RFC: Extend spec for Einstein tesellations

[junosuarez]

1. What

(© David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss, CC BY 4.0 - International)

A recent fundamental mathematical breakthrough by researchers at the University of Waterloo has resulted in a shape called the Einstein with the property that it tiles perfectly on a 2-dimensional plane without ever repeating, despite being an asymmetric (technically, "achiral") shape.

I propose we extend the StickersStandard to incorporate this new geometric object. This project has long sought to promote consistency and ease of use for Sticker Implementors, and the result over time has been broad community support and organic adoption, especially of the hexagonal Sticker Standard.

Although several different proposals over the years have sought to add support for new shapes, support has emerged for tessellating shapes which benefit most from standardization in terms of interoperability and end-user modularity.

Support for this new shape will allow Sticker Standard to stay up to date with the state of the art in geometry and continue benefiting various members of the community well into the future.

1.1. Further reading

• “Newfound Mathematical ‘Einstein’ Shape Creates a Never-Repeating Pattern | Scientific American.” Accessed April 16, 2024. https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/.
• Smith, David, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss. “An Aperiodic Monotile.” arXiv, May 29, 2023. https://doi.org/10.48550/arXiv.2303.10798.

2. Who benefits

Under this proposal, all memerbers of the Sticker community will continue to enjoy the benefits of standardization:

• interoperability reduces the cost and time-to-implement Stickers, especially through reusable templates
• the Total Cost of Sticking is lowered because end-users can expect stickers from diverse vendors and implementors to work well together. Applying one sticker will not preclude applying other stickers in the future nor require complex workarounds, up to and including removal and re-application
• Stickers are horizontally and vertically scalable for ease of operation and enhanced observability
• Easy to adopt starting with a single sticker (or 3 for high-availability deployment) yet scales infinitely

2.1. Sticker Users

Collecting and receiving stickers is a joyful, even exhilarating experience. Yet applying a sticker is a big commitment, particularly in the case of laptops, cars, spectral analyzers, or other capital-intensive assets. Sticker users will appreciate both the principled tiling properties of the Einstein shape as well as the "edgy" appearance of the unique patterns that can be created by combining multiple stickers.

2.2. Sticker Implementors

Designers, promotors, marketers, and community organizers benefit by being seen as cutting-edge. The novel shapes are eye catching both stand-alone and in the unique patterns they create when combined at various scales, increasing the desirability and eye-catching quality of the stickers.

2.3. Sticker Vendors

Digital printing and CNC die-cut or laser-cut technology makes it easy to produce stickers in a vast number of shapes. However, the UI and naming conventions that come from non-conventional shapes increases the turn-around time and lengthens the sales cycle for Sticker vendors, and increases the likelihood of unsatisfied customers. For example, in the early days before the initial Sticker Standard, different vendors produced hexagonal stickers with slight incompatibilities in size, angle, and printed orientation.

With a novel and asymmetric shape like the Einstein, these risks are increased and may sadly lead some vendors to drop support for the shape entirely, or charge increased prices. Standardization with precise measurements, realistic bleed/margin tolerances, and readily available templates in various popular graphics design formats and software packages will reduce the risk for vendors and create a market opportunity to offer this exciting new format to their existing customer base of Sticker Implementors.

3. Alternatives considered and prior art

Other infinite tessellations exist, such as Penrose tilings (see Wikipedia for more patterns). However, these predominantly have the property of involving many different shapes of widely varying sizes in order to perfectly fill the 2-d plane. By having uniform size and shape, the Einstein provides an incremental adoption strategy: since all stickers are the same size, less up-front planning around layout and emphasis. All tiles are given equal weight for graceful extensibility and continuous delivery.

4. Security considerations

The standard Safe Sticker Handling best practices still pertain with Einstein stickers. Tiles may have sharp edges; care should be taken when removing sticker backs and applying to various surfaces. Stickers may be used to conceal micro devices such as NFC tags which could compromise privacy. Further considerations should be brought to the attention of the draft author for discussion or inclusion final to publishing the final draft of this RFC.

5. Next steps

• Comment and discussion of this RFC
• Identify key stakeholder representatives from each of the groups in Section 2
• Prototyping, field trial and experience report-back
• Develop template
• Revise and publish final draft

Thank you for your consideration.

[terinjokes]

I considered adding this pattern after the announcement last year, but I'm not entirely sure it makes sense as a sticker design. Unlike the existing patterns, there's no consistent orientation of the shapes throughout the tessellation. While it looks slick with the solid colors as shown in the image, I don't think it will look good with project logos.