A point wanders around a square. Its X coordinate is sinusoidal with period 1, and Y with period phi (golden ratio). This traces out a Lissajous curve.
A billiard ball bounces at a 45 degree angle on a table with dimensions in golden ratio. Somewhat equivalently, a square table at angle arctan phi.
The orthogonal projections of a point to the sides of the box form a diamond of ever-changing shape.
Circles through points, tangent to edges, etc. Tangent to nearest edge gives a way to draw an infinitesimally small point as a blob.
For a given point in a rectangle, what is the largest circle within the rectangle that contains that point? Of those largest circles the same size, which has its center closest to the point? Balloon inflating.
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