Related

? orbits;

Calculate

orbits

orbits(x^2+a, 0, 50, ...

Calculate

? orbits;

Calculate

orbits

orbits(x^2+a, 0, 50, ...

Calculate

orbits

Run Example
```(%i1)F(r,x):=r*x*(1-x);
(%o1)                       F(r, x) := r x (1 - x)
(%o2)        /usr/share/maxima/5.21.1/share/dynamics/dynamics.mac
(%i3) set_random_state(make_random_state (true));
(%o3)                                done
(%i4) x[0]:random(1.0);
(%o4)                          0.38203793012021
(%i5) evolution(F(3.5,x),0.3,25,[y,0,1]);
(%o5)
(%i6) staircase(F(3.1,x),x[0],250,[x,0,1],[y,0,1]);
(%o6)
(%i7) orbits(F(r,x), x[0], 150, 200, [r, 2.5, 4], [style, dots]);
Graph passed to plot2d...
(%o7)
(%i8) ```
Run Example
```load("dynamics");
(%o1)        /usr/share/maxima/5.21.1/share/dynamics/dynamics.mac
(%i2)  evolution(cos(y), 2, 11);
(%o2)
(%i3)  staircase(cos(y), 1, 11, [y, 0, 1.2]);
(%o3)
(%i4)  orbits(x^2+a, 0, 50, 200, [a, -2, 0.25], [style, dots]);
Graph passed to plot2d...
(%o4)
(%i5)  orbits(x^2+a, 0, 100, 400, [a,-1,-1.53], [x,-1.6,-0.8],                  [nticks, 400], [style,dots]);
Graph passed to plot2d...
(%o5)
(%i6)  f: 0.6*x*(1+2*x)+0.8*y*(x-1)-y^2-0.9;
2
(%o6)            - y  + 0.8 (x - 1) y + 0.6 x (2 x + 1) - 0.9
(%i7)  g: 0.1*x*(1-6*x+4*y)+0.1*y*(1+9*y)-0.4;
(%o7)            0.1 y (9 y + 1) + 0.1 x (4 y - 6 x + 1) - 0.4
(%i8)  evolution2d([f,g], [x,y], [-0.5,0], 50000, [style,dots]);
Graph passed to plot2d...
(%o8)
(%i9)  evolution2d([f,g], [x,y], [-0.5,0], 300000, [x,-0.8,-0.6],                       [y,-0.4,-0.2], [style, dots]);
Graph passed to plot2d...
(%o9)
(%i10)  chaosgame([[0, 0], [1, 0], [0.5, sqrt(3)/2]], [0.1, 0.1], 1/2,                      30000, [style, dots]);
(%o10)
(%i11)  a1: matrix([0.85,0.04],[-0.04,0.85]);
[  0.85   0.04 ]
(%o11)                         [              ]
[ - 0.04  0.85 ]
(%i12)  a2: matrix([0.2,-0.26],[0.23,0.22]);
[ 0.2   - 0.26 ]
(%o12)                         [              ]
[ 0.23   0.22  ]
(%i13)  a3: matrix([-0.15,0.28],[0.26,0.24]);
[ - 0.15  0.28 ]
(%o13)                         [              ]
[  0.26   0.24 ]
(%i14)  a4: matrix([0,0],[0,0.16]);
[ 0   0   ]
(%o14)                            [         ]
[ 0  0.16 ]
(%i15)  p1: [0,1.6];
(%o15)                             [0, 1.6]
(%i16)  p2: [0,1.6];
(%o16)                             [0, 1.6]
(%i17)  p3: [0,0.44];
(%o17)                             [0, 0.44]
(%i18)  p4: [0,0];
(%o18)                              [0, 0]
(%i19)  w: [85,92,99,100];
(%o19)                         [85, 92, 99, 100]
(%i20)  ifs(w, [a1,a2,a3,a4], [p1,p2,p3,p4], [5,0], 50000, [style,dots]);
(%o20)
(%i21)  results: rk(t-x^2,x,1,[t,0,8,0.1]);
(%o21) [[0, 1], [0.1, 0.91379450358526], [0.2, 0.85119154446705],
[0.3, 0.80762204166078], [0.4, 0.77980783435484], [0.5, 0.76528121159931],
[0.6, 0.76209286663879], [0.7, 0.76862962035996], [0.8, 0.78349975719287],
[0.9, 0.80546209634068], [1.0, 0.83338438612904], [1.1, 0.86622162622296],
