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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 256 42 "Sensitiv
e Dependence on Initial Conditions" }{TEXT 257 1 " " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 34 "Computer Experiment 1.4, page 31.\n" }}{PARA 0 "" 0 "" {TEXT 
-1 109 "The parameter values below differ by 0.001.  How many iterates
 for such points until the distance is at least" }}{PARA 0 "" 0 "" 
{TEXT -1 54 "0.2   apart.  Try various pairs of initial conditions." }
}{PARA 0 "" 0 "" {TEXT -1 258 "\nThis iterates the function  f(x) = r*
x*(1-x) and displays the values for two different initinial conditions
, x0 & y0.\n\nr:  Parameter value.  \nn: The number n is the number of
 iterates calculated.\nx0:  First initial condition  \ny0:  Second ini
tial condition " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "r := 4.0;
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "g:= x -> r*x*(1-x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "x0 := 0.1;\ndelta := 0.001;\ny0 := \+
x0 + delta;\nn  := 20;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 253 "
printf(`\\t i \\t\\t xi \\t\\t\\t\\t yi \\t\\t\\t\\t |yi - xi|\\n`);\n
printf(`\\t 0 \\t %1.4f \\t %1.4f \\t %1.4f \\n`, x0, y0, abs(x0-y0));
\nfor i from 1 to n do\n   x0 := g(x0):\n   y0 := g(y0):\n   printf(`
\\t %d \\t %1.4f \\t %1.4f \\t %1.4f \\n`, i, x0, y0, abs(x0-y0)); \no
d:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 8 
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