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?Uw\\_VxIyA:^VLxfYFjysy^Rjysy:^JLB:E?vY:JeCk^RTGyay=::::::i?xyy;::::::::::::::::::::::i_HKa:yay=::::::::::: ::::::::::::<:J\\syfNLBC>:fNxyywY::::::::: :::LHCnNJabUZy=::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::<:J\\;E_>L<;:E_ymy;:::::::::::BsZ>W=vY::::::::::::::::::::::::::::: ::t@W\\HKAsyvY:::XGW\\H;jUsyvY:::::::::::::::::::::::::::::::::::::::: ::::::::::::::tBW\\HKqryvY:::::::::::::::::JA;W\\h;xI::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::bC :vY:::::::::::J\\CkdB:jysy^VLFC@:nTjy;::::::::::::C`>=Je;yA::::::::::Z ::xI::::::::::::::bMnCJA;W\\Hlysy:::::::::::::::::::::::vPt>W:RlvYxI:::::::::::::::::::::::i?nCjysy:ZqryvY::::::::::::::::: ::tBbMnGxIyA:vPJa:yay=::::::::::::::::::::::::::t@W\\H;:::::JqryvY:::: :::::::::::::::::::::::::::::::::::::::::::::::::::tBbMnGjy;:::::::::: :::::::W>nCt@ry::vPJa:yay=:::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::<:ry::::::::::::::ZZ@NbM:Zymy;:::::::::::::::::::::::i? nCjysy:ZqryvY:::::::::::::::::::XGi_ql^;yA:vPt>W:::::b]vYxI::::::::::::::::::::::::::::::::::::::::: ::::::::::::::roZql^;yA:::::::::::::::::vTjUSlZy=:jUcMnCjysy:::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::Z::xI:::::::::::::::W \\H;JqryvY:::::::::::::::::::::::jU;W:1:" }{TEXT -1 0 "" }}{PARA 18 "" 0 "" {TEXT 275 33 "Automate cellulaire feu de for\352t\n" }{TEXT 277 0 "" }{TEXT 276 40 "\251 App rendre Maple. Alain Le Stang. 2006\n" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Chaque cellule d'une grille carr\351e " }{TEXT 256 1 "n" } {TEXT -1 3 " x " }{TEXT 257 1 "n" }{TEXT -1 46 " peut se trouver dans \+ l'un des quatre \351tats: \n" }{TEXT 258 4 "vide" }{TEXT -1 21 " (blan c: code 0) ; " }{TEXT 259 5 "arbre" }{TEXT -1 19 " (vert: code 1) ; \+ " }{TEXT 260 6 "cendre" }{TEXT -1 18 " (gris: code 2); " }{TEXT 261 3 "feu" }{TEXT -1 293 " (rouge: code 3);\nDans la configuration d'orig ine, chaque cellule de la grille est selon une probabilit\351 p, un ar bre, et selon une probabilit\351 1-p, est vide. \nOn met le feu \340 u ne cellule et on suit la diffusion du feu \340 travers la grille selon la fonction de transition suivante: \nune cellule " }{TEXT 266 5 "arb re" }{TEXT -1 315 " prend feu \340 la g\351n\351ration t si l'une au m oins de ses 4 voisines (nord, est, sud, ouest) est en feu \340 la g \351n\351ration t-1. \nLes cellules en feu passeront en cendres \340 l a g\351n\351ration suivante.