Dilation Stars: A Symmetric Math Art Pattern Based on Scaling Transformations

① This example demonstrates a star-burst-like mathematical art pattern created through dilation (scaling) transformations and symmetric arrangements, producing a visually rhythmic radial design. ② Core mathematical concepts include dilation (homothety), symmetry, coordinate geometry, and sequence generation, with background inspiration from logarithmic functions and indefinite integrals, though the main construction relies on geometric objects. ③ Construction highlights: Using GeoGebra commands such as Circle, Ray, Point, and Sequence, with objects A, B, c, a, C, k, n, and multiple lists (list1, list2, list3, Blist, Clist, list4, list5) and parameter b, the pattern is built by generating sequences of points or shapes, then applying dilation and rotational symmetry to form the star-like arrangement. ④ Suitable for high school and above, this example is ideal for math art projects, teaching geometric transformations, or as a visual demonstration to spark interest in symmetry and scaling.