The squishing, stretching and folding of the horseshoe map are typical of chaotic systems, but not necessary or even sufficient.
Its rather strange tasting pavlova however, squishing sour pain with halcyon nostalgia.
One way to debug is through squishing the bugs with a mallet.
This is harder to describe without getting technical, but the essential notion is that two objects are homotopy equivalent if they both result from squishing some larger object.
This puddle may then be entered (usually accompanied by a watery squishing sound), and the traveler will emerge from a similar pool at the destination stargate.