Fibonacci x Kirigami

In a salute to the Armenian heritage of a clever and lovely woman, to whom my dear son, Peter, is engaged to be married, this Kirigami glows with the colors of the Flag of Armenia.

RedBlueCopper_3x2

Another one, made previously, now looks subdued by comparison:

GreenBlueCopper

Acknowledgements  The form is one of Guy Petzal’s simpler Ullagamis. A single piece of paper was cut and folded to make each model (plus the mount). The dots embody a mathematical pattern known as a golden ratio Fibonacci sequence, also seen in nature in  sunflowers or pine cones.

Harmoniously Askew

Emma visited the “Defibrillator Performance Arts Gallery” in Chicago with Joshua, where he took this photo of her.

In Chicago March 2017

It’s almost like a charmed stage set, with lovely highlights and shadows, the bow arch and the shadow profile of her, even the little puff of vapor. And so, I’ve rendered it as a  Kirigami!

Emma-at-gallery

The flowing waters behind the pop-up form may evoke her feelings for the ongoing  performance. Might this piece also try to infer his feelings (the photographer’s) for her?

This is my first use of skewed forms in a one-piece, right-angle pop-up (a Kirigami). Without the photo on the front, it looks like this.

Basic form

The concept is shown by a simple design diagram, as the form is visualized when opened out flat. It would be so before doing the physical preparation for folding (that is, before cutting and scoring).

Diagram of Kiri

 

 

Crystalline Kirigami

Three paper shells comprise this crystalline 3-D model: the folded surface shell, folded middle shell and a flat back shell. It has two, nested interior volumes. One is behind the front shell, and the other, behind the middle shell.

In the digitally designed model, these shells were a sequence of three planes. Those  planes were linked into one continuous, accordion-folded zig-zag. I suppose the product of this interesting method could still be classified among all other Kirigamis, although some might surmise I’m bending the definition to fit. In the digital model, as visualized with the origami plugin, it is one inflected but unbroken object. I had to print, cut and fold three separate paper prints to make it, in practice. It would have been too cumbersome to handle with two hands, otherwise.

pyramid_quilty_1024_6841_pauses

My recent post showed the same Kirigami form in a single shelled design. I imagined there still could be a way to impart more depth and volume than that one had. The outer ‘butterfly wing web’ was a fun design project while learning how to make a color gradient mosaic in Adobe Illustrator.

Strathmore 451-1 paper, watercolor textured, 8″ x 9″ unfolded; Epson P-600 pigment ink printer. Copyright 2017, rights reserved by William James. It’s OK to pin or link images to a noncommercial blog, and please credit this post as the source.

 

Imagine that!

This Kirigami is bit of a mechanical puzzle: how can this airy thing be folded up from one piece of paper?  I had found this interesting model on Pinterest:

6cba5f23a8f7bcc9c056fc9e286928ee

As a novice paper folder, I wanted to diagram the underlying architecture of this piece. Once I had grasped its plan, just to make sure that I had really understood it, I added a fourth floater:

cubes_fold_mount_gif

Notice the lines behind it? That’s the blueprint for cutting and folding it. It’s  clearly shown here:

cubes_illustrator_fold_pattern

The pop-up action mechanism is revealed by comparing this diagram to this partially folded state:

cubes_partial-fold_gif

This material is Frosted Gold, Canford Card; I think it would also look cool in sheet brass. The diagram is available from me upon request.

My learning curve has been greatly eased since I’ve started using an extension called Origami in Adobe Illustrator. It simulates folding of the working model (here, the ‘top’ is to the right):

origami_view

It can zoom, tilt and rotate the working model. Mistaken lines in one’s structural diagram are all specifically located, so it is a  great tool for self-directed study.

 

 

 

 

A classical form in an improvised space

The 2D pattern for this 3D volume developed as I played with the idea of a pyramid of interlocking planes.

