2D Vector Fields

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2016-04-11 14:03

This example demonstrates 2D vector fields. The core mathematical concepts involved are vectors and functions. Using GeoGebra commands such as Sequence, Textfield, and InputBox, the vector field can be constructed. Suitable for high school math education to help students understand the concept of vector fields.

GeoGebra Commands & Parameters

Sequence(Sequence[Vector[(j, k), (j + (scale * P(j, k)), k + (scale * Q(j, k)))], j, xmin, xmax, xstep], k, ymin, ymax, ystep) → vField, {{(0.39310588570054406, 0.3993755983071696), (0.3445783413196275, 0.38319742904359266), (0.25503221937022236, 0.32140346916742457), (0.1351270828854323, 0.22134966660835165), (-0.0008635704943336098, 0.09494641783985536), (-0.1367514245130832, -0.04275924474286752), (-0.2563604001423523, -0.17537485032857125), (-0.34545225470575086, -0.2871138480746316), (-0.39342150112265173, -0.3646748368282102), (-0.3945578842228717, -0.39882496283160096), (-0.3487261290551025, -0.3854989978784129), (-0.2613820440060508, -0.3262832637467761), (-0.14292306181630154, -0.22822679658461453), (-0.007450530037259373, -0.10300223022311883)}, {(0.34515907424362036, 0.3684597923105941), (0.2559142630588629, 0.3994379828078256), (0.13620543893016546, 0.38286710850064587), (0.00028273049112303994, 0.3207197649112916), (-0.13567363416245914, 0.22039396673776346), (-0.2554794205017489, 0.09383248878924277), (-0.3448729575195324, -0.043898800950424866), (-0.39321284588048666, -0.17640438101532707), (-0.3947447092277218, -0.2879107979918376), (-0.3492861946736704, -0.36514433712290284), (-0.26224868007290847, -0.39891112422709885), (-0.1439931040449305, -0.3851915637292431), (-0.008596600688279388, -0.3256188309889114), (0.12782324131120992, -0.22728445923920892)}, {(0.2567942050409946, 0.29439741919793194), (0.13728267638207736, 0.3689044296176571), (0.0014290291546434908, 0.3994970869074663), (-0.13459472958648222, 0.382533643645677), (-0.2545963427257989, 0.3200334267307752), (-0.344290828049834, 0.21943645687257463), (-0.39300096136150164, 0.09271778913542117), (-0.3949282923752607, -0.04503799663725716), (-0.34984339176486495, -0.17743246297378112), (-0.26311316241159477, -0.28870538342966334), (-0.14506196372421498, -0.36561083865456867), (-0.009742600739359508, -0.39899400954842923), (0.12673652064068652, -0.38488096617836587), (0.24812893696912797, -0.3249517240728803)}, {(0.13835878639431032, 0.18586116787301954), (0.00257531608220285, 0.2951722423727241), (-0.13351471964570116, 0.36934603728177806), (-0.25371117406681565, 0.3995529101206968), (-0.3437058710774181, 0.38219703721727993), (-0.3927858493058072, 0.31934446026245666), (-0.39510863215780423, 0.21847714487637448), (-0.3503977157526819, 0.09160232803290724), (-0.26397548392251224, -0.04617682244767218), (-0.14612963207610052, -0.17845908776076747), (-0.010888520778926436, -0.2894975978625429), (0.12564875914122609, -0.3660743375920448), (0.24722882104970445, -0.3990736181148933), (0.3393787843206524, -0.38456720777657694)}, {(0.0037215818598719252, 0.05556061140203139), (-0.13243361320974256, 0.18687544527857014), (-0.25282392179428337, 0.2959446414332225), (-0.3431180914062679, 0.36978461167623544), (-0.39256751148002, 0.3996054519890667), (-0.3952857270943043, 0.3818572919798489), (-0.3509491620847125, 0.3186528711645016), (-0.26483563752380984, 0.21751603862755264), (-0.1471961003323165, 0.0904861146424718), (-0.01203435139606468, -0.04731526902901606), (0.12455996574611516, -0.17948424694508724), (0.24632667475332526, -0.29028743478438246), (0.33877067654434123, -0.36653483012882715), (0.39088744470672454, -0.3991499492727022)}, {(-0.1313514191572378, -0.08124608142059375), (-0.25193459319479783, 0.056695571359404784), (-0.3425274938635485, 0.18788818796176865), (-0.39234594967724834, 0.29671461003606797), (-0.3954595757303614, 0.37022014919921886), (-0.3514977262321809, 0.3996547120810737), (-0.2656936161514404, 0.3815144107235558), (-0.14826135973444807, 0.3179586651166142), (-0.013180083180592383, 0.21655314601923392), (0.12347014939711498, 0.08936915813106361), (0.2454225054889041, -0.04845332703174887), (0.3381597865997865, -0.1805079321075781), (0.3906425543710723, -0.29107488770861323), (0.3966232644197021, -0.36699231248310116)}, {(-0.2510431955720076, -0.20853887455025671), (-0.34193408329956676, -0.0801233424927294), (-0.392121165717078, 0.057830065702044825), (-0.39563017663823663, 0.18889938760542394), (-0.3520434036899811, 0.29748214185786126), (-0.26654941275921884, 0.37065264627385835), (-0.1493254015340082, 0.39970068999216724), (-0.014325706723139889, 0.38116839626432714), (0.12237931904438737, 0.3172618478199903), (0.2445163206819687, 0.21558847495921393), (0.3375461195039462, 