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Florian Stecker 2024-01-10 11:14:13 -05:00
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# 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/