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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/

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