{VERSION 5 0 "IBM INTEL LINUX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple P lot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 198 "This worksheet iterates the function f(x)=rx(1-x ). \nIt plots the graph of the n-th iterate of f on the interval [ a,b].\nSo if n=4, then we plot the graph of f composed with itself 4 times. " }}{PARA 0 "" 0 "" {TEXT -1 138 "It also allows plot the g raphical representation of iterates of f^n for \nthe initial condition x0. (The process g is the power f^n.) " }}{PARA 0 "" 0 "" {TEXT -1 70 "The first n*n0 iterates of f are taken without plotting, then t he next" }}{PARA 0 "" 0 "" {TEXT -1 182 "n1 iterates of f^n are plotte d. If n0 or n1 =0 then this is not done.\n n iter of f plotted\n \+ x0 initial condition\n n0 number of iterates of x0 taken by f^n \+ without plotting" }}{PARA 0 "" 0 "" {TEXT -1 63 " n1 number of iterat es of x0 taken by f^n which are plotted" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "r := 4.0:\nn := 3:\nn0 := 0:\nn1 := 0:\na := 0.0:\nb := 1. 0:\nx0 := 0.1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f := x -> r*x*(1-x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "g := proc(x) \n local y,i :\n y := x: \n for i from 1 to n do\n y := f(y): \n od:\n y;\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "pic := \{plot(g(x),x=a..b, resolution = 2000,thickness=3,\n color=bl ack,tickmarks=[2,3])\}:\npic := pic union \{plot(x,x=a..b,thickness=3, \n color=black,tickmarks=[2,3])\}:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "for i from 1 to n0 do\n x1:= g(x0):\n x0:=x1:\no d:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "for i from 1 to n1 do\n \+ x1:= g(x0):\n pic := pic union \{plot([[x0,x0],[x 0,x1],[x1,x1]], color = blue)\}:\n x0:=x1:\nod:" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "display(pic);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6%7S7$$\"\"!F)F(7$$\"3dmmm;arz@!# >F+7$$\"3[LL$e9ui2%F-F/7$$\"3nmmm\"z_\"4iF-F27$$\"3[mmmT&phN)F-F57$$\" 3BLLe*=)H\\5!#=F87$$\"3gmm\"z/3uC\"F:F<7$$\"3%)***\\7LRDX\"F:F?7$$\"3^ mm\"zR'ok;F:FB7$$\"3w***\\i5`h(=F:FE7$$\"3YLLL3En$4#F:FH7$$\"3qmm;/RE& G#F:FK7$$\"3\")*****\\K]4]#F:FN7$$\"3$******\\PAvr#F:FQ7$$\"3(******\\ nHi#HF:FT7$$\"3jmm\"z*ev:JF:FW7$$\"3?LLL347TLF:FZ7$$\"3,LLLLY.KNF:Fgn7 $$\"3v***\\7o7Tv$F:Fjn7$$\"3'GLLLQ*o]RF:F]o7$$\"3A++D\"=lj;%F:F`o7$$\" 31++vV&RY2aF:Fbp7$$\"39mm;zXu 9cF:Fep7$$\"3l******\\y))GeF:Fhp7$$\"3'*)***\\i_QQgF:F[q7$$\"3@***\\7y %3TiF:F^q7$$\"36****\\P![hY'F:Faq7$$\"3jKLL$Qx$omF:Fdq7$$\"3!)