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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 44 "A Quick and Dirty Tool f
or Plotting Iterates" }}{PARA 19 "" 0 "" {TEXT -1 12 "Tim McLarnan" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 256 6 "itlist" }{TEXT -1 91 " produces a list \+
of the points in the \"web diagram\", the graphical trajectory of the \+
point " }{TEXT 259 1 "x" }{TEXT -1 8 " during " }{TEXT 258 1 "N" }
{TEXT -1 15 " iterations of " }{TEXT 257 1 "f" }{TEXT -1 46 ". It woul
d be more efficient to do this using " }{TEXT 269 3 "map" }{TEXT -1 
41 ", but this way was easier to think about." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 183 "itlist := \+
(f, x, N) -> ListTools[FlattenOnce]\n  ([seq([[(f@@n)(x),(f@@n)(x)],\n
         [(f@@n)(x),(f@@(n+1))(x)],\n         [(f@@(n+1))(x),(f@@(n+1)
)(x)]],\n    n=0..N)]);              " }}{PARA 12 "" 1 "" {XPPMATH 20 
"6#>%'itlistGf*6%%\"fG%\"xG%\"NG6\"6$%)operatorG%&arrowGF*-&%*ListTool
sG6#%,FlattenOnceG6#7#-%$seqG6$7%7$--%#@@G6$9$%\"nG6#9%F:7$F:--F<6$F>,
&F?\"\"\"FGFGF@7$FCFC/F?;\"\"!9&F*F*F*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "Finally, " }{TEXT 263 8 "p
lotiter" }{TEXT -1 7 " plots " }{TEXT 264 1 "f" }{TEXT -1 29 ", the id
entity function, and " }{TEXT 265 7 "howmany" }{TEXT -1 13 " iterates \+
of " }{TEXT 266 2 "f," }{TEXT -1 13 " starting at " }{TEXT 267 10 "sta
rtpoint" }{TEXT -1 38 ". The horizontal range of the plot is " }{TEXT 
268 5 "range" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "plotiter := (f, startpt, ho
wmany, range) ->\n  plot([x, f(x),itlist(f, startpt, howmany)],\n     \+
   range, color=[blue,black,red]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
>%)plotiterGf*6&%\"fG%(startptG%(howmanyG%&rangeG6\"6$%)operatorG%&arr
owGF+-%%plotG6%7%%\"xG-9$6#F3-%'itlistG6%F59%9&9'/%&colorG7%%%blueG%&b
lackG%$redGF+F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 63 "Here's an example, showing the development of a st
able 2-cycle:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 18 "f := x -> x^2-0.9;" }}{PARA 11 "" 1 "" {XPPMATH 
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