top of page
Abs 1.jpg
Full ep9.dxf.png

Thick-Material Parametric Iso-Area Origami Flashers

Georgia Tech Masters Thesis Project, 2020

Advisor: Lisa Marks

Thesis Committee: Glaucio Paulino, Athanos Economou 

My Georgia Tech Masters of Industrial Design Thesis Project examines a family of origami patterns known as Iso-Area Flashers. Flashers have qualities which make them desirable models for solar panel arrays, and have inspired many application concepts. However, there are many complicating factors when using thick materials to make origami, and the rotational nature of the Flasher pattern adds further degrees of complexity. The goal of this project is to explore and remove the obstacles that prevent the Flasher pattern from being utilized in solar arrays and other thick-material applications.

IMG_4830 lighter.jpg

Flashers are able to stow an arbitrarily large surface area into a small compact central volume, and maneuver smoothly between these configurations

Solar Energy and Geometry

Solar Energy is the most abundant source of power on the planet, with the daytime side receiving more than 10,000x times more than what is needed to power all of human civilization. As we continue to transition away from fossil fuel energy sources, solar energy will play an increasingly prominent role.

Solar panels are flat so they can interrupt the greatest amount of sunlight with the least amount of material. As solar panels are traditionally stationary fixtures, collecting solar energy requires devoting an area to that single purpose, and collecting more power means designating more area. This model is not scalable; our power needs will continue to grow, and we cannot endlessly requisition land to satisfy that need. It is desirable for solar panels to be non-static, such that they could collect energy from an area when desired, yet also easily stowed away compactly without manual removal of the panels. Solar energy collection should not be limited to huge facilities in remote areas, it should be integrated into our lives, close to where our power needs are.

Given the flat nature of solar panels, the art of origami has many solutions to offer to accomplish this.

Origami, and Nature

Most people are familiar with origami, the Japanese craft of folding paper into animals or shapes. As a mechanism, origami is the mathematically constrained movement of shapes where they are connected and folded along their shared edges. If we can fully understand these movements, we can replace the paper medium with other more structural materials, such as photovoltaic cells, which would give us solar panels that can do all the things that origami can do.

Screen Shot 2020-02-27 at 7.22.31 PM.png

The structure inside the bud of the Hornbeam leaf bears a striking resemblence to the miura-ori pattern. Photo from Mahadevan, 2005

With this broader view of origami, we find that origami mechanisms appear everywhere in the natural world. It's how leaves are folded up inside a bud before it opens, and how a beetle is able to stow its wings under a shell a quarter their size. These kinds of convergences occur because origami is extremely efficient at stowing large surface areas into small, compact volumes.

The wing folding structure of a ladybug beetle, and its mechanic reproduced in an origami model. Photo from Saito et al., 2017

Screen Shot 2020-02-27 at 7.22.14 PM.png

Iso-Area Flashers

Iso-Area Flashers are a family of origami patterns which store material by wrapping it around a polygonal base. The pattern was first published by Toshikazu Kawasaki in Origami for the Connoisseur in 1987, where he employed it to make a series of elegantly twising roses. Origami flashers capture the essence of a botanical circadian motion called nyctinasty, where flowers open during daylight and close with the onset of darkness. One of the best examples of this is the Datura flower, also known as Nightshade, Devil's Trumpet, and Jimsonweed. 

Screen Shot 2020-02-23 at 5.02.29 PM.png
Screen Shot 2020-02-23 at 5.06.56 PM.png

Flashers as Solar Panels

Screen Shot 2020-02-23 at 5.37.00 PM.png
Screen Shot 2020-02-23 at 6.14.35 PM.png
  • Our need and use-case is exactly the same as plants.

    • Opened configuration for maximum sunlight exposure

    • Closed configuration for protection from forces and hazards

    • Ability to maneuver between configurations

  • This structure is a product of evolution by natural selection.

    • Natural selection would not produce this structure if it were not highly functional

  • Supported from center​, high-mountability

    • Can be wrapped around a space shuttle chassis.

    • Can be mounted onto small area, (analogue: flower stalk)

  • The structure is beautiful to look at

    • Incentivize commercial areas to adopt​​

Concept rendering for orbital flasher solar array, Photo from BYU, 2014


Paper is so thin that it's thickness is usually discounted in origami patterns. When real-world structural materials are used in origami, accommodating their thicknesses requires altering the geometry of the crease patterns, which is different for every type of pattern. 


At the present, no complete process has been developed to generate Iso-Area Flasher geometry for thick-rigid materials.

This is why flashers, while having so much potential as solar arrays, are still confined to paper models and computer renderings. The goal of my thesis project is to explore this pattern, and develop a pathway such that later designers can procedurally generate functional thick-rigid flashers into products and structures of a variety of thicknesses.