*****\\P +V)oF:Fgq7$$\"3?mm\"zpe*zqF:Fjq7$$\"3%)*****\\#\\'QH(F:F]r7$$\"3GKLe9S 8&\\(F:F`r7$$\"3R***\\i?=bq(F:Fcr7$$\"3\"HLL$3s?6zF:Ffr7$$\"3a***\\7`W l7)F:Fir7$$\"3#pmmm'*RRL)F:F\\s7$$\"3Qmm;a<.Y&)F:F_s7$$\"3a#))yq\\F:7$$\"3HLLL3x&)*3\"F-$\"3!)eh+\"=k?^&F:7$$\"3gmm TN@Ki8F-$\"3Xz4T#R>A['F:7$$\"3$*****\\ilyM;F-$\"3(e_[XAw8J(F:7$$\"3DLL e*)4D2>F-$\"32tGq)[\\(4!)F:7$F+$\"3H-:Mhr3(e)F:7$$\"3IL$e*)4bQl#F-$\"3 D'*[.xodI$*F:7$$\"3-++D\"y%*z7$F-$\"3un\")oi%=8y*F:7$$\"3.LeRAY1lLF-$ \"3qGh%3%=>5**F:7$$\"3vm;ajW8-OF-$\"39E:Q62O\")**F:7$$\"3ND\"GQ#>ShOF- $\"3aNsy&f\"p!***F:7$$\"3D$e9TQp1s$F-$\"3!e')R'[8!***F:7$$\"3 dvoa&o1q,%F-$\"38uSf?!f5)**F:7$F/$\"3EndQvf:p**F:7$$\"3xm;H2Q\\4YF-$\" 3$>m[1)=OX(*F:7$$\"32++voMrU^F-$\"3=E$*yNiUU$*F:7$$\"3PL$3-8Lfn&F-$\"3 ,*z:TM51!))F:7$F2$\"3Oy7![!Grb\")F:7$$\"3$fmm\"zp!fu'F-$\"3Gl\"*>gVXMu F:7$$\"3emmmm6m#G(F-$\"3)fV$z>#H\"pmF:7$$\"3Anm;a`T>yF-$\"3!)=[j!)))Q% )eF:7$F5$\"3Kr,)Q%p[,^F:7$$\"3GL$3-js.*))F-$\"3EV$3Pt'4UVF:7$$\"36++v= ddC%*F-$\"3myFD&o.vh$F:7$$\"3al;H2)y(e**F-$\"3>GLh\"pQ,%HF:7$F8$\"3Gl! )34)e+K#F:7$$\"3&)***\\(=JN[6F:$\"3lG'4`dpsM\"F:7$F<$\"3E&og)3'HRI'F-7 $$\"3%)***\\(o3p)H\"F:$\"3#H[te__0l$F-7$$\"33LLe*ot*\\8F:$\"3,&*R]1'f^ s\"F-7$$\"3q*******4:cP\"F:$\"3*f@4bcmL.\"F-7$$\"3KmmT5lD,9F:$\"3O]J. \\SC*>&Fdu7$$\"3x**\\i:s299F:$\"3%[q(pztt$H$Fdu7$$\"3ALL$3#z*oU\"F:$\" 3P]72'Qk\\#=Fdu7$$\"3nm;/E'=(R9F:$\"3c-'QVX0E*y!#@7$F?$\"35$)RP9T$o#=F gbl7$$\"3,LL3F*o\"f9F:$\"3sYLAW\"Gqf$!#A7$$\"3Xmm\"H_)zl9F:$\"3U)*=on; hrA!#B7$$\"3!****\\(=\"GCZ\"F:$\"3c,*>?!R)f4)F`cl7$$\"3OLLe9x0z9F:$\"3 $)\\]7&o'*Qr#Fgbl7$$\"3'****\\i!pJ#\\\"F:$\"33$>1U:k![)*Fgbl7$$\"3emm \"z4wb]\"F:$\"3h?!)RJ#=q8#Fdu7$$\"3\")***\\7[%4K:F:$\"3T\">H>m;Xt&Fdu7 $$\"3/LLekGhe:F:$\"3<_FRfB[,6F-7$$\"3x***\\7j\\;h\"F:$\"3WAu3W+'4k#F-7 $FB$\"3dy95u-8'y%F-7$$\"38LL3_(>/x\"F:$\"3,x2A!)Qmm5F:7$FE$\"39\\O()pM gJ=F:7$$\"3KL3x\")H`I>F:$\"3%)pY&f/@)yAF:7$$\"3hm;HdG\"\\)>F:$\"3Djj\\ Af9aFF:7$$\"3!**\\7Gt#HR?F:$\"3$32&>tN<^KF:7$FH$\"3,^_OZ]ejPF:7$$\"34+ +Dc#o%*=#F:$\"3\"Q7:IlQ\\o%F:7$FK$\"34A)3jwmFg&F:7$$\"3CLLe9r5$R#F:$\" 37&>#3R#\\\\f'F:7$FN$\"39c8uh#)f2vF:7$$\"3()******\\jB4EF:$\"3F!yu,J&) =J)F:7$FQ$\"3Wges\">6t>-3$F:$\"3;0\\MRip****F:7$$\"3C$3_+7l? 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