\nLes cellules en cendres deviendront vide s \340 la g\351n\351ration suivante. \n(source: CIRAD)\n\nImpl\351ment ation de l'algorithme en Maple:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "with(plots):with(geometry):with(plottools):\n" }}{PARA 7 "" 1 "" {TEXT -1 43 "Warning, the name arrow has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 93 "Warning, these names have been redefined: circl e, ellipse, homothety, hyperbola, line, point\n" }}{PARA 7 "" 1 "" {TEXT -1 100 "Warning, these names have been redefined: arrow, circle, ellipse, homothety, hyperbola, line, point\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Dessin de la cellule de la position (" }{TEXT 267 13 " ligne,colonne" }{TEXT -1 16 ") dans la grille" }{TEXT 268 2 " n" } {TEXT -1 3 " x " }{TEXT 269 1 "n" }{TEXT -1 24 " , avec une couleur RG B(" }{TEXT 270 0 "" }{TEXT -1 9 "a,b,c) " }{TEXT 271 0 "" }{TEXT -1 20 "a,b,c entre 0 et 1: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "dessin:=proc(ligne::posint,colonne::posint,n::posint,a,b,c)\nloca l x,y;\nx:=colonne-1;y:=n-ligne;\npolygon([[x,y],[colonne,y],[colonne, y+1],[x,y+1]],color=COLOR(RGB,a,b,c));\nend proc; " }}{PARA 12 "" 1 " " {XPPMATH 20 "6#>%'dessinGf*6('%&ligneG%'posintG'%(colonneGF)'%\"nGF) %\"aG%\"bG%\"cG6$%\"xG%\"yG6\"F4C%>8$,&9%\"\"\"F:!\"\">8%,&9&F:9$F;-%( polygonG6$7&7$F7F=7$F9F=7$F9,&F=F:F:F:7$F7FH/%&colorG-%&COLORG6&%$RGBG 9'9(9)F4F4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "display([se q(seq(dessin(i,j,10,i/10,j/10,i*j/100),j=1..10),i=1..10)]);" }}{PARA 13 "" 1 "" {GLPLOT2D 275 262 262 {PLOTDATA 2 "6`q-%)POLYGONSG6$7&7$$\" \"!F)$\"\"*F)7$$\"\"\"F)F*7$F-$\"#5F)7$F(F0-%&COLORG6&%$RGBG#F.F1F7#F. \"$+\"-F$6$7&F,7$$\"\"#F)F*7$F>F0F/-F46&F6F7#F.\"\"&#F.\"#]-F$6$7&F=7$ $\"\"$F)F*7$FKF0F@-F46&F6F7#FLF1#FLF9-F$6$7&FJ7$$\"\"%F)F*7$FVF0FM-F46 &F6F7#F?FD#F.\"#D-F$6$7&FU7$$FDF)F*7$F\\oF0FX-F46&F6F7#F.F?#F.\"#?-F$6 $7&F[o7$$\"\"'F)F*7$FgoF0F]o-F46&F6F7#FLFD#FLFF-F$6$7&Ffo7$$\"\"(F)F*7 $FbpF0Fio-F46&F6F7#FcpF1#FcpF9-F$6$7&Fap7$$\"\")F)F*7$F]qF0Fdp-F46&F6F 7#FWFD#F?Fgn-F$6$7&F\\q7$F*F*7$F*F0F_q-F46&F6F7#F+F1#F+F9-F$6$7&Fgq7$F 0F*7$F0F0Fhq-F46&F6F7F.F7-F$6$7&7$F(F]q7$F-F]qF,F'-F46&F6FCF7FE-F$6$7& Fhr7$F>F]qF=F,-F46&F6FCFCFfn-F$6$7&F^s7$FKF]qFJF=-F46&F6FCFPF]p-F$6$7& Fds7$FVF]qFUFJ-F46&F6FCFenFcq-F$6$7&Fjs7$F\\oF]qF[oFU-F46&F6FCF`oF7-F$ 6$7&F`t7$FgoF]qFfoF[o-F46&F6FCF\\p#FLFgn-F$6$7&Fft7$FbpF]qFapFfo-F46&F 6FCFgp#FcpFF-F$6$7&F]u7$F]qF]qF\\qFap-F46&F6FCFbq#FWFgn-F$6$7&Fdu7$F*F ]qFgqF\\q-F46&F6FCF[r#F+FF-F$6$7&F[v7$F0F]qF`rFgq-F46&F6FCF.FC-F$6$7&7 $F(Fbp7$F-FbpFhrFgr-F46&F6FPF7FQ-F$6$7&Fiv7$F>FbpF^sFhr-F46&F6FPFCF]p- F$6$7&F_w7$FKFbpFdsF^s-F46&F6FPFPF\\r-F$6$7&Few7$FVFbpFjsFds-F46&F6FPF enFit-F$6$7&F[x7$F\\oFbpF`tFjs-F46&F6FPF`o#FLFbo-F$6$7&Fax7$FgoFbpFftF `t-F46&F6FPF\\pF^v-F$6$7&Fhx7$FbpFbpF]uFft-F46&F6FPFgp#\"#@F9-F$6$7&F^ y7$F]qFbpFduF]u-F46&F6FPFbq#FhoFgn-F$6$7&Ffy7$F*FbpF[vFdu-F46&F6FPF[r# \"#FF9-F$6$7&F]z7$F0FbpFbvF[v-F46&F6FPF.FP-F$6$7&7$F(Fgo7$F-FgoFivFhv- F46&F6FenF7Ffn-F$6$7&F\\[l7$F>FgoF_wFiv-F46&F6FenFCFcq-F$6$7&Fb[l7$FKF goFewF_w-F46&F6FenFPFit-F$6$7&Fh[l7$FVFgoF[xFew-F46&F6FenFenFgu-F$6$7& F^\\l7$F\\oFgoFaxF[x-F46&F6FenF`oFC-F$6$7&Fd\\l7$FgoFgoFhxFax-F46&F6Fe