The no-spiraling conjecture for triangle tilings

Let a triangle tiling be a tiling of the plane by congruent triangles. A trajectory spirals if its successive motion winds outward in a spiral-like manner rather than being periodic or escaping in a non-spiraling way.

Triangle no-spiraling conjecture. Trajectories on triangle tilings never spiral.

The paper contrasts this conjecture with a previously proved spiraling phenomenon for divisions of the plane by an odd number of lines, and reports that spiraling is not observed on triangle tilings.