Static Rotational Graph (SRG) kernel

The SRG kernel is designed to provide an extensible tiling, where neighbour/adjacency relations are generated during construction, rendering a subsequent computation of cell neighbours obsolete

[1]:

from hypertiling import HyperbolicTiling
from hypertiling.graphics.plot import plot_tiling
import matplotlib.pyplot as plt

[2]:

p, q, n = 7, 3, 2
T = HyperbolicTiling(p, q, n, kernel="SRG", center="vertex")
T.add_layer()

Access neighbours

[3]:

print(T.get_nbrs(1))
print(T.get_nbrs(9))

[0, 2, 3, 8, 9, 10, 11]
[1, 8, 10, 31, 32, 33, 34]

New layers can be added anytime

[4]:

T.add_layer()

[8]:

print(T.get_nbrs(17))

[3, 4, 16, 19, 53, 54, 55]

[9]:

plot_tiling(T, dpi=100)
for i in range(len(T)):
    z = T.get_center(i)
    l = T.get_layer(i)
    t = plt.text(z.real, z.imag, str(i), fontsize=18-3*l, ha="center", va="center")