File:Critical orbit for f(z) = z^15 - z.png
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DescriptionCritical orbit for f(z) = z^15 - z.png |
English: critical orbit for f(z) = z^15 - z[1] |
Date | |
Source | Own work |
Author | Adam majewski |
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Maxima CAS src code[edit]
kill(all); remvalue(all); /*------------- functions definitions ---------*/ /* function */ f(z):=z^15 -z; GiveListOfCriticalPoints(fun):= block( [d,s], /* derivative */ d:diff(fun,z,1), /* critical points z: d=0 */ s:solve(d=0,z), /* remove "z=" from list s */ s:map('rhs,s), /* convert to form x+y*%i */ s:map('rectform,s), s:map('float,s), return(s) )$ /* f(z) is used as a global function I do not know how to put it as a argument */ GiveOrbit(z0,OrbitLength):= block( [z,Orbit], z:z0, Orbit:[[realpart(z),imagpart(z)]], for i:1 thru OrbitLength step 1 do ( z:expand(f(z)), Orbit:endcons([realpart(z),imagpart(z)],Orbit)), return(Orbit) )$ /* find fixed points returns a list */ GiveFixedPoints():= block ( [s], s:solve(f(z)=z), /* remove "z=" from list s */ s:map('rhs,s), s:map('rectform,s), s:map('float,s), return(s) )$ /* gives scene for draw procedure from draw package */ GiveScene(critical,orbitn):= gr2d( user_preamble = "set border 0;set nokey;set size square;set noxtics ;set noytics;", point_type = filled_circle, points_joined = false, point_size = 0.7, /* critical orbit */ color =red, points(orbitn), /* parabolic fixed point */ color =black, point_size = 1.4, points([0],[0]), /* critical point */ color =blue, points([[realpart(critical),imagpart(critical)]]) )$ compile(all); /* ------------ */ iLength:1000; s:GiveListOfCriticalPoints(f(z)); multiplicities; length(s); Orbits:[]; for i:1 thru length(s) step 1 do ( Orbit:GiveOrbit(s[i],iLength), Orbits:append(Orbit,Orbits) ); /*-----------------------------------------------------------------------*/ load(draw); /* ( interface to gnuplot ) by Mario Rodriguez Riotorto http://www.telefonica.net/web2/biomates */ draw2d( title = "All orbits of 14 critical points for f(z)=z^15 -z ", terminal = png, file_name = concat("~/",string(iLength),"b"), /* put here path were you want to store an image */ pic_width = 1000, /* Since Maxima 5.23, pic_width and pic_height are deprecated. */ pic_height = 1000, /* See option dimensions. To get the same effect, write dimensions=[800,600] */ yrange = [-1.0,1.0], xrange = [-1.0,1.0], xlabel = "z.re ", ylabel = "z.im", point_type = filled_circle, points_joined = false, point_size = 0.7, key=" critical orbit ", color =red, points(Orbits), point_size = 1.2, key= "critical points", color = blue, points(map(realpart,s),map(imagpart,s)), key= "fixed parabolic point", color = black, points([[0,0]]) );
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:55, 4 March 2013 | 1,000 × 1,000 (18 KB) | Soul windsurfer (talk | contribs) | {{Information |Description ={{en|1=critical orbit for f(z) = z^15 - z}} |Source ={{own}} |Author =Adam majewski |Date =2013-03-03 |Permission = |other_versions = }} |
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