),o=rg),p=rg),q=rg)]:\nend: \nLsuitesV:=su itesV():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 346 "########## suites part iculi\350res ############################\n#----- wunderlich LsuitesV [171] soit [ID,IDR,ID,IDRr,IDr,IDRr,ID,IDR,ID]: \n#----- peano Lsuites V[1] soit [ID,SXr,ID,SX,IDr,SX,ID,SXr,ID]:\n#----- Colonnes sym\351tri ques LsuitesV[512] soit [SXR,IDR,SXR,IDRr,SXRr,IDRr,SXR,IDR,SXR]:\n## ######################################################" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 63 "#member([ID,IDR,ID, IDRr,IDr,IDRr, ID,IDR,ID] ,LsuitesV,'k');k;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1004 "#=== ===== K param\350tre entre 0 et 1 ============\nPeanoV:=proc(n,K,suite )\n local i,id,idr,sx,sxr,idR,idRr,sxR,sxRr,base,liste,liste1:\n \+ base:=[[-2,-2],[-2,0],[-2,2],[0,2],[0,0],[0,-2],[2,-2],[2,0],[2,2 ]]:\n liste := K*3*[-[1,1],[1,1]] :\n for i from 1 to n do \+ #id:=Lhomo(1/3,PeanoV(n-1,K,suite)):\n id:=Lhomo(1/3,liste ): idr:=renversetout(id): \n idR:=LrotO(Pi/2,id); id Rr:=renversetout(idR);\n sx:=LsymX(id); sxr:= renversetout(sx); \n sxR:=LrotO(Pi/2,sx); sxRr:=renv ersetout(sxR);\n liste1:=subs(ID=id,IDR=idR,IDRr=idRr,IDr=id r,SX=sx,SXr=sxr,SXR=sxR,SXRr=sxRr,suite): \n liste:=[seq(Lt rans(base[i],liste1[i]),i=1..9)];\n if i>1 then liste:=map(o p,liste); fi; #### pour garder le motif \351l\351mentaire \n od: \n liste:\nend:\npeanocontinuV:=proc(n,K,suite,coul) plot(L2pts (PeanoV(n,K,suite)),color=coul) end: \npeanomotifV:=proc(n,K,suite,co ul) display(Lplot(PeanoV(n,K,suite),coul)) end:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 17 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 446 "N,K:=2,0.1: #===== nombre d'it\351rations ======== =\nchoix:=LsuitesV[171]; # [ID,IDR,ID, IDRr,IDr,IDRr, ID,IDR,ID]:# \n#display([peanocontinuV(N,K,choix,red),quadrillage(N-1,1),display(fo nd,style=patch,thickness=2)],\n# thickness=2,scaling=constrain ed,axes=none);\ndisplay([peanomotifV(N,K,choix,blue),peanocontinuV(N,K ,choix,red),quadrillage(N,1),display(fond,style=patch,thickness=2)],\n thickness=2,scaling=constrained,axes=none);" }{TEXT -1 0 "" } }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 96 " Motif 1 en horizontal : colonnes sym\351triques, di verses courbes ( p\351ano, wunderlich ... etc.) " }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 799 "#=========================au sens pr\350s === =======================================\n#==== type Dm diagonale monta nte :ID=motif SXR=symOX(rot(Pi/2,ID)) ( IDr,SXRr sens inverse) \n#==== type Dd diagonale descendante :IDR=rot(Pi/2,motif) SX=symOX(ID) ( IDR r,SXr sens inverse)\n#==== forme des suites : [Dm,Dd,Dm, Dd,Dm,Dd, Dm, Dd,Dm] ==> 2^9 courbes possibles\nsuitesH:=proc() local forme,i,j,k,l ,m,n,o,p,q,tp,rg: global ID, IDr, SXr, SXR, IDR, SXRr:\n rg:=1..2: \n forme:=[ [ID,SXR],[SX,IDRr],[ID,SXR], [SXr,IDR],[IDr,SXRr],[SXr, IDR], [ID,SXR],[SX,IDRr],[ID,SXR]]:\n [seq(seq(seq( seq(seq(seq( se q(seq(seq([forme[1,i],forme[2,j],forme[3,k], forme[4,l],forme[5,m],for me[6,n],\n forme[7,o],forme[8,p],forme[9,q]],i=rg),j=rg),k=rg ),l=rg),m=rg),n=rg),o=rg),p=rg),q=rg)]:\nend: \nLsuitesH:=suitesH():" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "########## suites particuli\350r es ############################\n#----- wunderlich horizontal Lsuites H[171] soit [ID, IDRr, ID, IDR, IDr, IDR, ID, IDRr, ID]: \n#----- pean o horizontal