{VERSION 5 0 "IBM INTEL NT" "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 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 1 0 1 0 2 2 0 1 } {PSTYLE "Text Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 } 1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE " " -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author " -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 3 1 0 0 8 8 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 28 "Precision of an iterated \+ map" }}{PARA 19 "" 0 "" {TEXT -1 31 "by Alex Quandt, Uni Greifswald " }}{PARA 0 "" 0 "" {TEXT -1 56 "The following worksheet will demonstrat e the effects of " }{TEXT 258 17 "finite precision " }{TEXT -1 4 "for \+ " }}{PARA 0 "" 0 "" {TEXT 256 13 "iterated maps" }{TEXT -1 24 ". If th e results should " }{TEXT 259 5 "scare" }{TEXT -1 23 " you - fair enou gh ! " }{TEXT 257 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Gener al settings " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Let us specify a n umber of things : " }{MPLTEXT 1 0 1 " " }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 36 "Clear everything + general settings " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "restart; \nwith(plots): \nDigits:=15; " }} {PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been r edefined\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'DigitsG\"#:" }}}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 60 "Barry Martin's map (Spektrum d. W issenschaft 11/1986, p. 6) " }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 18 " I nitial settings " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Specify some \+ " }{TEXT 260 11 "parameters " }{TEXT -1 2 ": " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=12; b:=3; c:=36; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG\" \"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG\"#O" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 13 "Specify your " }{TEXT 261 17 "starting point :" } {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "x[0]:=0; \+ \ny[0]:=0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"!F'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"yG6#\"\"!F'" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 17 "Iterate your map " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "nit : number of " }{TEXT 262 16 "recursion steps " } {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "nit:=10000 0; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$nitG\"'++5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 15 "Iterate map:\n " }}{PARA 0 "" 0 "" {TEXT -1 41 "x[],y[] : coordinates of a " }{TEXT 267 6 "point " }{TEXT -1 13 "in the plane " }}{PARA 0 "" 0 "" {TEXT -1 41 "mappoint[] : array which contains " }{TEXT 268 3 "all" } {TEXT -1 29 " points of the interated map " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 304 "printlevel:=0; \n\nfor k from 1 to nit do\n\n if \+ (k mod 10000 = 0) then \n printf(\"step = %d\\n\",k);\n end if; \+ \n\n x[k]:= evalf(y[k-1]-sign(x[k-1])*\n sqrt(abs(b*x[k-1]-c))); \+ \n y[k]:=evalf(a-x[k-1]); \n \n# printf(\"[x,y] = [%20.15f,%20.15f] \\n #\\n\",x[k],y[k]); \n\n mappoint[k]:=[x[k],y[k]]; \n\nend do; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+printlevelG\"\"!" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 10000" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 20 000" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 30000" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 40000" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 50000 " }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 60000" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 70000" }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 80000 " }}{PARA 6 "" 1 "" {TEXT -1 12 "step = 90000" }}{PARA 6 "" 1 "" {TEXT -1 13 "step = 100000" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Plot that map" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 31 "Full plot to a postscript file " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "maplist:=\{seq(mappoint[k],k=1..nit)\}: \+ \nplotsetup(ps,plotoutput=`BMmapfull.ps`,plotoptions=`color=rgb`): \+ \npointplot(maplist,color=red,symbol=point,axes=boxed,title=\"Barry Ma rtin's map with ndigits=15\"); " }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 41 "Plot points lying within a certain window" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Specify " }{TEXT 264 10 "window :\n\n" }{TEXT -1 18 " xmin, xmax : " }{TEXT 265 7 "window " }{TEXT -1 28 "for x-coordin ates\nymin,ymax " }{TEXT 266 15 " : window " }{TEXT -1 17 "for y- coordinates" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "xmin:=-30; x max:=30; ymin:=-30; ymax:=30; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%x minG!#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%xmaxG\"#I" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%yminG!#I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %%ymaxG\"#I" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 269 15 "C ollect points " }{TEXT -1 25 "lying inside that window " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 274 "i:=0; \nfor k from 1 to nit do \n \+ if (mappoint[k][1] > xmin and mappoint[k][1] < xmax and mappoint[k][2 ] > ymin and mappoint[k][2] < ymax) then\n i:=i+1; \n windowpoint[i] [1]:=evalf(mappoint[k][1]); \n windowpoint[i][2]:=evalf(mappoint[k][2 ]); \n end if; \nend do; \nnwin:=i; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%nwinG\"&x3\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 270 5 "Plot " }{TEXT -1 32 "points lying within that window " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 240 "windowlist:=\{seq([windowpoint[k][1],windowpoint[k][ 2]],k=1..nwin)\}: \nplotsetup(ps,plotoutput=`BMmapwindow.ps`,plotoptio ns=`color=rgb`): \npointplot(windowlist,color=red,symbol=point,axes= boxed,title=\"Barry Martin's map with ndigits=15\"); " }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }