A cache of sunny cubes

A second sister to my recent prior floating cube piece. The whole relief is an intact, single piece of paper. A second flat graphic, attached behind the relief one, fills in the gap from which the relief sprang forth. It is not a pop-up.

A wider view is here.


Copyright William James 2017, general reproduction rights reserved, but images may be pinned or linked out elsewhere if  this post is credited as the source.

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.


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.


Cubes let the colors out

As always in Kirigami, only one sheet of worked paper makes the 3D object, and it is still intact. The folding of all the forms out and forward from the prime axis leaves a hole where that material was lifted away from the middle of the paper. The piece shown here is attached to an identical sheet behind it. This is done to fill the hole as though the sheet were both cut and uncut, and it enhances the 3D effect as follows.

Turning the piece,  one finds many unique angles at which the eye projects from a color streak on the 3D figure, back to its place of overlap on the two background planes. Follow the colored stripes outward as the colors merge in certain frames.


The cubes are sitting in a sunny space where they may be grazed by color streaks. Or, maybe the colors have just streaked out of them because they were opened?



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:


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:


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


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


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):


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.



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”).


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:


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.

Popping boxes

Happy holidays! Here’s a Kirigami of mock gift boxes, like a store window display. I’m avidly learning the basic methods for designing cut-and -fold pop-ups, these days. This is my first original Kirigami form.

In two dimensions, unadorned, it looks like this:


And like this with the graphics added:


… and when folded, like this in time and space:


All images copyright William James, 2016.


Rennaissance girl ISO radar boy for vivid copper patinas

Earthly contours seem to bake to warm and crusty orange in the sunlight. But when in shadow, this same topography appears fluid, more like a body of wind-rippled  water at night. Eerily greenish auroras billow across boundaries.  I like to imagine this as a conflation of a pagan icon from a Renaissance map with a data driven, aerial radar survey.

The vivid patinas of orange and green appeared spontaneously, without any treatment after etching. However, the etching fluid was already much used. I may never see this particular color effect again!

The dark blue resist film still there on this surface could be dissolved away to expose pure, shiny copper (see below). Other artists have advised me to leave this piece just as it is, to preserve the excitement of its strong contrasts.

When I had used exactly the same graphic image before, for the first time (below), copper surfaces that were actively etched by the chemicals took on a blackish cast, different to the orange and green.  Because I had stripped off the  blue resist film after etching, the lately-exposed bare copper slowly oxidized to a fetchingly iridescent sheen. The blob of blue in the center was a naive experiment with a patinating chemical.


This may display as a GIF animation. If not, here are the other angles:






Lines purposely etched into the copper allowed me to neatly fold the sheet with some slight angles and curves.   Because of folding, the visual drama of this darker piece is truly revealed only under dynamic lighting. (It’s supposed to display here as a GIF animation.)

Both pieces are 12.4 x 19.4 cm.

All images copyright William James, 2016.

Kirigamis in Copper Plate

Traditionally, Kirigamis are made from paper, yet, perhaps they could be made from metal? What would the advantages be? A typical piece of paper is limited by having an even texture, color and thickness. Etched metal can display its own color, surface relief and texture. As is best known to print makers and jewelers, metal’s properties can be varied in hundreds of interesting ways. A metal sheet of thicker gauges isn’t fragile, like papers or foils. Many kinds of oxidizing agents and paints can be applied to its surface.  My own intention has recently been to translate to metals the photo-Kirigami fusion process I had developed in my paper projects, as were displayed in my 2015 blog posts.

Hand made Kirigamis in metal 

To start with, I made a version of Guy Petzall’s Ullagami pattern, ‘3×3 Obloid‘, in thinnish, gold tone aluminum foil, which I cut and scored by hand using an Exacto knife (dimensions: 7.7 cm w x 10.2 cm h before folding x 38 gauge foil).


Pleased with this little piece, I next got some copper plate which had been pre-treated with a lovely dark patina on the surface, and used it in following model. The structure Kirigami (or Ullagami) , is a version of Guy Petzall’s ‘Mandala 1’ design (dimensions 12.7 cm x 12.6 cm before folding x 5 mil thickness). It was hand cut and scored with a box cutter. Some people have liked the rounded folds which give it a more hand-made feel.


I was now ready to attempt a metal piece meant to combine: a) an original graphic design, b) an original Kirigami design, and c) a sturdy metal plate too thick for cutting by hand.

Chemically Etched Plates

To serve this purpose, I learned and adapted a completely different technique,  UV resist etching.  Sherri Haab‘s jewelry-making tutorial was useful; also I bought and used UV photo resist material from her store. The Kiri lines would be chemically etched instead of hand inscribed, and coincidentally the process would be used to apply my own graphic design elements. My first etched model was inspired by the textbook, “Cut and Fold Techniques for Graphic Designs“. To the model graphic I added mechanical motifs which suggest steam punk style, by shadowing-on some small watch parts during the UV resist step. The appearance or disappearance of the graphics was dramatically affected by varying the angle of the light.


The visible markings were etched into the depth of the metal.  Score lines guide folding but not cutting; those are needed to construct a Kirigami. Score lines that will be folded up/out will make the peaks seen from the front. Those that will be folded down/in will make the complementary valleys. Score lines are made by allowing the etch to incise into the surface, either only from the front (for out-set folds) or only from the back (for in-set folds). All score lines on both sides of the sheet must go only half way through the thickness of the plate. The thickness of metal that remains in the score lines after etching should yield to hand folding much as stiff paper does.