[1.2, 0.90300766215569], [1.3, 0.94285500283235], [1.4, 0.98495890353412],
[1.5, 1.028602655744726], [1.6, 1.073161868443532], [1.7, 1.118106337679893],
[1.8, 1.162998846308774], [1.9, 1.207490859391788], [2.0, 1.251315539722856],
[2.1, 1.294278785459053], [2.2, 1.336249099869959], [2.3, 1.377147075451045],
[2.4, 1.416935155456955], [2.5, 1.455608169722248], [2.6, 1.493184965398314],
[2.7, 1.529701292830062], [2.8, 1.565203976807658], [2.9, 1.599746309038329],
[3.0, 1.633384537470932], [3.1, 1.666175296833841], [3.2, 1.698173815612652],
[3.3, 1.729432740882358], [3.4, 1.760001437982126], [3.5, 1.789925642304432],
[3.6, 1.819247362095182], [3.7, 1.848004951916355], [3.8, 1.876233295024788],
[3.9, 1.903964048771379], [4.0, 1.931225920092155],
[4.100000000000001, 1.958044948404142], [4.2, 1.984444781050193],
[4.3, 2.010446932238823], [4.4, 2.036071020584224], [4.5, 2.061334983225331],
[4.600000000000001, 2.086255266401461], [4.7, 2.110846993543088],
[4.800000000000001, 2.135124112605639], [4.9, 2.159099524690948],
[5.0, 2.182785196084777], [5.100000000000001, 2.206192255776835],
[5.2, 2.229331080383641], [5.300000000000001, 2.252211368206678],
[5.4, 2.274842203956185], [5.5, 2.297232115472118],
[5.600000000000001, 2.319389123588096], [5.7, 2.341320786116751],
[5.800000000000001, 2.363034236787538], [5.9, 2.384536219840627],
[6.0, 2.405833120871673], [6.100000000000001, 2.426930994430188],
[6.2, 2.447835588796759], [6.300000000000001, 2.468552368299581],
[6.4, 2.489086533476515], [6.5, 2.509443039343724],
[6.600000000000001, 2.529626611994107], [6.7, 2.549641763717191],
[6.800000000000001, 2.56949280680564], [6.9, 2.589183866191267],
[7.0, 2.608718891034662], [7.100000000000001, 2.628101665376626],
[7.2, 2.647335817946111], [7.300000000000001, 2.666424831207797],
[7.4, 2.685372049722584], [7.5, 2.704180687885738],
[7.600000000000001, 2.722853837100146], [7.7, 2.741394472435695],
[7.800000000000001, 2.759805458820331], [7.9, 2.778089556803467],
[8.0, 2.796249427928215]]
(%i22)  sol: rk([4-x^2-4*y^2,y^2-x^2+1],[x,y],[-1.25,0.75],[t,0,4,0.02]);
(%o22) [[0, - 1.25, 0.75], [0.02, - 1.246158635495058, 0.7500961423125],
[0.04, - 1.242144941379386, 0.75039399436677],
[0.06, - 1.237976472056585, 0.75090732826793],
[0.08, - 1.233673457277453, 0.75164931753197],
[0.1, - 1.229258873619521, 0.75263240053122],
[0.12, - 1.224758503438085, 0.75386814110392],
[0.14, - 1.220200979969758, 0.75536708687718],
[0.16, - 1.215617817198364, 0.75713862578296],
[0.18, - 1.211043423014684, 0.75919084115962],
[0.2, - 1.206515094116293, 0.76153036572607],
[0.22, - 1.202072991001326, 0.76416223459446],
[0.24, - 1.19776009131054, 0.76708973735372],
[0.26, - 1.193622119665029, 0.77031426911211],
[0.28, - 1.189707452032219, 0.77383518023857],
[0.3, - 1.186066992529512, 0.77764962439414],
[0.32, - 1.182754020442842, 0.7817524043038],
[0.34, - 1.179824005095815, 0.78613581459336],
[0.36, - 1.177334386054157, 0.79078948091588],
[0.38, - 1.175344315990573, 0.7957001945274],
