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https://github.com/vmagnin/penrose_tiling
This project generates a SVG file with a Penrose tiling, using the cairo-fortran bindings.
https://github.com/vmagnin/penrose_tiling
cairo fortran fortran-package-manager penrose-tilings
Last synced: about 1 month ago
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This project generates a SVG file with a Penrose tiling, using the cairo-fortran bindings.
- Host: GitHub
- URL: https://github.com/vmagnin/penrose_tiling
- Owner: vmagnin
- License: gpl-3.0
- Created: 2023-06-06T18:26:19.000Z (over 1 year ago)
- Default Branch: main
- Last Pushed: 2024-04-20T11:12:08.000Z (9 months ago)
- Last Synced: 2024-10-25T09:24:49.372Z (3 months ago)
- Topics: cairo, fortran, fortran-package-manager, penrose-tilings
- Language: Fortran
- Homepage:
- Size: 191 KB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- License: LICENSE
Awesome Lists containing this project
README
# A Penrose tiling
This project generates a SVG file with a *Penrose tiling* (an aperiodic tiling of the plane with two tiles), using the [cairo-fortran](https://github.com/vmagnin/cairo-fortran) bindings as a fpm (Fortran Package Manager) dependency.
The algorithm uses acute and obtuse golden triangles, with two interlaced recursive procedures. See the figures in https://fr.wikipedia.org/wiki/Pavage_de_Penrose to understand.
See the project https://github.com/vmagnin/hat_polykite for more information on the *ein Stein* problem and the tiling of the plane, and the most recent results in this domain.
Be careful with the number of recursions: the SVG file is growing like the Fibonacci sequence! 12 recursions will generate a 12.7 Mio SVG file. 15 recursions will give a 228 Mio file and your SVG viewer may freeze or crash...
## Requirements and dependencies
You need:
* a modern Fortran compiler, for example GFortran or the Intel ifort/ifx compilers. See the [Fortran-lang.org compilers page](https://fortran-lang.org/compilers/) for other compilers.
* The Cairo development files (`libcairo2-dev` package in Ubuntu).
* The Fortran Package Manager [fpm](https://fpm.fortran-lang.org/).
## Running the program
Just type `fpm run` and fpm will manage the dependencies and build and run the program:
```bash
$ fpm run
+ mkdir -p build/dependencies
Initialized empty Git repository in penrose_tiling/build/dependencies/cairo-fortran/.git/
remote: Enumerating objects: 23, done.
remote: Counting objects: 100% (23/23), done.
remote: Compressing objects: 100% (22/22), done.
remote: Total 23 (delta 0), reused 14 (delta 0), pack-reused 0
Unpacking objects: 100% (23/23), 82.99 KiB | 1.51 MiB/s, done.
From https://github.com/vmagnin/cairo-fortran
* branch HEAD -> FETCH_HEAD
cairo-enums.f90 done.
cairo-auto.f90 done.
triangles.f90 done.
libpenrose_tiling.a done.
main.f90 done.
penrose_tiling done.
[100%] Project compiled successfully.
----------------------------------
8 recursions
These are Fibonacci numbers:
610 blue acute triangles
377 yellow obtuse triangles
----------------------------------
Output file: penrose_tiling.svg
----------------------------------
```
## Licenses
This project is licensed under the [GNU General Public License version 3 or later](http://www.gnu.org/licenses/gpl.html).
The documentation is under the [GNU Free Documentation License 1.3 or any later version](http://www.gnu.org/licenses/fdl.html). The figures are under [CC-BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) license.
## Cairo documentation
* https://cairographics.org/documentation/
* API Reference Manual: https://cairographics.org/manual/
## Bibliography
* Roger Penrose, Set of tiles for covering a surface, Patent GB1548164A ([US-4133152-A](https://patents.google.com/patent/US4133152A/en)), filed 1975-06-25.
* Hargittai, Istvan, et Balazs Hargittai. « 2020 Physics Nobel Laureate Roger Penrose and the Penrose Pattern as a Forerunner of Generalized Crystallography ». *Structural Chemistry* 32, no.1 (1st February 2021): 1‑7. https://doi.org/10.1007/s11224-020-01669-8
* https://en.wikipedia.org/wiki/Einstein_problem
* https://en.wikipedia.org/wiki/Penrose_tiling
* https://fr.wikipedia.org/wiki/Pavage_de_Penrose
* https://en.wikipedia.org/wiki/Golden_ratio
* https://en.wikipedia.org/wiki/Golden_triangle_(mathematics)