Getting Started

This Jupyter notebook demonstrates how a hyperbolic tiling can be constructed and plotted using only very few lines of code.

Import tiling object from hypertiling library

[1]:
from hypertiling import HyperbolicTiling

Set parameters, initialize and generate the tiling

[2]:
p = 7
q = 3
nlayers = 5

T = HyperbolicTiling(p,q,nlayers)
T.generate()

The size of the tiling can be queried like this

[3]:
print("Number of cells:", len(T))
Number of cells: 232

Import and use available script for a quick plot

[10]:
from hypertiling.plot import plot_tiling
[12]:
import matplotlib.cm as cmap
import numpy as np
colors = np.random.rand(len(T))

plot_tiling(T, colors, cmap=cmap.RdBu, edgecolor="k", linewidth=0.12);
../_images/nbcopies_examples_10_0.png

By default, tilings are centered around a “cell”. They can also be centered around a vertex at the origin, using the following syntax

[29]:
p = 4
q = 5
nlayers = 4

T = HyperbolicTiling(p,q,nlayers, center="vertex")
T.generate()
print("Number of cells:", len(T))
Number of cells: 480
[37]:
plot_tiling??

This example also demonstrates how keyword arguments like “clim” can easily be passed through the plot function

[38]:
plot_tiling(T, np.random.rand(len(T)), cmap=cmap.OrRd, edgecolor="w", lw=0.5, clim=[-1,2]);
../_images/nbcopies_examples_15_0.png

In the next example we demonstrate how one can easily iterate over the cells of a tiling, e.g. in order to access their attributes

[65]:
T = HyperbolicTiling(7,3,7, center="cell")
T.generate()

Paint cells by number of layer in which they reside

[67]:
colors = []
for t in T:
    colors.append(t.layer)

plot_tiling(T, colors, cmap=cmap.GnBu, edgecolor="k", lw=0.2);
../_images/nbcopies_examples_19_0.png

Finally, something which just looks nice :)

[73]:
T = HyperbolicTiling(3, 12, 4, center="vertex")
T.generate()
[81]:
plot_tiling(T, np.random.rand(len(T)), cmap=cmap.OrRd, edgecolor="w", lw=0.4, clim=[-1,2]);
../_images/nbcopies_examples_22_0.png