Anatomy of Flasher Origami Pattern

Screen Shot 2020-02-23 at 6.19.48 PM.png

Any flat material can theoretically be folded into a flasher. First a central polygon is determined, and then the area surrounding the polygon is divided and creased based on the polygon's measurements. Any regular polygon can be used in the center; the flasher will have the same number of spiraling arms as its central polygon sides. 

While any polygon can be used, I have chosen to use hexagonal flashers for iteration. This is due to the structural nature of hexagons, the implications of modularity and tile-ability, and the fact that the edges of hexagons can be extended to generate isometric grids, which is extremely valuable to digital modeling

The rotational sections of folding material are all identical. The panels and creases can be categorized by their qualities: how many layers out they are from the center polygon, whether they face inwards or outwards during stowage, the types of creases and vertices that surround them. The crease pattern in entirety is quite complicated, so it's useful to delineate subdivisions of the pattern which contain one of each type of panel. There are two subdivisions of panels which are representative of the pattern as a whole: the wedge is highlighted to right in yellow, and includes panels on either side of the main diagonal mountain creases. The other subdivision is a hextant, and these panels "scrunch" up together onto one side of the polygon during stowage. 

Screen Shot 2020-02-23 at 6.25.05 PM.png
Screen Shot 2020-02-27 at 6.20.55 PM.png







What is Thick Origami?

The thickness of the material used in origami affects the pattern at multiple scales, and as a result there are different levels at which thickness accommodation is visualized in literature. At close-up scales, there's the consideration of where the material thickness fits in relation to the hinges, vertices, and neighboring panels. In addition, the outer layers of material must wrap around all interior layers, which requires a gradual increase in panel dimension. Considerations for material layers and their immediate neighboring panels will be considered micro-thickness accomodation, and the increase of panel size in outer panels to accommodate the built-up thickness of more inner panels will be considered macro-thickness accomodation.  

Micro-thickness Accommodation #1:

Hinge Cross Section

Top View

Screen Shot 2020-02-24 at 3.14.12 PM.png
Screen Shot 2020-02-24 at 3.14.28 PM.png
Screen Shot 2020-02-24 at 3.26.18 PM.png

Edge View

The most basic way to visualize thickness in origami is at the hinge intersection of two thick panels. To make the accordion-fold piece (above) from thick panels, the hinge's location must be determined in relation to the material's thickness. There are many ways to go about this. Flexible Joint Technique bends material along crease lines, similar to flexible origami materials such paper. Hinge Shift Technique reassigns hinge locations to panel edges, indicating a clear rotational axis. Flexible Membrane Technique affixes thick panels to a thin flexible material, leaving space around valley creases for the material thickness to close into.

Flexible Joint Technique

Hinge Shift Technique

Flexible Membrane Technique

Screen Shot 2020-02-27 at 12.39.28

Crease Pattern

Crease Pattern

Crease Pattern

Thick Material

Thick Material

Panels on Top of Pattern

Fabrication of Joints

Hinges Assigned to Edge

Gaps at Valley Folds

Straining of Joints

Rotation about Axes

Rotation about Axes




Micro-thickness Accommodation #2:

Vertex Isolation View

Flexible Joint Technique translates directly from 2D to 3D, but it's not a viable option in most thick rigid materials, it's more a representation of what paper is doing. Flexible Membrane Technique also translates easily, simply requiring an offset of 1 material thickness distance from all valley folds. However, this increase of number of hinges greatly reduces rigidity of the system, leading to "limp" origami models. Hinge Shift Technique preserves its single degree-of-freedom rigid movement, and the edges of the material make ready vectors for hinges in both digital and physical models. It is most suited for alternating mountain-valley sections, like the accordion example above.

Screen Shot 2020-02-24 at 4.19.08 PM.png
Screen Shot 2020-02-24 at 4.18.48 PM.png
Screen Shot 2020-02-24 at 4.19.16 PM.png
Screen Shot 2020-02-24 at 4.18.56 PM.png

Vertices are where two or more origami hinges intersect at angles. When thick materials are used, mountain and valley crease are on opposite sides of the material from one another, and some panels which want to be face-to-face sometimes have other panels forced between them. Vertices can be "cut out" from their origami patterns and examined in isolation, which is extremely helpful in understanding where the material thickness need to store during folding.

Screen Shot 2020-02-24 at 4.22.56 PM.png

Types of vertex in a flasher:

  • Diagonal Crease Vertices

    • 4 hinges intersecting​

  • Bottom Planar Vertices

    • 4 hinges intersecting​

  • Polygon Edge Vertices

    • 5 hinges intersecting​

Each type of vertex in the pattern must have its panel thicknesses resolved in this way to know the exact stowing location of all panels. There are 3 different types of vertex in flashers:

Macro-thickness Accommodation:

Stowed Layer "Girth"

When a magazine, bound at one end, is rolled into a tube, the unbound end spreads out of alignment due to the difference between distances that either cover travels. 


