Honeycombs in nature are not entirely regular. In a 2016 study, Nazzi found that cell size variation in honeycomb averaged just 2.1%, with standard deviation across samples of ±0.6%. This highlights how remarkably consistent bees are — yet not perfectly so.
A little irregularity might actually help bees, by making the environment less predictable for their enemies
- Mites might find entirely regular honeycombs easier to deal with
- Entirely regular honeycombs might produce bees with less variety in sizes
- This might make it easier for predators and parasites to specialise given less variance in the bees
- It might slightly reduce the variety of foods bees eat
When we manage hives, we often insert wax foundation sheets embossed with perfect hexagons to guide the bees' construction. But maybe we shouldn’t.
Maybe our foundation should closely match the natural variation bees already produce. It might be a small change — but one that works with evolution, not against it.
Here’s the code I used to simulate a naturally varied honeycomb layout.
import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi
from shapely.geometry import Polygon, Point
def generate_jittered_hex_points(rows, cols, spacing=1.0, jitter=0.05):
"""Generate a grid of points in a hexagonal layout with jitter applied."""
points = []
h = np.sqrt(3) * spacing / 2 # vertical distance between rows
for row in range(rows):
for col in range(cols):
x = col * 1.5 * spacing
y = row * h * 2 + (h if col % 2 else 0)
# Add jitter
x += np.random.uniform(-jitter, jitter) * spacing
y += np.random.uniform(-jitter, jitter) * spacing
points.append((x, y))
return np.array(points)
def filtered_voronoi_polygons(vor, points, margin):
"""Return only Voronoi regions that are within the central margin area."""
regions = []
valid_polygon_centers = []
center_x = (np.max(points[:, 0]) + np.min(points[:, 0])) / 2
center_y = (np.max(points[:, 1]) + np.min(points[:, 1])) / 2
width = np.max(points[:, 0]) - np.min(points[:, 0])
height = np.max(points[:, 1]) - np.min(points[:, 1])
allowed_box = Polygon([
(center_x - width/2 + margin, center_y - height/2 + margin),
(center_x - width/2 + margin, center_y + height/2 - margin),
(center_x + width/2 - margin, center_y + height/2 - margin),
(center_x + width/2 - margin, center_y - height/2 + margin),
])
for point_idx, region_index in enumerate(vor.point_region):
region = vor.regions[region_index]
if not region or -1 in region:
continue
polygon = Polygon([vor.vertices[i] for i in region])
if allowed_box.contains(Point(points[point_idx])):
regions.append(polygon)
valid_polygon_centers.append(points[point_idx])
return regions
# Parameters
rows, cols = 20, 20
spacing = 1.0
jitter = 0.042 # to get an average of 2.1% jitter
points = generate_jittered_hex_points(rows, cols, spacing, jitter)
# Voronoi diagram
vor = Voronoi(points)
# Margin (in same units as spacing)
margin = spacing * 1.0 # Leave one cell of wax space around
# Get filtered polygons
filtered_polygons = filtered_voronoi_polygons(vor, points, margin)
# Plotting
fig, ax = plt.subplots(figsize=(10, 10))
ax.set_aspect('equal')
ax.axis('off')
for poly in filtered_polygons:
x, y = poly.exterior.xy
ax.plot(x, y, color='black', linewidth=0.5)
plt.savefig("jittered_voronoi_clean_edges.png", dpi=300, bbox_inches='tight', pad_inches=0)
plt.close()
As well as encouraging natural variation in cell size, I would also like to see foundation sheets reflect the natural tilt of honeycomb cells.
Bees build each cell with a slight upward slope, typically between 9 and 13 degrees, averaging around 9°.
While bees in managed hives do seem to recreate this slope reliably on their own, adding a subtly varied tilt to the foundation embossing rather than a perfectly uniform angle. Mind you, since bees usually reproduce this slope, sloped embossing is likely less useful than capturing variation in cell size.
There's also a theory that a small number of undersized cells in the comb may help control Varroa mites. The idea is that bees raised in smaller cells hatch slightly earlier, disrupting the mites' reproductive cycle. While results from studies are mixed to negative, it's another reason to consider embracing natural variation, rather than enforcing a rigid cell size across the hive.
