# triangle_group_limit_set - visualizer for triangle group limit sets in the projective plane

This program visualizes the fractal limit set of triangle groups in SL(3,R) in the projective plane.

## Installation & Prerequisites ##

This program is written C and exclusively for Linux. It uses [Cairo] for drawing and X11 for input, which means it will only run in the X window system. Besides these, the only required library is the [Gnu Scientific Library (GSL)] including CBLAS.

To build, make sure GCC as well as these libraries are installed, and run

    make

Then we can run it for example like this:

    ./limit_set 5 5 5 1 1 1 1.0 1.0

The arguments are 6 integers (p1, p2, p3, q1, q2, q3) and two floating point numbers (t,s) describing the triangle group under consideration (initially, t and s can be changed with the arrow keys).
The last argument is optional; if it is not given, it defaults to s = 1.

## Key bindings

Drag the mouse to move the image, drag with Shift pressed to rotate.

| Key      | function                                                                                            |
|----------|-----------------------------------------------------------------------------------------------------|
| PageUp   | increase t by 2%                                                                                    |
| PageDown | decrease t by 2%                                                                                    |
| Right    | increase t by 0.2%                                                                                  |
| Left     | decreaes t by 0.2%                                                                                  |
| Up       | increase t by 0.002%                                                                                |
| Down     | decrease t by 0.002%                                                                                |
| Space    | (reset t to original value)                                                                         |
| R        | cycle through affine charts                                                                         |
| l        | show limit curve                                                                                    |
| L        | show limit curve as line or as points                                                               |
| f        | generate limit curve using attracting / repelling fixed points of conjugates of the Coxeter element |
| d        | show dual limit curve                                                                               |
| r        | show fixed points and lines of generating reflections                                               |
| a        | show fixed points and lines of Coxeter elements                                                     |
| c        | show the orbit of an arbitrary point (point can be changed with Shift+Click)                        |
| b        | show certain conics touching the limit curve                                                        |
| B        | show the "boxes" used to approximate the limit curve                                                |
| p        | save a screenshot of the current image (in PDF format)                                              |
| t        | toggle info text                                                                                    |
| i        | (print some info to terminal?)                                                                      |
| x        | (show rotated reflectors?)                                                                          |
| M        | (make a movie)                                                                                      |

[Cairo]: https://cairographics.org/
[Gnu Scientific Library (GSL)]: https://www.gnu.org/software/gsl/