51 lines
3.8 KiB
Markdown
51 lines
3.8 KiB
Markdown
# triangle_group_limit_set - visualizer for triangle group limit sets in the projective plane
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This program visualizes the fractal limit set of triangle groups in SL(3,R) in the projective plane. For the mathematical details, see [our paper].
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## Installation & Prerequisites ##
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This program is written C and only runs on Linux with the X window system (because that's what I happen to be using). It uses [Cairo] for drawing and X11 for input. We also require the [Gnu Scientific Library (GSL)] including CBLAS.
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To build, just make sure GCC as well as these libraries are installed, and run
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make
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Then we can run it for example like this:
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./limit_set 5 5 5 1 1 1 1.0
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The arguments are 6 integers (p1, p2, p3, q1, q2, q3) and a floating point numbers t. Together they discribe the triangle group under consideration (t can be changed with the arrow keys).
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## Key bindings
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Drag the mouse to move the image, drag with Shift pressed to rotate.
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| Key | function |
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|----------|-----------------------------------------------------------------------------------------------------|
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| PageUp | increase t by 2% |
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| PageDown | decrease t by 2% |
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| Right | increase t by 0.2% |
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| Left | decreaes t by 0.2% |
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| Up | increase t by 0.002% |
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| Down | decrease t by 0.002% |
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| Space | (reset t to original value) |
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| R | cycle through affine charts |
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| l | show limit curve |
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| L | show limit curve as line or as points |
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| f | generate limit curve using attracting / repelling fixed points of conjugates of the Coxeter element |
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| d | show dual limit curve |
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| r | show fixed points and lines of generating reflections |
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| a | show fixed points and lines of Coxeter elements |
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| c | show the orbit of an arbitrary point (point can be changed with Shift+Click) |
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| b | show certain conics touching the limit curve |
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| B | show the "boxes" used to approximate the limit curve |
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| p | save a screenshot of the current image (in PDF format) |
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| t | toggle info text |
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| i | (print some info to terminal?) |
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| x | (show rotated reflectors?) |
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| M | (make a movie) |
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[Cairo]: https://cairographics.org/
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[Gnu Scientific Library (GSL)]: https://www.gnu.org/software/gsl/
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[our paper]: https://arxiv.org/abs/2106.11349
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