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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 22 "Iterating the tent map
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "This worksheet iterates the t
ent map." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart;\nwith(
plots):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Define the general ten
t map.\nThe parameter  r  is the slope of the map.  " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 76 "f := proc(x) \n   global r; \n   if x < 0
.5 then r*x \n   else r*(1-x) \nfi\nend;" }{TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 39 "Intial conditions and number of iteates" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "X := 2/7;\nn1 := 6;\nr :=
 1.7;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Make a table of the itea
tes from 1 to n1." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "for n \+
from 1 to n1 do\n X := f(X) od;" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 73 "Intial conditions, number of iteates, and ends of th
e interval to use for" }}{PARA 0 "" 0 "" {TEXT -1 64 "a plot of the co
bweb (stairstep) graphical method of iteration. " }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 40 "x0 := 11/37:\nn1 := 20:\na  := 0:\nb  := 1:" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Plot the cobweb for the values \+
above.  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 233 "pic := \{plot(
x ,x=a..b, color=black)\}:\npic := pic union \{plot(f, a..b, color=bla
ck)\}:\nfor i from 1 to n1 do\n        x1:= f(x0):\n        pic := pic
 union \{plot([[x0,x0],[x0,x1],[x1,x1]], color=blue)\}:\n        x0:=x
1:\nod:\ndisplay(pic);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG 
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1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }