Instructions
This applet alows one to get a feel for the discrete model predicted to converge to the Liouville quantum gravity as in recent work by Scott Sheffield. In this work, there is a way of associating to each triangulation of the sphere a 2D excursion. If one wished to examine this correspondence directly, the 'n', 's', 'e', and 'w' keys may be used to manually step the path, which is displayed in the lower left corner. Space bar clears the path. The resulting surface is illustated embedded in the main view, with the pair of embedded spanning trees highlighted in red and blue. To rotate the resulting view, you may click and drag the mouse. The view may be scaled with '-' and '=' keys. Pressing the number keys '1-0' yields random surfaces of increasingly larger size as one presses number keys farther to the right.
Higher quality rendering, and mouse wheel zooming available if source is downloaded, opened in Processing, and all lines with the comment "//***TOGGLE THIS***" after them are either changed from commented to uncommented or uncommented to commented depending on current state.
Below are a few more keboard commands:
- '\' - toggle highlighting of faces as added by the path
- '[' - step highlighted face back along path
- ']' - step highlighted face forward along path
- ''' - reset highlighted face to first face
- 'x' - toggle written path
- 'p' - toggle drawing the path in the lower left corner
- 'l' - toggle lighting on main rendering
- 't' - toggle transpacency in main rendering
- 'd' - toggle drawing edges in main rendering
- 'm' - toggle drawing faces in main rendering
- 'o' - toggle depth sorting mesh in main rendering (only in downloaded version)
- 'r' - generate new path of length 32 with random embedding
- 'b' - generate new path of length 512 with random embedding
- 'j' - randomly jitter embedding (for getting out of embeddings which are locally flat, but globally intersecting)
- 'a' - regenerate random embedding
- 'u' - toggle updating embedding (spring and repulsive force)
- 'c' - toggle repulsive force
Source code: DiscreteQGWeb
Built with Processing