I am trying to graph the function $f : (x,y) \mapsto \frac{3x^2 y}{x^2+y^2}$ on a TI-89 Titanium. I have noticed that no matter how many times I zoom in toward the origin the graph appears identical. I know that $f(x,y)$ is continuous and differentiable everywhere except $(0,0)$ and that $f(x,y)$ approaches $0$ as $(x,y)$ approaches $(0,0)$ but I have no idea why the fractal behavior is occurring.
2026-04-22 21:34:01.1776893641
Graph of $f(x,y) = \frac{3x^2 y}{x^2+y^2}$ near the origin
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It happens because $f(ax,ay) = af(x,y)$