nF\\pFiy-F$6$7&Fj\\l7$FbpFgoF^yFhx-F46&F6FenFgp#FcpFgn-F$6$7&F`]l7$F]q FgoFfyF^y-F46&F6FenFbq#F^qFgn-F$6$7&Fg]l7$F*FgoF]zFfy-F46&F6FenF[r#F+F gn-F$6$7&F^^l7$F0FgoFezF]z-F46&F6FenF.Fen-F$6$7&7$F(F\\o7$F-F\\oF\\[lF [[l-F46&F6F`oF7Fao-F$6$7&F\\_l7$F>F\\oFb[lF\\[l-F46&F6F`oFCF7-F$6$7&Fb _l7$FKF\\oFh[lFb[l-F46&F6F`oFPFdx-F$6$7&Fh_l7$FVF\\oF^\\lFh[l-F46&F6F` oFenFC-F$6$7&F^`l7$F\\oF\\oFd\\lF^\\l-F46&F6F`oF`o#F.FW-F$6$7&Fd`l7$Fg oF\\oFj\\lFd\\l-F46&F6F`oF\\pFP-F$6$7&F[al7$FbpF\\oF`]lFj\\l-F46&F6F`o Fgp#FcpFbo-F$6$7&Faal7$F]qF\\oFg]lF`]l-F46&F6F`oFbqFen-F$6$7&Fhal7$F*F \\oF^^lFg]l-F46&F6F`oF[r#F+Fbo-F$6$7&F^bl7$F0F\\oFe^lF^^l-F46&F6F`oF.F `o-F$6$7&7$F(FV7$F-FVF\\_lF[_l-F46&F6F\\pF7F]p-F$6$7&F\\cl7$F>FVFb_lF \\_l-F46&F6F\\pFCFit-F$6$7&Fbcl7$FKFVFh_lFb_l-F46&F6F\\pFPF^v-F$6$7&Fh cl7$FVFVF^`lFh_l-F46&F6F\\pFenFiy-F$6$7&F^dl7$F\\oFVFd`lF^`l-F46&F6F\\ pF`oFP-F$6$7&Fddl7$FgoFVF[alFd`l-F46&F6F\\pF\\pFa^l-F$6$7&Fjdl7$FbpFVF aalF[al-F46&F6F\\pFgp#FbyFF-F$6$7&F`el7$F]qFVFhalFaal-F46&F6F\\pFbq#\" #7Fgn-F$6$7&Fgel7$F*FVF^blFhal-F46&F6F\\pF[r#FazFF-F$6$7&F_fl7$F0FVFeb lF^bl-F46&F6F\\pF.F\\p-F$6$7&7$F(FK7$F-FKF\\clF[cl-F46&F6FgpF7Fhp-F$6$ 7&F]gl7$F>FKFbclF\\cl-F46&F6FgpFCF`u-F$6$7&Fcgl7$FKFKFhclFbcl-F46&F6Fg pFPFay-F$6$7&Figl7$FVFKF^dlFhcl-F46&F6FgpFenFc]l-F$6$7&F_hl7$F\\oFKFdd lF^dl-F46&F6FgpF`oFdal-F$6$7&Fehl7$FgoFKFjdlFddl-F46&F6FgpF\\pFcel-F$6 $7&F[il7$FbpFKF`elFjdl-F46&F6FgpFgp#\"#\\F9-F$6$7&Fail7$F]qFKFgelF`el- F46&F6FgpFbq#\"#9Fgn-F$6$7&Fiil7$F*FKF_flFgel-F46&F6FgpF[r#\"#jF9-F$6$ 7&Fajl7$F0FKFfflF_fl-F46&F6FgpF.Fgp-F$6$7&7$F(F>7$F-F>F]glF\\gl-F46&F6 FbqF7Fcq-F$6$7&F`[m7$F>F>FcglF]gl-F46&F6FbqFCFgu-F$6$7&Ff[m7$FKF>FiglF cgl-F46&F6FbqFPFiy-F$6$7&F\\\\m7$FVF>F_hlFigl-F46&F6FbqFenFj]l-F$6$7&F b\\m7$F\\oF>FehlF_hl-F46&F6FbqF`oFen-F$6$7&Fh\\m7$FgoF>F[ilFehl-F46&F6 FbqF\\pFjel-F$6$7&F^]m7$FbpF>FailF[il-F46&F6FbqFgpF\\jl-F$6$7&Fd]m7$F] qF>FiilFail-F46&F6FbqFbq#\"#;Fgn-F$6$7&Fj]m7$F*F>FajlFiil-F46&F6FbqF[r #\"#=Fgn-F$6$7&Fb^m7$F0F>FijlFajl-F46&F6FbqF.Fbq-F$6$7&7$F(F-7$F-F-F`[ mF_[m-F46&F6F[rF7F\\r-F$6$7&Fa_m7$F>F-Ff[mF`[m-F46&F6F[rFCF^v-F$6$7&Fg _m7$FKF-F\\\\mFf[m-F46&F6F[rFPF`z-F$6$7&F]`m7$FVF-Fb\\mF\\\\m-F46&F6F[ rFenFa^l-F$6$7&Fc`m7$F\\oF-Fh\\mFb\\m-F46&F6F[rF`oFabl-F$6$7&Fi`m7$Fgo F-F^]mFh\\m-F46&F6F[rF\\pFbfl-F$6$7&F_am7$FbpF-Fd]mF^]m-F46&F6F[rFgpFd jl-F$6$7&Feam7$F]qF-Fj]mFd]m-F46&F6F[rFbqFe^m-F$6$7&F[bm7$F*F-Fb^mFj]m -F46&F6F[rF[r#\"#\")F9-F$6$7&Fabm7$F0F-Fj^mFb^m-F46&F6F[rF.F[r-F$6$7&7 $F(F(7$F-F(Fa_mF`_m-F46&F6F.F7F7-F$6$7&F`cm7$F>F(Fg_mFa_m-F46&F6F.FCFC -F$6$7&Ffcm7$FKF(F]`mFg_m-F46&F6F.FPFP-F$6$7&F\\dm7$FVF(Fc`mF]`m-F46&F 6F.FenFen-F$6$7&Fbdm7$F\\oF(Fi`mFc`m-F46&F6F.F`oF`o-F$6$7&Fhdm7$FgoF(F _amFi`m-F46&F6F.F\\pF\\p-F$6$7&F^em7$FbpF(FeamF_am-F46&F6F.FgpFgp-F$6$ 7&Fdem7$F]qF(F[bmFeam-F46&F6F.FbqFbq-F$6$7&Fjem7$F*F(FabmF[bm-F46&F6F. F[rF[r-F$6$7&F`fm7$F0F(FibmFabm-F46&F6F.F.F." 