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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 20 "Define the tent map." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "f := proc(x)  \n   if x <
 0.5 then 2*x \n   else 2*(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 18 "X := 2/7;\nn1 := 6;" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "Make a table of t
he iteates 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 "" }}{PARA 11 "" 
1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "Intial condi
tions, number of iteates, and ends of the interval to use for" }}
{PARA 0 "" 0 "" {TEXT -1 64 "a plot of the cobweb (stairstep) graphica
l 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=bla
ck)\}:\npic := pic union \{plot(f, a..b, color=black)\}:\nfor i from 1
 to n1 do\n        x1:= f(x0):\n        pic := pic union \{plot([[x0,x
0],[x0,x1],[x1,x1]], color=blue)\}:\n        x0:=x1:\nod:\ndisplay(pic
);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
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1 1 }{PAGENUMBERS 0 1 2 33 1 1 }