Sliceform of a Monkey Saddle

This example demonstrates how to construct a sliceform model of a monkey saddle using a series of intersecting planar slices, revealing the intricate geometry of this special surface. The monkey saddle is a classic multi-saddle surface, typically defined by z = x³ - 3xy², featuring three descending and three ascending directions at the origin, unlike the ordinary saddle which has two. The construction uses GeoGebra's Sequence command to generate a set of parallel or rotated slicing planes, with objects a, L1, l4, and l5 controlling the spacing, orientation, and number of slices, resulting in an interactive 3D slice structure. This example is suitable for high school to university-level mathematics, aiding in the understanding of multivariable function surfaces, the slicing method (cross-section method), and 3D visualization, and can also serve as an extension topic for fractal geometry or similarity transformations.