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 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" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17 " "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "C urve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36 " "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "C urve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55 " "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "C urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74 " "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C urve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93 " "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "C urve 100" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Configuration initia le: grille" }{TEXT 272 2 " n" }{TEXT -1 3 " x " }{TEXT 273 2 "n," } {TEXT -1 12 " probabilit\351" }{TEXT 274 3 " p " }{TEXT -1 27 "(entre \+ 0 et 1) cf pr\351ambule" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 500 "init:=proc(n::posint,p::numeric)\nlocal hasard,h,i,j,L,T,V;\nT:=NULL; \nhasard:=rand(1..n^2);\nfor i to n^2 do\n h:=hasard();\n if h<=n^2* p then T:=T,1 else T:=T,0 end if;\n # on met un code 1 (arbre) avec u ne probabilit\351 p\n # et un code 0 (vide) avec une probabilit\351 1 -p\nend do;\n# construction d'une liste de n sous-listes \n# (chaque s ous-liste correspond \340 une ligne de la grille)\nV:=NULL;\nfor i to \+ n do\n L:=NULL:\n for j to n do\n L:=L,T[n*(i-1)+j]\n end do; \+ \n V:=V,[L]\nend do;\n[V]\nend proc; \n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%initGf*6$'%\"nG%'posintG'%\"pG%(numericG6)%'hasardG% \"hG%\"iG%\"jG%\"LG%\"TG%\"VG6\"F5C(>8)%%NULLG>8$-%%randG6#;\"\"\"*$)9 $\"\"#F@?(8&F@F@FA%%trueGC$>8%-F;F5@%1FJ*&FBF@9%F@>F86$F8F@>F86$F8\"\" !>8*F9?(FFF@F@FCFGC%>8(F9?(8'F@F@FCFG>FZ6$FZ&F86#,&*&FCF@,&FFF@F@!\"\" F@F@FfnF@>FV6$FV7#FZ7#FVF5F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "a:=init(10,0.6);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"aG7,7, \"\"!F'F'\"\"\"F'F'F(F(F(F(7,F'F(F'F'F'F'F(F(F(F(7,F'F'F(F(F'F(F'F'F(F (7,F(F'F'F(F(F(F(F'F'F(7,F(F(F(F(F'F(F'F(F'F'7,F(F(F'F(F'F'F(F(F(F(7,F (F'F(F(F'F'F(F'F'F(7,F'F(F(F(F(F(F(F(F(F(7,F(F(F(F(F'F'F'F'F(F(7,F'F'F 'F(F(F(F'F'F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "\nAffichage de la grille \340 partir de la liste courante L:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 491 "afficher:=proc(L::list(list(numeric)))\nlocal i,j,n,T;\nn:=nops(L):\nT:=NULL;\nfor i to n do\n for j to n do\n \+ if L[i][j]=0 then T:=T,dessin(i,j,n,1,1,1) # 0 vide: blan c\n elif L[i][j]=1 then T:=T,dessin(i,j,n,0,1,0) # 1 arbre : vert\n elif L[i][j]=2 then T:=T,dessin(i,j,n,0.75,0.75,0.75) # 2 cendre: gris\n else T:=T,dessin(i,j,n,1,0,0) \+ # 3 feu: rouge \n end if;\n end do;\nend do;\ndisplay(\{T\}, scaling=constrained,axes=none);\nend proc;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%)afficherGf*6#'%\"LG-%%listG6#-F*6#%(numericG6&%\"iG% \"jG%\"nG%\"TG6\"F4C&>8&-%%nopsG6#9$>8'%%NULLG?