Hilbert Curve Cake

Three years ago, I entered an Ashley Book of Knots Cake into the Johns Hopkins University Sheridan Libraries’ third annual Edible Book Festival. For this year’s contest, I figured I could apply my 3D-printed Hilbert curve microwave absorber research to craft a cake for Hans Sagan’s Space-Filling Curves book1 on the eponymous topic. Thus began an endeavor involving thermoplastic, silicone, and sugar.

Hilbert curve cake Continue reading


  1. H. Sagan, Space-Filling Curves (Springer-Verlag, 1994). ISBN: 9780387942650. DOI: 10.1007/978-1-4612-0871-6

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3D-Printed Tea Bag Holder

When readily available containers do not come in the desired form factor, 3D-printing can be quite useful. In this case, I wanted a tea bag holder that fit on a small ledge, allowed the tea bag labels to be read, and allowed the tea bags to be easily removed. Although there are some similar products available commercially that would fit the space, they either seemed a bit flimsy or looked to be a tight fit around the tea bags, which would make them more difficult to remove. Thus, I designed and 3D-printed a modular holder that can be stacked. The holder was printed out of PLA, and the design files are available.

Tea Bag Holder

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Color Cycle Survey

A previous post about randomly generating color sets with a minimum perceptual distance addresses the technical aspects of generating sets of colors that are visually distinct for those with normal color vision as well as for those with color vision deficiencies. However, it does not address the aesthetic aspect, which I will start to address here. To create an aesthetically pleasing color cycle—an ordered set of colors for visualizing categorical data—two aspects need to be addressed, the colors that are used and the order that they are used in. While one could take an ontological approach to this by trying to define a set of rules that make a pleasing color cycle, as is done by I Want Hue,1 such a method is error-prone and substantially biased toward the personal preferences of the drafter of the rules. Instead of using ontologies, an alternative approach that is gaining traction in many fields is to infer a pattern from a large data set using machine learning techniques. This is the approach I wish to pursue.

To this end, I’ve created a Color Cycle Survey. After presenting the user with an introduction, colorblindness questionnaire, and directions, the primary survey starts. In it, the user is presented with two color sets and is asked to choose the one that is, in the user’s opinion, more aesthetically pleasing. Then, four orderings of the chosen set are displayed, and the user again makes a selection to taste. This basic process is then repeated again and again, with sets of either six, eight, or ten colors. For the choice of color set, each set is presented ordered by hue, since this makes the two sets easier to compare than if they were randomly ordered (or ordered by RGB values). Only two sets are presented, to make for an easier choice. Additionally, a line plot or scatter plot rendering is shown with each color set. For the choice of ordering, four orders are presented, since multiple orderings are easier to compare than sets, since the colors are all the same. I considered asking the user to order the colors to taste, instead of presenting possible orderings, but I decided that while such an approach yields more information per response, it takes much longer and requires more effort, so each user will likely respond many fewer times. Thus, I went with the simpler approach.

If all goes well, I’ll amass a sizable data set from the survey, which will remain available for at least a few months. Once I have data to experiment with, I’ll work out the exact analysis method. In addition to generating an “optimal” color cycle, it would also be interesting to create a model that allows for additional constraints, such as being able to choose the first color or being able to choose the exact number of colors in the cycle. Once anonymized, I’ll release the survey data under a permissive license, probably CC BY 4.0 CC0 (I’m open to suggestions). Any generated color cycles will be release into the public domain via the CC0 public domain dedication.


  1. I Want Hue takes a fairly rudimentary approach to color vision deficiency simulation, which I find lacking; I personally have difficulty differentiating colors in the many of the sets it generates, even when its colorblind mode is turned on. It also doesn’t really address the ordering of the color set into a cycle.  

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Randomly Generating Color Sets with a Minimum Perceptual Distance

Earlier this year, I released a color cycle picker that enforces a minimum perceptual distance between colors, including color vision deficiency simulations, with the goal of creating a better color cycle to replace the “category 10” color palette used by default in Matplotlib, along with other data visualization packages. While the picker works well for what it was designed for—allowing a user to create a color cycle—it requires user intervention to create color sets or cycles.1 The basic technique used—performing color vision deficiency simulations2 for various types of deficiencies and enforcing a minimum perceptual difference for the simulated colors using the CAM02-UCS3 perceptually uniform color space (where each type of deficiency is treated separately) and a minimum lightness distance (for grayscale)—is still valid for the random generation of color sets; it just needs to be extended to randomly sample the color space.

A few different color sets
Continue reading


  1. A color set doesn’t have a defined order, while a color cycle does. 

  2. G. M. Machado, M. M. Oliveira, and L. A. F. Fernandes, “A Physiologically-based Model for Simulation of Color Vision Deficiency,” in IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 6, pp. 1291-1298, Nov.-Dec. 2009. doi:10.1109/TVCG.2009.113  

  3. Luo M.R., Li C. (2013) CIECAM02 and Its Recent Developments. In: Fernandez-Maloigne C. (eds) Advanced Color Image Processing and Analysis. Springer, New York, NY. doi:10.1007/978-1-4419-6190-7_2  

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3D-Printed Hilbert Curve Absorbers

Fused filament fabrication (FFF) 3D printers are good for many things,1 but production of sharp points is not among those strengths. Thus, the traditional structure of millimeter wave absorbers—a periodic array of square pyramids—is poorly suited for production via FFF printers. Millimeter wave absorbers serve a crucial role in Cosmic Microwave Background (CMB) telescopes by terminating stray light, which is necessary for reducing systematic errors. Not only are the points difficult to produce; they’re also fragile, since a print is generally weakest along its layer lines. Thus, a new geometry was needed, as is detailed in my paper titled A 3D-printed broadband millimeter wave absorber.

Space-filling curves such as the Hilbert curve completely fill the unit square. Furthermore, the Hilbert curve can be described by a sequence of physically realizable geometric approximations. Tracing a wedge along such an approximation creates a geometry with similar optical properties as a pyramidal array but with enhanced mechanical robustness. Importantly, this geometry can be printed without repeatedly starting and stopping extrusion, making it well suited for FFF printers.

Hilbert Curve Absorber (Detail) Continue reading


  1. A LulzBot TAZ 6, in this case. 

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