[0.4, - 1.173914363368994, 0.80085174145758],
[0.42, - 1.173106171938508, 0.8062247254695],
[0.44, - 1.172982073862906, 0.81179638413311],
[0.46, - 1.173604653162043, 0.81754039756529],
[0.48, - 1.175036256021339, 0.82342668973751],
[0.5, - 1.177338444456589, 0.82942122273944],
[0.52, - 1.180571389830834, 0.83548578503706],
[0.54, - 1.184793202844304, 0.84157777559722],
[0.56, - 1.190059196902732, 0.84764998678961],
[0.58, - 1.196421082268372, 0.85365039023767],
[0.6, - 1.203926089176909, 0.85952193128647],
[0.62, - 1.212616019236172, 0.86520233949172],
[0.64, - 1.222526225991132, 0.87062396450331],
[0.66, - 1.233684527630206, 0.87571364889616],
[0.68, - 1.246110057506133, 0.88039265184607],
[0.7, - 1.259812061528131, 0.88457663998791],
[0.72, - 1.27478865560981, 0.88817576422219],
[0.74, - 1.291025561257321, 0.891094843511],
[0.76, - 1.308494843034196, 0.89323367863657],
[0.78, - 1.327153677956811, 0.8944875202516],
[0.8, - 1.346943193683259, 0.89474771604966],
[0.82, - 1.367787419377332, 0.893902561208],
[0.84, - 1.389592399951448, 0.89183837406095],
[0.86, - 1.412245530475424, 0.88844081490592],
[0.88, - 1.435615172204431, 0.88359645961467],
[0.9, - 1.459550614134664, 0.87719463108888],
[0.92, - 1.483882443368076, 0.8691294804605],
[0.94, - 1.508423382976587, 0.85930229638978],
[0.96, - 1.532969646706263, 0.84762400520355],
[0.98, - 1.557302845163907, 0.83401780759101],
[1.0, - 1.581192457837714, 0.81842188011072],
[1.02, - 1.604398859658908, 0.8007920531503],
[1.04, - 1.626676860652782, 0.78110436277011],
[1.06, - 1.647779684066543, 0.75935736374658],
[1.08, - 1.667463274373376, 0.73557408677807],
[1.1, - 1.68549079447145, 0.70980352565783],
[1.12, - 1.701637144300846, 0.68212155121849],
[1.14, - 1.715693314095556, 0.65263116828952],
[1.16, - 1.727470377317508, 0.62146205922151],
[1.18, - 1.736802932967154, 0.58876939124868],
[1.2, - 1.743551825294321, 0.55473190277193],
[1.22, - 1.747606000453641, 0.5195493225885],
[1.24, - 1.748883402457086, 0.48343921287441],
[1.26, - 1.747330861699193, 0.44663335810262],
[1.28, - 1.742922984267544, 0.40937384526926],
[1.3, - 1.735660104660618, 0.37190899382822],
[1.32, - 1.725565413992604, 0.33448929567365],
[1.34, - 1.712681416494298, 0.29736351656559],
[1.36, - 1.697065896414707, 0.26077509182898],
[1.38, - 1.678787593899442, 0.22495892307371],
[1.4, - 1.657921792039812, 0.19013865171734],
[1.42, - 1.634546009236189, 0.15652445205651],
[1.44, - 1.608735973409778, 0.12431135419629],
[1.46, - 1.580562030085215, 0.093678077571801],
[1.48, - 1.550086107766431, 0.06478633077445],
[1.5, - 1.517359333961232, 0.037780513984503],
[1.52, - 1.482420365838711, 0.012787746965167],
[1.54, - 1.445294472367309, - 0.010081861768805],
[1.56, - 1.405993380736445, - 0.030734790768411],
[1.58, - 1.364515879113663, - 0.049093609490117],
[1.6, - 1.320849149981307, - 0.065096485948111],
[1.62, - 1.274970792673916, - 0.078696763377846],
[1.64, - 1.226851479309073, - 0.089862657889942],
[1.66, - 1.176458174031112, - 0.098577113876137],
