Visual Pattern 86: A Dynamically Growing Square Sequence

① This example demonstrates a visually engaging pattern where squares expand outward in a dynamic sequence, accompanied by circles, vectors, and auxiliary lines that evolve step by step, creating a rhythmic geometric growth. ② Core mathematical concepts include quadratic functions (area or side length varying with step index), sequences and series (terms increasing by a pattern), properties of squares and polygons, and the interplay between function graphs and geometric diagrams; also involving circles, vectors, and coordinate operations. ③ Construction highlights: using GeoGebra commands such as Circle to draw circles, Point to define key points, Vector to create direction vectors, and Sequence to generate series of objects (e.g., lists l1 through l6) parameterized by i and n, with sliders or parameters enabling dynamic updates, resulting in an interactive visual sequence. ④ Suitable for upper secondary to early university students, this example is ideal for exploring the connection between algebra and geometry, visualizing sequence patterns, and serving as a resource for mathematical modeling or art-integrated math lessons.