 | PolycutA program for visualizing multiple universes connected by a certain kind of wormhole |
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Polycut Description
The Polycut application was designed to be a program for visualizing multiple universes connected by a certain kind of wormhole. In mathematical terms, Polycut shows what a branched covering space of 3-space would look like from the inside. If you know nothing of covering spaces, you should now read enough of section 4 of this documentation to get some idea. Each sheet (or universe) of the covering space is colored a different color at infinity: red, green, blue, ... . The branch curves are dashed black and white. The observer is located in one of the sheets (red to start with) and looks toward the branch curves, seeing other colors in the background as the line of sight passes to other sheets. The screen thus shows regions of constant color separated by dashed branch curve. The user may rotate the branch curve with the mouse. The purpose of Polycut is to illustrate the author's contention that soap films are best viewed as minimal cuts in covering spaces. In particular, any covering space has associated to it a set that is the minimal area cut that can separate the red sheet from the others. To illustrate that, each of the example covering spaces comes with a soap film that may be inserted into the covering space, showing how it blocks all lines of sight to the other sheets.
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