Knot Explorer

Explore the wonderful world of knots! Knot Explorer is a fun and engaging app for visualising and manipulating topological knots. A topological knot is a closed loop in space that is entangled or knotted, and cannot be unentangled without cutting. Picture a piece of string. Tie it in a knot in whatever way you like, and glue the ends together. This is what a topologist calls a knot. Two such knots are considered to be the same only if you can manipulate one to look like the other, without cutting. Knot theory has unexpected applications in many areas of science, from Quantum Field Theory to the structure of DNA. To study knots is to see the hidden patterns in the fabric of reality itself! Knot Explorer is your guide. Knot Explorer includes a catalogue of all knots up to 8 crossings, with hand-crafted projections and elegant 3D-embeddings. These knots can be viewed in 3d, rotated in space, and they can be manipulated and deformed. In addition to the knot catalogue, Knot Explorer can make all torus knots. A torus is a doughnut shape, with a big hole in the middle. A torus knot is a knot that can be drawn on the surface of a torus by winding around it multiple times. But wait, there's more! Knot Explorer can make satellite knots. A satellite knot is a knot tied in a knot. We take a knot drawn on the surface of a torus (or inside), and we tie the torus in a knot. In this way Knot Explorer can generate many beautifully complex knots. Unlock the fascinating world of knots with Knot Explorer!