(8$\"\"\"FAF7%%trueG?(8 %FAFAF7FB@)/&&F;6#F@6#FD\"\"!>F=6$F=-%'dessinG6(F@FDF7FAFAFA/FGFA>F=6$ F=-FO6(F@FDF7FKFAFK/FG\"\"#>F=6$F=-FO6(F@FDF7$\"#v!\"#FfnFfn>F=6$F=-FO 6(F@FDF7FAFKFK-%(displayG6%<#F=/%(scalingG%,constrainedG/%%axesG%%none GF4F4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "afficher(a);" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6bq-%)POLYGONSG6$7 &7$$\"\"\"\"\"!$\"\"&F*7$$\"\"#F*F+7$F.$\"\"'F*7$F(F1-%&COLORG6&%$RGBG F*F)F*-F$6$7&F-7$$\"\"$F*F+7$FF4-F$6$7&FE7$F1F+7$F1F1FFF4-F$6$7&FP7$ $\"\"(F*F+7$FVF1FQFH-F$6$7&FU7$$\"\")F*F+7$FgnF1FXF4-F$6$7&7$F.FC7$FF`clF\\clFH-F$6$7&F3F0F\\clFhblFH-F$6$7&FGFFFhclFaclF4-F$6$ 7&F>FGFaclF`clF4-F$6$7&FQFXF`dlF\\dlF4-F$6$7&FFFQF\\dlFhclF4-F$6$7&FXF inFddlF`dlFH-F$6$7&FcpFbpF]elF\\elF4-F$6$7&FinFcpF\\elFddlFH-F$6$7&Feo F'F3FhdlF4-%(SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "C urve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "C urve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22 " "Curve 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "C urve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36" "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41 " "Curve 42" "Curve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "C urve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55" "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60 " "Curve 61" "Curve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "C urve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74" "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79 " "Curve 80" "Curve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "C urve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93" "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98 " "Curve 99" "Curve 100" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 126 "Calc ul du nb de cellules en feu autour de la cellule (ligne r - colonne c) (nord - sud - ouest - est) dans la configuration L " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 302 "nb_en_feu:=proc(L::list(list(numeric)),r ::posint,c::posint)\n local n,nb,rr,cc;\n n:=nops(L);\n nb:=0;\n i f r>1 and L[r-1][c]=3 then nb:=nb+1 end if;\n if r1 and L[r][c-1]=3 then nb:=nb+1 end if; \n if c%*nb_en_feuGf*6%'%\"LG-%%listG6#-F*6# %(numericG'%\"rG%'posintG'%\"cGF16&%\"nG%#nbG%#rrG%#ccG6\"F9C)>8$-%%no psG6#9$>8%\"\"!@$32\"\"\"9%/&&F@6#,&FHFGFG!