{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&R
Y2aF: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$$\"3Qmm;a<.Y&)F:F_s7$$\"3