Number of building permits by type for counties and municipalities in Colorado from 2010 to 2016 from the Colorado Department of Local Affairs (DOLA).

United States GDPS: 2000p: Colorado: PI: Construction data was reported at 7.000 USD bn in 2008. This records a decrease from the previous number of 7.288 USD bn for 2007. United States GDPS: 2000p: Colorado: PI: Construction data is updated yearly, averaging 9.002 USD bn from Dec 1997 (Median) to 2008, with 12 observations. The data reached an all-time high of 10.460 USD bn in 2001 and a record low of 7.000 USD bn in 2008. United States GDPS: 2000p: Colorado: PI: Construction data remains active status in CEIC and is reported by Bureau of Economic Analysis. The data is categorized under Global Database’s USA – Table US.A193: NIPA 2003: Gross Domestic Product by State: 2000 Price: Chain Linked.

Honeybees are renowned for their skills in building intricate and adaptive hives that display notable variation in cell size. However, the extent of their adaptability in constructing honeycombs with varied cell sizes has not been investigated thoroughly. We use 3D-printing and X-ray Microscopy to quantify honeybees' capacity in adjusting the comb to different initial conditions. Using the average area of natural worker cells as a reference, our findings suggest three distinct construction modes when faced with foundations of varying cell sizes. For smaller cell size, bees occasionally merge cells to compensate for the reduced space. However, for larger cell sizes, the hive uses adaptive strategies like tilting for cells up to twice the reference size, and layering for cells that are three times larger than the reference cell. Our findings shed light on honeybees’ adaptive comb construction strategies with potential to find applications in additive manufacturing, bio-inspired materials, and entomology. Methods Experimental data Collection

All of our experiments are performed using colonies of European honeybees Apis melifera L. at the Peleg lab apiary in Boulder, Colorado, USA.

Fused deposition modeling (FDM) technology was used for 3D-printing of experimental frames using Polylactic Acid (PLA) material, and the designs are made in SolidWorks 2019 CAD design software. Each frame consists of a pair of 3D-printed plates that are placed opposite to each other. For our control set with S=1, each hexagonal element on the 3D-printed plates has a side-length of 2.7 mm. All the other configurations are designed relative to the area of our control set.

All photographs of honeycomb are captured using a Nikon DSLR camera and controlled lighting and a black background.

XRM data collection was performed at MIMIC facility, at CU Boulder (RRID:SCR_019307).

All tomography scans are performed using Micro CT ZEISS Xradia 520 Versa (Carl Zeiss X-ray Microscopy Inc, Pleasanton, CA, USA).

Image processing and segmentation on the X-ray data is conducted using Python and Dragonfly (Object Research Systems, Montreal, QC, Canada).

Dataset Contents

The raw data obtained from X-ray microscopy of our control dataset, S=1, in the form of a stack of tiff images. 2D images of honeycomb that captured using a Nikon DSLR camera and controlled lighting, and a black background. Stacks of thresholded tiff images for reproducing the 3D volumes, obtained from X-ray Microscopy. CSV files that show the angle of tilt (in degrees) for each cell on the X-rayed sample. CSV files that contain the xy coordinates of cell centers, and their area. Movies showing the 3D-reconstruction of the sample, made using the thresholded X-ray data in Dragonfly software.

X-ray data Processing

X-ray tomography scanning of our experimental samples generate stacks of cross-sectional tomography images which form a 3D model of the samples when digitally stitched together. Each tomography image comprises of the following elements-- air, honeycomb, and the plastic base, each captured with a different pixel intensity which is a function of the radiodensity of the element. We develop an image processing pipeline that converts the stack of tomography images to filter out unwanted parts of the raw X-ray image data and segment particular regions of interest. We mainly used computer vision techniques, with OpenCV [1] library in Python 3.0, to conduct all our image analyses. For creating clear 3D visualizations, we use a combination of convolution with a specially designed kernel and morphological operations to segment the plastic cell edges. We use the second derivative of the image histogram to find the optimum threshold value for the effective segmentation of air from data (i.e., honeycomb and plastic). Next, we identify pixels that mark the boundary of the plastic base and air using convolution with a specially designed kernel that detects changes in pixel intensities.Using this we create a kernel which is convolved over the image as a sliding window and at each row, the result of convolution is maximized precisely when the kernel is at the boundary of the plastic base. As a result, this process generates a mask that marks the boundary pixels. With this mask as a seed, we use morphological operations to generate an enhanced mask that covers the plastic base entirely.

Tilt angle calculation

For the comb built on the 3D-printed frames with size S=1, 1.25, 1.5, 1.75, and 2 we compare and quantify the cell tilt values relative to the plastic base. We achieve this by creating two parallel planes intersecting the honeycomb at the base and the upper layer. Then, in each plane we identify the intersecting hexagonal cross-sections (components) corresponding to the hexagonal cavities of individual cells. Subsequently, we identify the centroids of each of these hexagonal components and their centroids by running Connected Component Analysis on each plane in the Dragonfly software [2]. Once these contours are established, the angle of tilt for each honeycomb cell is computed through simple geometric analysis using the displacement value of the cell centroids.

References

[1] G. Bradski, Dr. Dobb’s Journal of Software Tools (2000). [2] Comet Technologies Canada Inc., Montreal, Canada, Dragonfly.