Italy through fourier
Italy's boot is drawn entirely by spinning circles. One chain of rotating arms rebuilds the east-west position, the other the north-south, and the pen moves where their guide lines cross. With one harmonic per coordinate, you get a plain ellipse, 7.1% off. By 8, the boot appears. The heel, the Gargano spur and the jagged Alpine border need many small, fast circles working together. At 100 harmonics per coordinate, 200 circles trace the mainland to within 0.11%.