The through-cuts that entirely penetrate the plate, making horizontal and curved cut lines, are etched into both the front and back sides so they overlap lengthwise. Those must penetrate  halfway into the plate to meet within the thickness. The final etching time was found by simply noticing an interval until light was seen to pass through all of the cut lines, yet it was not seen through any score lines.

Next, I was very excited to work out a way to add a photographic component to the piece while using same process. Below is a frame removed from the featured animated image at the top of this posting. This is my first such successful piece (dimensions 8.7 cm w x 6.9 cm h x 20 gauge thickness). When lit from a certain angle it has a subtle iridescent patina.


In my first try, the piece was etched for too long:

Emma crouch flat plate overetched

Interestingly, the very thin, lacy ‘metal foam’ which formed in the woman’s body could be used in the future for dramatic effects. I couldn’t fold this piece, for the foam would have broken off at the folds. (Size before folding: 8.7 cm w. x 6.9 cm h. x 36 gauge thickness.)

All still photos and animations in this blog post are subject to copyright by William M. James, 2016.





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



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


Flow, elasticity, parcels of space

Upward, downward and forward flows

Right-angled reliefs

These Ulligami formats generally do not entail a major pivot axis of rotation for the piece.

Locomotive on 3X3 Obloid
Locomotive on 3X3 Obloid


In this cinematic treatment, with a foreshortened perspective, smoke shoots aloft to the treetops as the engine speeds toward the camera. Accentuating the mobilization, the smoke is floating atop 3D prisms, while the narrow central gap in the circles suggest two quick frames taken in instantaneous succession. To exaggerate the animation:

Steam Loco - 3X3 Obloid

The GIF animation can capture horizontal, vertical or mixed rotations. Both are limited in comparison to actual binocular experience of the real models. For example, two GIFs of color swooshes (on a 5X5 Eck Cross Ullagami), and below it, two GIFs of a rock climber (on 5X5 Obloid Spiral Ullagami):

Color swooshes - vertical panvertical pivot

Swooshes on 5X5 Eck Cross - horizontal turn

horizontal pivot

Rock climber on 5X5 Obloid spiral - vertical pivot
Rock climber on 5X5 Obloid spiral – vertical pivot

Climbers on 5X5 Obloid spiral, H pivot



When one holds such models in one’s hands. the natural thing is to want move it every which way, to explore the emergent parcels of space and their mutual perspectives.

‘Zebra’s eye’ (on 7X7 Zigzag Ullagami) conjures free-form elastic the stripes like rubber bands projecting across the tops of a zigzag relief of delicate paper bands.

Zebra eye

Below is ‘Star Clipper’ (on 3X3 Obloid), as pictured from my precarious seat on top of the bowsprit (at the very front end of the ship). We were then under sail toward Grand Canary Island in the Atlantic Ocean. The model’s setbacks seem to heighten the loftier upper sails.

Star Clipper - 3X3 Obloid

Star Clipper from bow


Here’s a pair of Olympic Ice skaters doing a very difficult thrown jump (also on 5X5 Obloid spiral Ullagami). She is smiling while spinning two meters up in midair !

Skate throw jump 5X5 Obloid Spiral
Pairs event skaters do a throw jump – 5X5  Obloid Spiral Ullagami
Woman rocky perch
Emma in Italy – 9X9 Obloid Zigzag Ullagami


Original photo

Here is a landscape, shown both right side out and inside out. The photo was taken on a country lane in the fall. Although the normally folded piece is the more sculptural, the inversion piece opens up inwardly, orienting the beholder within it, and confronting more active folks with a challenging hike. 

Orange trees 7X7 Spiral + fold
Lane in Fall on 7X7 Spiral Ullagami – normal folding
Orange Trees 7X7 Spriral -Fold
Lane on 7X7 Spiral Ullagami – inverted folding
Ornage symmetric tree road Japan
Photo found on Pinterest

The next piece is reverse-folded, and like that above, although it is less  sculptural, this inversion piece opens up inwardly, orienting the beholder within its spaces. 

Antelope Canyon, UT - KopiSusu - inverse fold

The Wave Utah
The Wave, Utah

Obliquely tessellated reliefs – Torsion Ullagamis

The following pieces are photo transformations into the Torsion series. 

Very gentle seepage of seawater is implied by elevation with the Torsion 5 Ullagami. The photo is of my partner Betsy’s feet once seen on Cannon Beach in Oregon (the shiny blob is a jellyfish):

Feet On Beach - Torsion 3
Betsy’s feet – Torsion 5 Ullagami


Torsion 5 Ullagami
Stamps 1 Torsion 3
Hearts and Minds. Custom rubber stamps on Torsion 5 Ullagami

Here is a photo of the Potomac River near my Maryland home. The scene is colonial era fish ladder built in a side channel. I rotated and mirrored Guy Petzall’s Torsion 3 Ullagami,  to align it to the flow of the current, which gushes forward.

Potomac River Chute - Torsion 3
Potomac River on Torsion 3 Ullagami
Torsion 3 Ullagami
Rock Climber v2 Torsion 3
Photo credit: climbing-beauty.tumblr.com on Vexilloid Ullagami

GIFs were made by me using the program, Webrotate 360 SpotEditor, available for free at http://www.webrotate360.com/360-product-viewer.html

All Ullagami patterns used were purchased at Guy Petzall’s Etsy store https://www.etsy.com/shop/Ullagami

All works shown are © William James, 2015.. Creative Commons License Type BY  Attribution