A few weeks ago I wrote a post outlining seven principles for designing geometric art, illustrating those principles by “reverse engineering” an interesting model to see how I could design new works based upon it. (For those who are interested, I’ve continued to explore those variations, and will reveal the fruits of those investigations in an upcoming post soon!).
Since then I realized that I neglected to mention at least one more important principle, because it didn’t arise in that context:
I recently designed a new piece that illustrates this perfectly.
The Starting Point
My starting point for this project was a piece of pop-up kirigami (cut paper) that I designed and created many years ago:
(Sorry about the picture quality – my wife is on vacation with the good camera so I had to use my iPhone!)
This piece was an exploration of fractal cube stacking, and has always been one of my favorites. (Hey newsletter folks — anything here look familiar?!) I had always noticed that the envelope of all those stacked cubes — especially if one were to trim away all the extra flat paper on the sides — looked a lot like one quarter of an octahedron, but had never thought through how I might capitalize on that. Now, hold that thought for a moment…
The New (Old) Idea
As I discussed in another post two months ago, I recently attended an origami convention, which exposed me anew to many basic origami forms that I had not worked with actively in many years, including the traditional origami bases. One of these is called the “Preliminary Fold” base (because it is the starting point for several other classic bases), and looks like this:
The New Combination
So, recently returned from the conference, I looked at my old kirigami model with new origami-sensitized eyes and realized that my old model (again, with all that extra flat material on the sides removed) was exactly 1/4 of a preliminary fold! Combining four of my model on the four quarters of a full preliminary fold would make the complete octahedron that had always been implied in the original model. Once I had the flash of insight about how to combine these two concepts, generating the pattern for the full model was fairly straightforward:
And so, I proudly present (at various stage of cutting and folding, the result of applying this principle: my newly designed “fractal cubes octahedron”:
In this view you can clearly see two copies of the original model, laying on their side.
Getting all the folds to fold the right way is a delicate process — almost there!
There are some minor problems with this (dare I call it “preliminary”?!) version, which I hope to correct in a future version, but all in all it came out pretty nicely. Two fairly simple ideas, combined in a new and interesting way, yielded a much richer and more interesting piece of art. Please let me know what you think, and especially if you’ve ever used this principle in your own work.