[1.68, - 1.123757830463672, - 0.10483783726982],
[1.7, - 1.068721465894, - 0.10865750918186],
[1.72, - 1.011328492844869, - 0.11006416446679],
[1.74, - 0.95157116975769, - 0.10910170204279],
[1.76, - 0.88945901358345, - 0.10583047704081],
[1.78, - 0.82502299987185, - 0.10032791000042],
[1.8, - 0.75831936274078, - 0.092689036420568],
[1.82, - 0.68943280055308, - 0.083026912163662],
[1.84, - 0.61847889596849, - 0.071472787641811],
[1.86, - 0.54560557372284, - 0.058175967361257],
[1.88, - 0.47099344772285, - 0.04330328189707],
[1.9, - 0.39485495136432, - 0.027038116815153],
[1.92, - 0.31743220037595, - 0.0095789668703652],
[1.94, - 0.23899360322501, 0.0088624873577983],
[1.96, - 0.15982930577941, 0.028063751459608],
[1.98, - 0.080245628749145, 0.047794276845619],
[2.0, - 5.5872194056019731E-4, 0.067818517746725],
[2.02, 0.078912287858366, 0.087899171563284],
[2.04, 0.15785234392838, 0.10780047299255],
[2.06, 0.23595737740323, 0.12729140659961],
[2.08, 0.31294078200983, 0.14614870716788],
[2.1, 0.3885391644033, 0.16415953175317],
[2.12, 0.46251713958638, 0.18112371028507],
[2.14, 0.53467100480505, 0.19685551040611],
[2.16, 0.60483119585457, 0.21118488413384],
[2.18, 0.672863500356, 0.22395819592459],
[2.2, 0.738669067395, 0.23503846115147],
[2.22, 0.80218330738573, 0.24430514880255],
[2.24, 0.86337381724314, 0.25165362101064],
[2.26, 0.92223749277781, 0.25699429427021],
[2.28, 0.97879700312078, 0.26025161299741],
[2.3, 1.033096802638808, 0.26136292610666],
[2.32, 1.085198846733021, 0.26027735252227],
[2.34, 1.135178162034419, 0.25695471318086],
[2.36, 1.183118401735505, 0.25136459626464],
[2.38, 1.229107495765184, 0.24348561015192],
[2.4, 1.273233485391501, 0.23330486567967],
[2.42, 1.315580614224897, 0.22081771633539],
[2.44, 1.356225733508668, 0.20602777224303],
[2.46, 1.395235069482341, 0.18894719138595],
[2.48, 1.432661394451872, 0.16959723937565],
[2.5, 1.468541640539402, 0.14800909710023],
[2.52, 1.50289499510812, 0.12422488363511],
[2.54, 1.535721518480782, 0.098298849791736],
[2.56, 1.567001326502234, 0.070298685670217],
[2.58, 1.596694381312285, 0.040306873804636],
[2.6, 1.624740931923304, 0.0084220084109984],
[2.62, 1.651062640423985, - 0.025240008418945],
[2.64, 1.675564418633595, - 0.060544990037619],
[2.66, 1.698136982931449, - 0.097339808333381],
[2.68, 1.718660111420895, - 0.13545215591234],
[2.7, 1.737006557873029, - 0.17469081982519],
[2.72, 1.753046542164934, - 0.21484654555327],
[2.74, 1.766652699194394, - 0.25569354883486],
[2.76, 1.777705330376788, - 0.29699170451503],
[2.78, 1.786097767345707, - 0.33848940687405],
[2.8, 1.791741630285331, - 0.37992705665473],
[2.82, 1.794571747239096, - 0.42104108894124],
[2.84, 1.794550498979624, - 0.46156841648525],
[2.86, 1.791671368664455, - 0.50125112871796],
[2.88, 1.785961507031818, - 0.53984126112351],
[2.9, 1.777483170955909, - 0.57710543589363],
[2.92, 1.766333952578675, - 0.61282917480321],
[2.94, 1.752645783198569, - 0.64682069962716],
