Generative Reflection (GR) kernel

In this notebook we provide examples of how tilings made with the generative reflection (GR) kernel can be used

from hypertiling import HyperbolicTiling
from hypertiling.graphics.plot import plot_tiling

import matplotlib.cm as cmap
import numpy as np
import time

Example 1: The hypertiling logo

t1 = time.time()
t = HyperbolicTiling(7, 3, 3, kernel="GR")
print(f"Generation of {len(t): d} polygons took {time.time() - t1} s")

Generation of  29 polygons took 0.0010960102081298828 s

ct = np.zeros(len(t))
for i, poly in enumerate(t):
    val = np.real(poly[0])-np.imag(poly[0])
    ct[i] = np.sign(val)*(np.abs(val))**1.4

plot_tiling(t, ct, cmap=cmap.RdYlGn, edgecolor="w", lw=5, clim=[-1,1]);

Example 2: Save as vector graphics

from hypertiling import HyperbolicTiling
import hypertiling.graphics.svg as svg
import numpy as np

tiling = HyperbolicTiling(5,4,6, kernel="GR")
colors = [0.0, 0.2, 0.4, 0.6, 0.8, 1.0]

# query layer information
tiling_colors = [colors[tiling.get_layer(i) % len(colors)] for i in range(len(tiling))]
# create and draw svg image
tiling_svg = svg.make_svg(tiling, tiling_colors, unitcircle=True, cmap="RdBu_r")
svg.draw_svg(tiling_svg)

Layers are not yet mapped. Start mapping

Example 3: Voter model

In this simple statistic model, cells will always take on the color of the majority of their adjacent cells

from hypertiling.graphics.plot import plot_tiling

import random
import matplotlib.pyplot as plt
import matplotlib.cm as cmap

t1 = time.time()
p, q, n = 7, 3, 11
t = HyperbolicTiling(p, q, n, kernel="GR")
print(f"Generation of {len(t): d} polygons took {time.time() - t1} s")

Generation of  76616 polygons took 0.07186460494995117 s

Extract the neighbours

nbrs = t.get_nbrs_list()

The actual voter model

# initial state
states = np.random.randint(0, 2, size=len(t))
plot_tiling(t, states, cmap=cmap.Greys, edgecolor="k", cutoff=0.01, lw=0.7, clim=[0,2]);

# final state
its = 2 * len(t)  # 2 times is a bit lazy but it is just an example
p_2 = p // 2

for i in range(its):
    index = int(len(t) * np.random.random())
    sum_ = sum([states[nbr] for nbr in t.get_nbrs_mapping(index)])
    # sum_ = sum([states[nbr] for nbr in nbrs[index]]) # faster neighbor access but more memory requiered
    if sum_ > p_2:
        states[index] = 1
    else:
        states[index] = 0

plot_tiling(t, states, cmap=cmap.Greys, edgecolor="k", cutoff=0.01, lw=0.7, clim=[0,2]);