\"\"6#9&\"\"$>FB,&FBFGFGFG@ $32FHFFBFS@$32FGFP/&&F@6#FH6#,&FPFGFGFNFQ>FBFS@ $32FPFFBFSFBF9F9F9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "nb_en_feu(a,6,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Mettre le feu \340 parti r de la cellule centrale de la configuration L" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 147 "mettre_feu:=proc(L::list(list(numeric)))\nloc al n,r,c,M;\n M:=L;\n n:=nops(L);\n r:=floor(n/2)+1; \n c:=floor( n/2)+1;\n M[r][c]:=3;\n M\n end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+mettre_feuGf*6#'%\"LG-%%listG6#-F*6#%(numericG6&%\"nG%\"rG%\" cG%\"MG6\"F4C(>8'9$>8$-%%nopsG6#F8>8%,&-%&floorG6#,$F:#\"\"\"\"\"#FFFF FF>8&F@>&&F76#F?6#FI\"\"$F7F4F4F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "afficher(mettre_feu(a));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6bq-%)POLYGONSG6$7&7$$\"\"\"\"\"!$ \"\"&F*7$$\"\"#F*F+7$F.$\"\"'F*7$F(F1-%&COLORG6&%$RGBGF*F)F*-F$6$7&F-7 $$\"\"$F*F+7$FF4-F$6$7&FE7$F1F+7$F1F1FFF4-F$6$7&FP7$$\"\"(F*F+7$FVF1 FQFH-F$6$7&FU7$$\"\")F*F+7$FgnF1FXF4-F$6$7&7$F.FC7$FF]clFiblFH-F$6$7&F3F0FiblFeblFH-F$6$7&FGFFFeclF^clF4-F$6$7&F>FGF^clF] clF4-F$6$7&FQFXFbdlFiclF4-F$6$7&FFFQFiclFeclF4-F$6$7&FXFinFfdlFbdlFH-F $6$7&FcpFbpF_elF^elF4-F$6$7&FinFcpF^elFfdlFH-F$6$7&FeoF'F3FjdlF4-%(SCA LINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG" 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" "Curve \+ 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17 " "Curve 18" "Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "C urve 24" "Curve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36 " "Curve 37" "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "C urve 43" "Curve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55 " "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "C urve 62" "Curve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74 " "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C urve 81" "Curve 82" "Curve 83" "Curve 84" "Curve 85" "Curve 86" "Curve 87" "Curve 88" "Curve 89" "Curve 90" "Curve 91" "Curve 92" "Curve 93 " "Curve 94" "Curve 95" "Curve 96" "Curve 97" "Curve 98" "Curve 99" "C urve 100" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 129 "Calcul d'une nouvel le configuration \340 partir de la configuration L en suivant la fonct ion de transition donn\351e dans le pr\351ambule:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 470 "nouvelle_config:=proc(L::list(list(numeric) ))\n local n,nb,r,c,nouveau,ligne,cellule;\n n:=nops(L);\n nouveau: =NULL;\n for r from 1 to n do\n ligne:=NULL;\n for c from 1 to \+ n do\n cellule:=L[r][c];\n nb:=nb_en_feu(L,r,c);\n if n b>0 and L[r][c]=1 then cellule:=3 end if;\n if L[r][c]=3 then cel lule:=2 end if;\n if L[r][c]=2 then cellule:=0 end if;\n lig ne:=ligne,cellule;\n end do;\n nouveau:=nouveau,[ligne];\n end \+ do;\n [nouveau];\nend;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%0nouvel le_configGf*6#'%\"LG-%%listG6#-F*6#%(numericG6)%\"nG%#nbG%\"rG%\"cG%(n ouveauG%&ligneG%(celluleG6\"F7C&>8$-%%nopsG6#9$>8(%%NULLG?