Cutting finer

Drag Cuts, or press play and let it cut by itself: at every cut each rhomb is split into smaller thick and thin ones, the half cut off joining the half next door into a new rhomb, and the gold and ice-blue arcs still meet across every shared edge. The corner counts the thick and thin rhombs whose centres fall inside the frame (a half-rhomb at the wheel's rim counts as ½), and the small chart shows that ratio at every cut for the same view (left blank while no thin rhomb is counted). At every cut the ratio is one whole number over another; it wanders around φ and need not come closer at every cut, but as the cutting goes on it tends to φ ≈ 1.618. That is no fraction, so this is not a pattern that repeats like wallpaper. Then drag Zoom: the view closes in on a point a little off the centre and the tiles grow; zoom in by φ (1.62, 2.62, 4.24…) and cut once more, and they are back to their old size, the pattern splitting and growing back with no bottom to reach. Switch to Highlight arcs: the tiles fade back and the arcs join into smooth curves, many of which close into loops.