LsuitesH[1] soit [ID, SX, ID, SXr, IDr, SXr, ID, SX, ID] :\n#----- Lignes sym\351triques LsuitesH[512] soit [SXR, IDRr, SXR, I DR, SXRr, IDR, SXR, IDRr, SXR]:\n##################################### ###################" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "#member([ID, IDR,ID, IDRr,IDr,IDRr, ID,IDR,ID],LsuitesV,'k');k;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 972 "#======== K param\350tre entre 0 et 1 == ==========\nPeanoH:=proc(n,K,suite)\n local i,id,idr,sx,sxr,idR,i dRr,sxR,sxRr,base,liste,liste1:\n base:=[[-2,-2],[0,-2],[2,-2], \+ [2,0],[0,0],[-2,0], [-2,2],[0,2],[2,2]];:\n liste := K*3*[-[1,1] ,[1,1]] :\n for i from 1 to n do \n id:=Lhomo(1/3,lis te): idr:=renversetout(id): \n idR:=LrotO(Pi/2,id); \+ idRr:=renversetout(idR);\n sx:=LsymX(id); sxr :=renversetout(sx); \n sxR:=LrotO(Pi/2,sx); sxRr:=re nversetout(sxR);\n liste1:=subs(ID=id,IDR=idR,IDRr=idRr,IDr= idr,SX=sx,SXr=sxr,SXR=sxR,SXRr=sxRr,suite): \n liste:=[seq( Ltrans(base[i],liste1[i]),i=1..9)];\n if i>1 then liste:=map (op,liste); fi; #### pour garder le motif \351l\351mentaire \n od :\n liste:\nend:\npeanocontinuH:=proc(n,K,suite,coul) plot(L2pt s(PeanoH(n,K,suite)),color=coul) end: \npeanomotifH:=proc(n,K,suite,c oul) display(Lplot(PeanoH(n,K,suite),coul)) end:" }}}{PARA 0 "> " 0 " " {MPLTEXT 1 0 17 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 446 "N,K:=2,0.1: #===== nombre d'it\351rations ======== =\nchoix:=LsuitesH[171]; # [ID,IDR,ID, IDRr,IDr,IDRr, ID,IDR,ID]:# \n#display([peanocontinuH(N,K,choix,red),quadrillage(N-1,1),display(fo nd,style=patch,thickness=2)],\n# thickness=2,scaling=constrain ed,axes=none);\ndisplay([peanomotifH(N,K,choix,blue),peanocontinuH(N,K ,choix,red),quadrillage(N,1),display(fond,style=patch,thickness=2)],\n thickness=2,scaling=constrained,axes=none);" }{TEXT -1 0 "" } }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 " Labyrinthe" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 668 "demilabPeano:=proc(n)\n local bN,bSr,base1,suite,bSXr,bSYr: \n base1:=[[-2,-2],[-2,0],[-2,2],[0,2],[0,0],[0,-2],[2,-2],[2,0], [2,2]];\n if n=0 then print(\"Applicable pour n sup\351rieur ou \+ \351gal \340 1 seulement\"): \n elif n=1 then \n [[-3,-1 ],[-3,3],[1,3],[1,-1],[1,3]]: \n else\n bN:=Lhomo(1 /3,demilabPeano(n-1)): bSXr:=renverse(LsymX(bN));bSYr:=renverse(LsymY (bN));\n suite:=[bN,bSXr,bN, bSYr,-bN,bSYr, bN,bSXr,bN]:\n \+ [seq(Ltrans(base1[i],suite[i]),i=1..9)];\n map(op,%); \n \+ fi;\nend:\nlabPeano:=proc(n,coul) local L:\n L:=[[-3,-3],op(dem ilabPeano(n))];plot(\{L, map(u -> -u,L)\},thickness=2,color=coul);\nen d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 488 "#=== relancer peano \+ vertical\nN,K:=2,0.2;\ndisplay( [labPeano(N,blue),display(peanocontinu V(N,K,LsuitesV[1],red),thickness=2,linestyle=3),\n display(fo nd,style=patchnogrid)], scaling=constrained,axes=none);\n#=== laby rinthe anim\351 ==========\nL:=map(op,PeanoV(N,K,LsuitesV[1])): nL:=no ps(L)/3:\ndisplay( [display([seq(plot(L[1..3*i],thickness=2,linestyle= 3),i=1..nL)],insequence=true),labPeano(N,blue),\n display(fon d,style=patchnogrid)], scaling=constrained,axes=none);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%\"NG%\"KG6$\"\"#$F(!\"\"" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 51 " motif 2 ayant ses extr\351mit\351s sur un cot\351 du carr\351" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "Pour le motif cidessous le trajet \+ possible de bords des motifs est le trajet ci-contre " }{GLPLOT2D 152 138 138 {PLOTDATA 2 "6A-%'CURVESG6%7+7$$!3_mmmmmmmE!