(8&\"\"\"FDF :%%trueGC%>8)FA?(8'FDFDF:FEC(>8*&&F>6#FC6#FJ>8%-%*nb_en_feuG6%F>FCFJ@$ 32\"\"!FS/FNFD>FM\"\"$@$/FNFgn>FM\"\"#@$/FNF[o>FMFZ>FH6$FHFM>F@6$F@7#F H7#F@F7F7F7" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Animation de l' \351volution du feu:\n" }{TEXT 262 1 "n" }{TEXT -1 3 " x " }{TEXT 263 1 "n" }{TEXT -1 25 " : taille de la grille, " }{TEXT 264 8 "nbgener \+ " }{TEXT -1 22 ": nb de g\351n\351rations, " }{TEXT 265 1 "p" }{TEXT -1 42 " : probabilit\351 (entre 0 et 1) cf pr\351ambule" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 380 "animation:=proc(n::posint,nbgener: :posint,p::numeric)\n local anime,config,i;\n anime:=NULL;\n config :=init(n,p);\n anime:=anime,afficher(config);\n config:=mettre_feu(c onfig);\n anime:=anime,afficher(config);\n for i to nbgener do\n \+ config:=nouvelle_config(config);\n anime:=anime,afficher(config);\n end do;\n display([anime],insequence=true,scaling=constrained):\nen d proc;\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*animationGf*6%'%\"nG%' posintG'%(nbgenerGF)'%\"pG%(numericG6%%&animeG%'configG%\"iG6\"F3C)>8$ %%NULLG>8%-%%initG6$9$9&>F66$F6-%)afficherG6#F9>F9-%+mettre_feuGFC>F6F @?(8&\"\"\"FJ9%%%trueGC$>F9-%0nouvelle_configGFC>F6F@-%(displayG6%7#F6 /%+insequenceGFL/%(scalingG%,constrainedGF3F3F3" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 111 "# cliquer sur l'image puis sur l'icone play d e la barre des menus pour jouer l'animation\nanimation(15,40,0.65);" } }{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6$-%(ANIMATEG6L7_ y-%)POLYGONSG6$7&7$$\"\"\"\"\"!$\"\"&F.7$$\"\"#F.F/7$F2$\"\"'F.7$F,F5- %&COLORG6&%$RGBGF.F-F.-F(6$7&7$$\"#5F.F,7$$\"#6F.F,7$FCF27$F@F2-F96&F; F-F-F--F(6$7&7$$\"\"$F.$\"\"(F.7$$\"\"%F.FO7$FR$\"\")F.7$FMFUFG-F(6$7& 7$$\"#9F.F/7$$\"#:F.F/7$FinF57$FfnF5FG-F(6$7&7$$\"#7F.$\"\"*F.7$$\"#8F .Fco7$FfoF@7$FaoF@F8-F(6$7&Feo7$FfnFco7$FfnF@FhoF8-F(6$7&F]p7$FinFco7$ FinF@F^pFG-F(6$7&FB7$FaoF,7$FaoF2FEFG-F(6$7&7$$F.F.FR7$F,FRF+7$F]qF/FG -F(6$7&7$FOFO7$FUFO7$FUFU7$FOFUF8-F(6$7&Fgp7$FfoF,7$FfoF2FhpFG-F(6$7&7 $FfnF,7$FinF,7$FinF27$FfnF2F8-F(6$7&Fdq7$FcoFO7$FcoFUFeqFG-F(6$7&FjqF_ rFbrF[rFG-F(6$7&7$F2FR7$FMFR7$FMF/F1F8-F(6$7&7$F]qFU7$F,FU7$F,Fco7$F]q FcoF8-F(6$7&7$F@FO7$FCFO7$FCFU7$F@FUF8-F(6$7&F_s7$FRFR7$FRF/F`sFG-F(6$ 7&FfrF[tF^tFgrFG-F(6$7&F\\t7$FaoFO7$FaoFUF]tFG-F(6$7&7$F/FR7$F5FR7$F5F /7$F/F/FG-F(6$7&7$F2F]q7$FMF]q7$FMF,7$F2F,F8-F(6$7&F1F`s7$FMF5F4F8-F(6 $7&7$F,F]qFfuFiu7$F,F,F8-F(6$7&7$FOF]q7$FUF]q7$FUF,7$FOF,F8-F(6$7&7$F2 FUFW7$FMFco7$F2FcoF8-F(6$7&7$F5F]qFfvFiv7$F5F,F8-F(6$7&Fjt7$FfoFO7$Ffo 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