[2.96, 1.736582764843979, - 0.67891406320449],
[2.98, 1.718337946919963, - 0.7089714930326],
[3.0, 1.698129219916344, - 0.73688487546786],
[3.02, 1.676194538526089, - 0.76257635795598],
[3.04, 1.652786709967479, - 0.78599809483159],
[3.06, 1.628167989078809, - 0.80713120514527],
[3.08, 1.602604710962057, - 0.82598404560251],
[3.1, 1.576362167224759, - 0.84258992608305],
[3.12, 1.549699896874009, - 0.85700440863567],
[3.14, 1.522867521788193, - 0.86930233373915],
[3.16, 1.496101213496702, - 0.87957471132779],
[3.18, 1.469620836299947, - 0.88792560054859],
[3.2, 1.443627774339149, - 0.894469083688],
[3.22, 1.418303418939926, - 0.89932641841163],
[3.24, 1.393808268362109, - 0.90262343040992],
[3.26, 1.370281575154091, - 0.90448818737051],
[3.28, 1.347841466178198, - 0.90504897609848],
[3.3, 1.326585456166837, - 0.9044325883339],
[3.32, 1.306591276277128, - 0.9027629077295],
[3.34, 1.28791794335027, - 0.90015978058846],
[3.36, 1.270607002314689, - 0.89673814612262],
[3.38, 1.25468388239122, - 0.89260739782273],
[3.4, 1.240159316628883, - 0.88787094559704],
[3.42, 1.227030783173497, - 0.88262594817405],
[3.44, 1.215283935081674, - 0.87696318643432],
[3.46, 1.204893993133896, - 0.87096705043501],
[3.48, 1.195827082800739, - 0.86471561557774],
[3.5, 1.188041502209304, - 0.85828078636638],
[3.52, 1.181488912652862, - 0.85172848928993],
[3.54, 1.176115446949019, - 0.84511889938696],
[3.56, 1.171862733875521, - 0.83850668789052],
[3.58, 1.168668839110036, - 0.83194128094465],
[3.6, 1.166469124687022, - 0.82546712168594],
[3.62, 1.165197030073474, - 0.81912392998059],
[3.64, 1.164784778659338, - 0.81294695580037],
[3.66, 1.165164013848899, - 0.80696722362472],
[3.68, 1.16626636910422, - 0.8012117663909],
[3.7, 1.168023976295294, - 0.79570384840806],
[3.72, 1.170369916605404, - 0.7904631773297],
[3.74, 1.173238618064621, - 0.78550610577341],
[3.76, 1.176566203569474, - 0.78084582351228],
[3.78, 1.180290793014432, - 0.77649254136635],
[3.8, 1.184352762925982, - 0.77245366801793],
[3.82, 1.18869496676223, - 0.76873398098354],
[3.84, 1.193262918825848, - 0.76533579291598],
[3.86, 1.198004944538232, - 0.76225911430051],
[3.88, 1.202872299638759, - 0.75950181346277],
[3.9, 1.207819260704247, - 0.75705977463589],
[3.92, 1.212803189229044, - 0.75492705465095],
[3.94, 1.217784571363951, - 0.75309603862692],
[3.96, 1.22272703528115, - 0.75155759485097],
[3.98, 1.227597348011203, - 0.75030122886372],
[4.0, 1.232365393486131, - 0.74931523660082]]
(%i23) ```
Run Example
```debugmode(true);
(%o1)                                true
(%o2)        /usr/share/maxima/5.21.1/share/dynamics/dynamics.mac
(%i3) set_random_state(make_random_state (true));
(%o3)                                done
(%i4) x[0]:random(1.0);
(%o4)                          0.69084197547386
(%i5) F(r,x):=r*x*(1-x);
(%o5)                       F(r, x) := r x (1 - x)
(%i6) orbits(F(r,x), x[0], 150, 200, [r, 2.5, 4], [style, dots]);
Graph passed to plot2d...
(%o6)
(%i7) ```

Help for Orbits