# " 0 "" {MPLTEXT 1 0 794 "#=========================au sens pr\350 s ==========================================\n#==== type cb cot\351 ba s :ID=motif, -SX \n#==== type cot\351 gauche :SXR=rot(Pi/2,SX), -IDR\n #==== type cot\351 droit : -SXR , IDR\n#==== type ch cot\351 haut :-ID , SX \n#==== forme des suites : [cg,cg,cb, cb,cb,ch, cd,cd,cb] ==> 2^9 courbes possibles\nsuitestruc:=proc() local forme,i,j,k,l,m,n,o,p,q, tp,rg: global ID, IDr,SX, SXr, SXR, IDR,IDRr, SXRr:\n rg:=1..2:\n \+ forme:=[ [-IDRr,SXR],[-IDRr,SXR],[ID,-SXr], [ID,-SXr],[ID,-SXr],[-ID ,SXr], [IDRr,-SXR],[IDRr,-SXR],[ID,-SXr]]:\n [seq(seq(seq( seq(seq( seq( seq(seq(seq([forme[1,i],forme[2,j],forme[3,k], forme[4,l],forme[5 ,m],forme[6,n],\n forme[7,o],forme[8,p],forme[9,q]],i=rg),j=r g),k=rg),l=rg),m=rg),n=rg),o=rg),p=rg),q=rg)]:\nend: \nLsuitestruc:=su itestruc():" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1005 "truc:=proc (n,suite)\n local i,id,idr,sx,sxr,idR,idRr,sxR,sxRr,base,liste,li ste1,K:\n base:=[[-2,-2],[-2,0],[-2,2], [0,2],[2,2],[2,0], [0 ,0],[0,-2], [2,-2]]:\n # K:=1.5: liste :=K*[[-1,-1],[1,-1]]: \+ # pour obtenir des formes avec protub\351rances plus aplaties \n \+ liste := base : #\n for i from 1 to n do \n id:=Lh omo(1/3,liste): idr:=renversetout(id): \n idR:=LrotO(Pi/2,id ); idRr:=renversetout(idR);\n sx:=LsymX(id); \+ sxr:=renversetout(sx); \n sxR:=LrotO(Pi/2,sx); \+ sxRr:=renversetout(sxR);\n liste1:=subs(ID=id,IDR=idR,IDR r=idRr,IDr=idr,SX=sx,SXr=sxr,SXR=sxR,SXRr=sxRr,suite): \n l iste:=[seq(Ltrans(base[i],liste1[i]),i=1..9)];\n if i>1 then liste:=map(op,liste); fi; #### pour garder le motif \351l\351mentaire \n od:\n liste:\nend:\ntruccontinu:=proc(n,suite,coul) plot (L2pts(truc(n,suite)),color=coul) end: \ntrucmotif:=proc(n,suite,coul ) display(Lplot(truc(n,suite),coul)) end:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 525 "N:=1: #===== nombre d'it\351rations =========\nc hoix:=Lsuitestruc[100]; # \n#display([truccontinuV(N,choix,red),qua drillage(N-1,1),display(fond,style=patch,thickness=2)],\n# thi ckness=2,scaling=constrained,axes=none);\n#plotsetup(gif,plotoutput=\" j:/grec_aplati_L[100].gif\",plotoptions=\"width=400,height=400\"):\n\n display([display(trucmotif(N,choix,blue),thickness=2),truccontinu(N,ch oix,blue),quadrillage(N,1),display(fond,style=patch,thickness=2)],\n \+ thickness=2,scaling=constrained,axes=none);\nplotsetup(inline); " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 25 " construction du princ ipe" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 745 "eps:=0.1:\n\n#plotse tup(gif,plotoutput=\"j:/motif_grec.gif\",plotoptions=\"width=500,heigh t=500\"):\n\ndisplay([display(trucmotif(1,choix,blue),thickness=1),\n \+ plot(\{[[-3+eps,-3+eps],[-3+eps,-1-eps]],[[-3+eps,-1+e ps], [-3+eps,1-eps]],\n [[-3+eps,1+eps],[- 1-eps,1+eps]], [[-1+eps,1+eps],[1-eps,1+eps]],\n \+ [[1+eps,1+eps],[3-eps,1+eps]], [[3-eps,1-eps],[1+eps,1-eps]], \n [[1-eps,1-eps],[1-eps,-1+eps]],[[1-eps, -1-eps],[1-eps,-3+eps]],\n [[3-eps,-3+eps] ,[1+eps,-3+eps]] \n\} \n,color=red,thickne ss=3,linestyle=3),quadrillage(1,1),display(fond,thickness=2)],scaling= constrained,axes=none);\nplotsetup(inline);" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "10" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }