Folding, Creasing, Snipping & Tucking

What a Kirigami Star Reveals about the Complexity of Nature

There is nothing quite like the holidays to provide the crafter motivation to acquire new skills and techniques with the purpose of adorning their Christmas tree with new ornaments. On our trees, past years saw handmade ornaments that were crocheted, cut on a scroll saw or lathe, made from bead kits, hand sewn from felt, or even molded and shaped from heavily-scented cinnamon dough.  The latest crafting obsession in our home is a star: a paper-crafted kirigami star.

Kirigami is a variation of origami. Whereas origami is the Japanese art of paper folding, kirigami involves folding and cutting. No longer merely a past-time for hobbyists, concepts contained within both of these arts have been applied to a wide variety of engineering applications looking to leverage folding and cutting techniques and applying them to two-dimensional surfaces, in order to fabricate three-dimensional objects.¹ The fact that adroitly-placed folds enable otherwise three-dimensional objects to lie flat and compact, allows the applications of these ancient art forms to range from automobile air bags, to biomedical devices such as heart stents, to foldable and stretchable electronics and even space exploration with foldable telescope lenses.²

Back to kirigami stars. Now as a skilled crafter, I assumed these would be quite easy, as the website providing the directions revealed there are merely ten steps which go something like this:³

1. Fold square sheet of paper in half.
2. Orient the paper so it opens at the top, and the fold is at the bottom.
3. Fold up the right bottom corner in valley fold, then open.
4. Fold down the right top corner in valley fold, and open. Note where the two folds intersect, forming a cross.
5. Take the bottom left corner, and place it at the center of the cross, and fold. 
6. With the flap formed from Step 5, valley-fold so that the edge of the flap aligns with the leftmost edge of your work; do not open that fold up.
7. Take the right bottom corner and have the folded edge meet the folded edge of the flap, lining up the two edges. 
8. Flip the paper over.
9. Valley fold down the center so the edges of both flaps you created are aligned.
10. With scissors clip about one third of the way down at an angle from the tip.

While these directions all sound easy enough, it is not difficult to generate a failed star—you have after all, any or all of ten steps in which to fail, giving the novice folder hundreds of ways to not build a star. Fortunately, I only discovered three. My tenacity was rewarded with several lovely, symmetrical stars, due in no small part to the crafter providing process images and an image of the finished project as a reference.

Waxing philosophical through this crafting experience, I recalled Oscar Wilde's quote, "Life imitates art far more than art imitates life." Recalling much of my coursework as a molecular biology major, I had to smirk at this thought, acknowledging that the kirigami skills of folding, creasing, snipping and tucking are widely represented in natural systems: such as whenever DNA compacts itself into chromosomes; during protein synthesis and folding; and most remarkably in embryogenesis. In the case of kirigami—art imitates life, and even then, not with near as much sophistication or beauty. 

Let us consider just embryogenesis: when any of us were but a single cell—a zygote, machines, motors and scaffolding structures within that cell enabled our very young selves to cleave (cut) ourselves into two daughter cells (whether you are male or female—this is what the cells are called). These two cells underwent yet another cleavage event to form eight cells; eight cells gave rise to sixteen—with this process continuing until we formed a hollow ball of 128 cells called a blastula. As a blastula we underwent a further process called gastrulation wherein valley folds, mountain folds, tucking, creasing and snipping continued with extreme precision, until we reached our fourth week.

At four weeks gestational age, we now look much like a flat, two-dimensional disc. Through the process of embryonic folding (it is really called that), we are converted to a complex three-dimensional cylinder by the eighth week of development. Around nine weeks, we are now entering the fetal period, where all the structures that were cleverly formed, fashioned, folded, and molded, with remarkable fidelity during embryogenesis continue to grow and differentiate.⁴

Back to kirigami. Recognizing that embryogenesis precedes the very earliest of dates recorded for the human activity of kirigami, the assertion that art really does imitate life—more so than the reverse—is objectively true. As no surprise, if one were to write out step-by-step instructions for the building of an embryo, the number of steps would well exceed the mere ten it took to make our original kirigami star. Even when compared to the steps involved in the unfurling of the James Webb telescope (demanding teams of scientists and engineers, along with an impressive budget in the billions), embryonic folding is amazingly much more complex. Whereas we estimated there are conservatively speaking several hundred ways to mess up a simple kirigami star, there are an infinite number of ways to mess up an embryo: making it seem a miracle anyone survives to birth!

No sensible person would argue against the notion that kirigami is an activity carried out by intellectual agency; crisp, paper stars do not randomly form from undirected and blind processes acting on a paper substrate. Even the simplest kirigami star requires adroit paper-folding skills, and in no amount of time would we expect a piece of paper to self-organize into such. Contemporary Darwinian orthodoxy would suggest however, that the valley folds, mountain folds, creasing, snipping and tucking that occurs during embryogenesis are the result of purely undirected and blind processes occurring over the course of several hundred-million years, and completely void of intellectual agency. 

Perhaps those who hold to this view might try their hand placing random, undirected folds in a piece of paper and seeing what it takes for a kirigami star to be born? Go ahead, we will oblige you with an unlimited amount of time, and paper; just clean up your mess, please, when you are done.

Notes
1. Xu, L., Shyu, T. C., & Kotov, N. A. (2017). Origami and kirigami nanocomposites. ACS Nano, 11(8), 7587-7599.
2. Lv, C. (2016). Theoretical and finite element analysis of origami and kirigami based structures (Order No. 10144120). Available from ProQuest Dissertations & Theses A&I; ProQuest Dissertations & Theses Global; Technology Collection. (1811633453). Retrieved from https://search-proquest-com.proxy.libraries.uc.edu/docview/1811633453?accountid=2909
3. Directions were modified from: https://www.redtedart.com/3d-paper-star-kirigami/
4. Derrickson, B., & Tortora, G. J. (2007). Introduction to the human body: the essentials of anatomy and physiology. J. Wiley & Sons.