Thomas' Attractor

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2017-08-30 18:37

Function Parametric Equation

This example demonstrates the dynamic changes of Thomas' attractor, a chaotic attractor defined by parametric equations. By adjusting parameters, the shape of the attractor can be observed. The example uses GeoGebra's parametric equation commands, suitable for high school mathematics education and chaos theory research.

GeoGebra Commands & Parameters

Numeric strength(5)
Numeric n(12)
Numeric h(0.01)
Numeric speed(1)
Numeric t(4.41)
Numeric b(0.208186)
x(CornerThreeD[-1, 3])
x(CornerThreeD[-1, 1])
y(CornerThreeD[-1, 3])
y(CornerThreeD[-1, 1])
z(CornerThreeD[-1, 5])
z(CornerThreeD[-1, 3])
{(-3.088783806756721, 1.168136040091289, 2.4092146463877135), (-1.067266093085597, -4.526392273525671, -1.2647999308806441), (4.543682308993006, -0.8625165719344299, 3.758402273622612), (5.31874067749
{4.035969339822303, 2.5640068684061235, -0.5488025204846856, 1.6973833705951398, -1.6089006075240053, 3.255710387114754, -1.2449332890219835, 0.44041183228428177, 1.6012293652475966, -1.90560109628771
{2.733327134413032, -3.5747872338096442, 0.8433804981200355, 0.4696137096695083, -0.3634135696995436, -5.534989044346133, 1.1011617143616148, -2.2392210889929838, 0.7845254086839506, -0.45671631349686
{2.8886657735972325, 1.4402279875984714, -1.3523016627727336, -0.37930893474328625, 0.25207991548283737, -2.745374055522856, -1.7256404176220146, 1.6141422251964177, -2.883298518282407, -0.30129472715
{4.0188274657474246, 2.5974154682502486, -0.5634828276654941, 1.6832501793784087, -1.5960168705620137, 3.357840639225082, -1.2651891520660596, 0.48715650315538567, 1.5969562696763235, -1.8907077403827
{2.75544405271308, -3.5907998692147105, 0.8705302878924062, 0.4752751566388502, -0.3669496704258893, -5.562715723832097, 1.1117752441773454, -2.2677237377267794, 0.8449377770925273, -0.447866117655487
{2.9342290483083877, 1.429948070893332, -1.3379561392625487, -0.4149909263812776, 0.28584729899567424, -2.670452048143659, -1.7477251882917264, 1.6024807305199102, -2.908313334254466, -0.2615642672040
{4.018944145262599, 2.597447943441865, -0.5639701335031142, 1.6832597064937516, -1.5960399724077812, 3.357900626825879, -1.2653412387215845, 0.487535439595482, 1.5972880854285365, -1.8908818901504358,
{2.75589495234996, -3.5904696886653493, 0.870053976020716, 0.4760077145817293, -0.3676580062148446, -5.561035690594278, 1.1119269501779971, -2.2672851604418014, 0.8451808595859309, -0.4487660983664943
{2.9337379831643204, 1.4299598809136986, -1.3378348979967352, -0.41449098804038825, 0.28539001606491615, -2.6689256977786524, -1.7481158058834454, 1.6021940059448658, -2.9080763482125427, -0.262070361
{4.000970668974891, 2.6294993366879513, -0.5790601859665776, 1.669094113635437, -1.5831468273852227, 3.4580034165260995, -1.2857177025138662, 0.5343227749771753, 1.5932584430439134, -1.876118572243801
{2.7775122031002066, -3.606085005399855, 0.8968066245626816, 0.48236157568022076, -0.3718702062845805, -5.586527643657149, 1.1223437798494862, -2.2953698777911393, 0.905344240154623, -0.44078037574610
{2.977192464233033, 1.4188492949226017, -1.3233227695140966, -0.44984063058479073, 0.3188605759133678, -2.5915598602557766, -1.770606201293751, 1.590214769504517, -2.932865104308529, -0.22256788772390
F(x, y, z) = (strength * (sin(y) - (b * x)))
G(x, y, z) = (strength * (sin(z) - (b * y)))
H(x, y, z) = (strength * (sin(x) - (b * z)))

AI Drawing Prompt Reference

Draw Thomas' Attractor, a chaotic attractor defined by parametric equations. First, set the parameters strength to 5, n to 12, h to 0.01, speed to 1, t to 4.41, and b to 0.208186. Then, use the parametric equations F(x, y, z) = strength * (sin(y) - (b * x)), G(x, y, z) = strength * (sin(z) - (b * y)), and H(x, y, z) = strength * (sin(x) - (b * z)) to draw the attractor.

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