Lissajous Fly and the Cat

① This example uses an animated cat to vividly demonstrate the generation of Lissajous curves, merging abstract mathematics with playful visuals. ② Core mathematical concepts include parametric equations, trigonometric functions, curve sketching, and geometric constructions involving intersections and polygons. ③ Construction details: The GeoGebra commands used are CurveCartesian, Circle, Ray, Intersect, and Polygon; objects include a, b, c, p, d, A, image1, t, C, D, E, e, f, F, g, h, i, G, k, B, image2, j, image3, H, I, image4, image5, Speed, J, K, L, M, poly1, j_1, k_1, l, m. A Speed slider controls the animation. ④ Suitable for middle school to early college students to intuitively understand parametric curves and trigonometric relationships, or as a math-art teaching demonstration.