WolframLang: Plane Tiling Package 📦
PlaneTiling is a WolframLang / Mathematica package that draws any possible wallpaper patterns, and useful for creating any periodic tiling illustrations.
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Notebook Example
![plane tiling mathematica 2016-05-04 35001](plane_tiling_mathematica_2016-05-04_35001.png)
![plane tiling mathematica 2016-05-04](plane_tiling_mathematica_2016-05-04.png)
Features Gallery
Map a Motif to Lattice
generate patterns by mapping a motif to lattice.
![plane tiling 2024-03-12 234639](plane_tiling_2024-03-12_234639.png)
![islamic](islamic.png)
![plane tiling 2024-03-12 234300](plane_tiling_2024-03-12_234300.png)
![xunre tarci](xunre_tarci.png)
perturb the lattice to get a slight random effect:
![starry night](starry_night.png)
Wallpaper Design by Specifying Symmetry
The function WallpaperPlot
allows plotting of any periodic wallpaper design.
User specifies the symmetry type and motif.
This means that it'll plot any periodic tilings, Islamic patterns, or Celtic knots designs
![starSky 2024-03-12 gyds](i/starSky_2024-03-12_gyds.png)
![wallpaper16 1001](wallpaper16_1001.png)
Plot the Symmetry Diagram of Wallpapers
plot the symmetry diagram of wallpapers.
Any symmetry element graphics can be user specified.
![plane tiling 2024-03-12 233921](plane_tiling_2024-03-12_233921.png)
![plane tiling 2024-03-12 233934](plane_tiling_2024-03-12_233934.png)
![plane tiling 2024-03-12 233952](plane_tiling_2024-03-12_233952.png)
Dissect Graphics
![cutStar](cutStar.png)
StarMotif
with parallel lines in four directidions using CutPolygon
, then scaling the polygons apart.
Lattice and Network
Function to generate lattice colored regularly. This allows you to map motif to dots, accordin to color code.
![plane tiling 2024-03-12 234055](plane_tiling_2024-03-12_234055.png)
Function to generates directed graph laid out in a regular lattice. This allows you to apply line transform to the edges according to the arrow direction.
![directedNetwork1](directedNetwork1.png)
![directedNetwork2](directedNetwork2.png)
![directedNetwork3](directedNetwork3.png)
![directedNetwork4](directedNetwork4.png)
Line Tranform on Edges of Tiling
One technique of generating patterns is to apply Line Transform on the edges of regular tilings.
![plane tiling 2024-03-12 234143](plane_tiling_2024-03-12_234143.png)
Line Transform is recursively applied to a triangular network.
![plane tiling 2024-03-12 234712](plane_tiling_2024-03-12_234712.png)
![lineTransformRecurse](lineTransformRecurse.png)
![plane tiling 2024-03-12 234234](plane_tiling_2024-03-12_234234.png)