0.08825146767173432), (0.3903944558672259, -0.04959098710952198), (0.39677026813345595, -0.18153013484118347), (0.35591458013192634, -0.2918599501682457)}, {(-0.3413378645877314, -0.31141180767112053), (-0.3918931614455563, -0.2075598291531507), (-0.39579752841686267, -0.07899994554858869), (-0.35258618997671465, 0.05896408511286974), (-0.26740302031887997, 0.18990903590501684), (-0.15038821699250948, 0.29824723059521546), (-0.015471212615226215, 0.37108209934825387), (0.12128748364642172, 0.39974338534475173), (0.24360812777459928, 0.380819251443821), (0.3369296802965873, 0.3165624249972709), (0.3901431512327045, 0.21462203336989383), (0.39691401335491205, 0.08713305244356317), (0.3564362637899543, -0.05072823991925486), (0.27352837053546963, -0.1825508467510207)}, {(-0.3916619387351781, -0.3778184811326462), (-0.39596162969185644, -0.31069110182264936), (-0.3531260806347263, -0.2065790791623316), (-0.2682544318201363, -0.07787589981411563), (-0.15144979738153563, 0.060097620278697805), (-0.016616591449336693, 0.19091712456876908), (0.12019465216996184, 0.2990098699648076), (0.24269793422536778, 0.3715085048955039), (0.3363104740402423, 0.3997827977881899), (0.38988864253135813, 0.38046697912940386), (0.3970544989035567, 0.31586040239249513), (0.3569550202003693, 0.21365382918821518), (0.2743636450869871, 0.08601392163158184), (0.159112044101966, -0.05186507612121177)}, {(-0.39612247911552867, -0.39998268691089667), (-0.3536630712301416, -0.3774405093418199), (-0.2691036402707354, -0.3099678444106071), (-0.15251013398281388, -0.20559663263224937), (-0.017761833819000095, -0.07675121452058264), (0.11910083358993145, 0.06123066189032467), (0.24178574750927662, 0.19192364531771022), (0.33568850582016835, 0.29977005370343), (0.3896309318533496, 0.3719318594137355), (0.3971917236256466, 0.3998189269988055), (0.357470845102863, 0.38011158221412655), (0.27519666641567997, 0.31515578577105274), (0.160163099066021, 0.2126838703655951), (0.02606372950288094, 0.08489408442669844)}, {(-0.35419715735290325, -0.3753090009945055), (-0.2699506386965178, -0.3999917095979326), (-0.15356921808828572, -0.3770594378051422), (-0.018906930318866033, -0.3092420413747752), (0.11800603688936107, -0.20461249763128708), (0.24087157511769697, -0.07562589890451421), (0.33506378074430515, 0.062363200642598926), (0.389370021315139, 0.19292858988574713), (0.3973256863942177, 0.3005277755680422), (0.3579837342612018, 0.37235215942613187), (0.27602742768032584, 0.3998517726798856), (0.16121283868397596, 0.37975306361670125), (0.02720748655588001, 0.3144485809196367), (-0.11003664254659551, 0.21171216486786082)}, {(-0.27079542014147373, -0.3066867070111836), (-0.1546270410001791, -0.37570396160457764), (-0.02005187154478172, -0.39999744733644893), (0.11691027105931417, -0.3766752696521791), (0.23995542455830754, -0.308513698675841), (0.3344363039432334, -0.2036266822416939), (0.3891059130594647, -0.0744999622076119), (0.3974563861090956, 0.06349522723449885), (0.3584936834632626, 0.19393195001973051), (0.27685592205826337, 0.3012830293358222), (0.162261254334801, 0.37276940148096194), (0.028351020166266006, 0.39988133456168407), (-0.1089341171241025, 0.3793914262814764), (-0.2332517460214667, 0.3137387936461966)}, {(-0.15568359403107923, -0.20215146169960563), (-0.021196648093869896, -0.30742135573677887), (0.11581354509881292, -0.3760958367302689), (0.23903730335503304, -0.3999999000793244), (0.3338060805701324, -0.3762880080379274), (0.3888386092553268, -0.3077828222953496), (0.3975838216969034, -0.20263919455951962), (0.35900068852106587, -0.07337341367667705), (0.277682142745448, 0.06462673236920957), (0.16330833740833928, 0.19493371747952426), (0.029494320942721863, 0.30203580880421677), (-0.10783069707565063, 0.3731835821516081), (-0.23231955773334034, 0.3999076124014225), (-0.3291531172392881, 0.3790266731784142)}, {(-0.022341250564605897, -0.073944321131449), (0.11471586801476485, -0.20313977132362426), (0.23811721904798144, -0.30815347975172847), (0.3331731158007376, -0.37648462315328834), (0.38856811209796893, -0.3999990678064156), (0.39770799211107094, -0.37589765614278914), (0.3595047452708119, -0.30704941823565335), (0.27850608295650836, -0.20165004269454823), (0.16435407930537738, -0.0722462625635365), (0.030637379495842887, 0.0657577067541979), (-0.10672639146312246, 0.19593388403807088), (-0.23138546151120187, 0.30278610779099324), (-0.3285004251454251, 0.37359469803659406), (-0.38651072503756456, 0.3999306059832932)}}
Textfield(P) → InputBox1
Textfield(Q) → InputBox2

AI Drawing Prompt Reference

Create a 2D vector field with vectors emanating from each point, whose directions and lengths are determined by functions P and Q. First input functions P and Q, then generate the vector field based on these functions.

The prompt above was compiled from the original drawing commands and is for reference only.