 

kirigami-design

It was my partner Betsy’s creative quilting practice that inspired me to put a batik-like graphic on a Kirigami popup. I picked the tonally coordinated color pallet for my pyramid, and then a vibrantly colored random network which seemed the best as my base image (credit: Adobe stock image bank, “Wired”).

flat-graphic

Printed 20 cm x 20 cm flat.

Like a quilt, it will only ever be one sheet of paper (except for the backing sheet), even after folding as a 3D sculpture:

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Folding a 3D form is a gradual process that takes a couple of hours. (In the diagram above: Black = cut; red = fold forward, blue = fold backward.)  Tensions arise, both physically and emotionally,  while trying to coordinate the gradual folding of more than 100 right angles. All of those angles most be partially folded in small changes through many cycles.  Like all Kirigami forms, one might either open it back out again to retrieve a single flat layer, or continue to collapse it inward almost to flatness, except for the thickness of four layers of folded paper.

A strong but disorderly web of vivid red links and nodes binds the pyramid to the seven edges of its two framing planes (one edge is shared). It appears as though the pyramid is nested into two sides of a partial outer box or prism. As both the pyramid and its ‘container’ are classical rectilinear forms, I was excited to find that the linking lines which connect those appear messy, improvised, exploratory, non-classical.

Text and images copyright William James, 2016; reproduction is allowed.

Immersion, Submersion, Emersion

1. Bursting through a plane

A very two dimensional image was exploded out of the plane by attaching it to an energetic, asymmetric  3D form.

Tree Rings Trochoid Meridians v6

Photo image: Found on Pinterest; Google found “not filtered by license”,  traced to an inactive Tumblr account.
Trochoid Meridians

 

 

 

“Trochoid Meridians” courtesy of Guy Petzall (c).

 

 

I like about this, the way those nested rings in the tree trunk appear as a calm inner center, while in contrast, the 3D model makes a centrifugal outburst of energy. What a nice pairing of Yin and Yang energies!

2.  Perilous Birding

Suppose one were to join a pair of identical 3D forms, one of which is  folded inside out. Can an image bridge two opposite forms?  Maybe for example, a mirrored image?

Flamingos reflected pos neg 3X3 BB

The birds arise on the normally extroverted space above, and their reflections are more deeply immersed in the oddly introverted space below.

Flamingos reflected    “Flamingo Dance”  (c) Basie Van Zyle

3X3 Building Blocks     Guy Petzall’s 3X3 Building Blocks (folded normally).

 

3. Deep inversion!

 

Deck From Mast 2 hourglasses

This perspective, looking down onto the deck of the schooner  Sagitta from high atop her masthead, suggests vertigo. The void volume and sheer pull of gravity of a double negative perspective is accentuated by some inward-inclined ribs.

Schooner Saggitta from maintop Deck of Schooner Sagitta, from the mast top.

5X5 Hourglass 5X5 Building Blocks, as doubled in the Hourglass, (c) Guy Petzall

4. Lights in the darkness

The swirl of bright spots spirals mysteriously among looming prisms. If the man has conjured up only the happy spiral, is he opposed by an ominous, unseen force?

Man spots dark 5X5 Obloid Spiral

 

Articule

Image from Adrien M/Claire B dance troupe

5X5 Obloid Spiral

5X5 Obloid Spiral (c) Guy Petzall

5. Fish don’t swim straight

Guy Petzall had the insight, to make Ullagamis with curved cuts, and he sent me an example. What a pleasure, to make use of the extra fluidity for this swarm of fluttering fish!

Reef Fishes Wavy Trochoid v1

Here’s the same composition but with straight cuts:

Reef Fishes Trochoid 4th

There’s lots of wiggle room for creativity using filters such as waves, foreshortening and other Photoshop effects, on Kirigami/Ullagami patterns.

Trochoid Trochoid (c) Guy Petzall

School of fish for Trochoid Photo credit: Phillipines Underwater World