Growing an infinite walk by photocopier

A real run of anchor-guided amplification in 2D. Rule of the game: the walk may only use hops from a fixed menu (all 24 vectors with coordinates in −2…2), may never revisit a point, and no three of its points may ever lie on one straight line. Each level enlarges the previous walk by the matrix M=[[4,−1],[1,4]] — scale ×√17 ≈ 4.12, rotation ≈ 14.0° (an irrational angle, so no two levels ever align) — then stitches the enlarged skeleton back together with legal hops.

Level:

show previous level (gray, before enlargement) show enlarged skeleton (dashed)

anchor — inherited from previous level, safe for free stitch — new point, checked against everything previous level / skeleton

Try to break it: click any three points. The exact integer test (q−p)×(r−p) is zero only for collinear points.

Every coordinate here is real output of the search code (seed 11), and every level was re-verified exactly — this page also re-runs the full integer check in your browser when it loads (see badge in the top-right of the diagram). The same construction in 3D, with 124 menu vectors and a modulus-3 rotation matrix, chained 6 levels to a verified 28,271-step walk. Code & data: github.com/ekalvi/erdos-193.