Click points on S² and watch their fibers appear in real time — build your own fibration
Your turn: place points on the sphere and build the Hopf fibration one circle at a time.
Click the map of S² (top edge north pole, bottom edge south pole) and each point's fiber appears in the 3D view. Click along a row to build a torus, down a column to get circles growing toward a line, or scatter points and see that every pair links.
Equirectangular projection of S² — top = north pole, bottom = south pole
Click anywhere on the equirectangular map of S² to place a base point. The corresponding Hopf fiber instantly appears in the 3D viewer below. Build up your own collection of fibers and watch the structure emerge.
Try clicking along a latitude line to see a torus form. Click scattered points to see how fibers from distant base points still link with each other.
Try this: Click a vertical line of points (same longitude, varying latitude) to see a family of linked circles that grow from the unit circle at the top toward a near-line at the bottom.
For comparison, here is the full fibration with evenly spaced base points. The mathematical structure you built by hand in the explorer above is the same structure — just more densely sampled.
Spot a mistake or have an idea?