Flashers experience this same effect because they wrap up in a similar manner. As the material of the flasher stows into its closed configuration, it wraps around the base polygon. As these layers accumulate, the hexagon side length that each successive layer must wrap around is larger than the previous more inside panel. This means that the panels must gradually distort larger to compensate for the greater distance that must be traveled.

Screen Shot 2020-02-24 at 9.11.31 PM.png
Screen Shot 2020-02-24 at 9.59.09 PM.png
Screen Shot 2020-02-24 at 9.58.47 PM.png

Fusion 360   Rhino6   Grasshopper

Laser-Cut    3D Printing

Quad Reverse.png

I used a combination of digital modeling softwares to combine these micro and macro thickness scales into a single parametric model.

This allowed live exploration of the parametric relationships, calculation of panel dimensions, and digital fabrication of physical prototypes.

All Prototypes together.png

Early Prototyping

Early prototyping focused on building a large number of models with varying parametrics in order to build a more intuitive understanding of the functionality of the pattern. These physical models allowed me to closely examine the locations of the panels and hinges, and the effects of changing variables between models.

This phase of iteration was based a process developed by origami artist Robert Lang, which addresses  the macro-thickness conditions specified above. The main challenge of this phase was determining how to integrate the Lang's 2D crease pattern process into increasingly-thick 3D materials. A variety of materials were used; stiff paper was used in the thinnest models, intermediate thickness models used poster-board, and the thickest material used was foam-core and cardboard.

After several dozen models, I understood the system well enough to begin to construct my own parametric framework.

Canvas 6.1.png

Canvas of parametrically updating thick-material Flasher model, made with Grasshopper fro Rhino 6:

Parametric Analysis

Prototyping in the early phase identified a large number of parameters, and in this next phase I built a variety of digital models to simplify these relationships. It's necessary to fully understand which parameters are driving, which are driven, and which should be expressed in terms of another for the sake of simplifying the design process. I used the following tools in this phase: Fusion360 for creating basic parameter-driven solid modeling, Microsoft Excel for analyzing data from digital model, and ultimately Rhino6 and Grasshopper for creating digital models with algorithmic inputs. This phase was more technically challenging than other phases of the project, but it ultimately allowed me see the exact effects of different parameter configurations on the model without physically building new prototypes.

Screen Shot 2020-02-26 at 3.46.33 PM.png
Screen Shot 2020-02-26 at 4.11.40 PM.png
Screen Shot 2020-02-26 at 4.19.49 PM.png
Screen Shot 2020-02-26 at 4.08.21 PM.png
Screen Shot 2020-02-26 at 4.37.02 PM.png

During this phase I developed a modeling process that combined the micro- and macro-thickness aspects, and came up with a new type of thick-material origami vertex for this unique type of fixture.

Digital Prototyping and Fabrication

With the new integrated framework and joint mechanics, I was able to model hinge geometry directly into panels, ensuring the correct rotational axes. In this phase I constructed models with thick and rigid materials. The main challenge of this phase was determining how to integrate hinges into the very small space that they had available to them

The first models were 3D printed. The panel geometry was determined via my new framework, I modeled hinge geometry onto the panel bodies, and then I 3D printed and assembled the panels by hand.

This model was mechanically operational and stowed compactly, so I scaled up to a larger proof of concept.


Large Scale Thick-Material Prototype

flat bottom.png

To show that all aspects of thickness accommodation have been addressed, I built a model from a completely thick-rigid material. This model is made from 1/4" (6.3mm) basswood, and opens and closes smoothly. Due to exclusively using the hinge-shift technique and using inherent parameters to calculate panel geometries, the model both retains effective single degree-of-freedom movement (openable by articulating a single hinge), and also optimally compact during stowage. This model also retained planarity of bottom hinges, as shown by the flat bottom on the right.  There are 4 panel layers on this model, but this was only due to the limitations of feasibility of building the physical prototype: my thickness accommodation framework allows for an arbitrary number of panels to be stowed around the central polygon.

Product Applications

I believe that this type of product will help our civilization transition away from a reliance on fossil-fuel energy sources. There are 3 scales at which I hope to see this product come to life:

  1. Customer Level

    • People are drawn to the elegance of this pattern, and would be attracted to product that utilize it well. A customer-scale flasher solar array​ could provide power to electric vehicles, mobile work sites, or umbrella-type products

  2. ​Commercial Level​

    • Commercial areas strive to be beautiful, and solar panels are considered unsightly by some. ​A pedestrian mall with a covering of tiled flashers could provide power to retailers in the area, while also contributing and elegant and unique esthetic. Flashers could easily be installed anywhere due to their centralized structure. Imagine a corporation sponsoring a "solar flower garden," with dozens of flashers together as both functional infrastructure and an attractive artistic destination.

  3. Infrastructural Level

    • In order to capture enough solar energy to make a difference, a large amount of surface must be covered by solar arrays. As stated previously, we cannot continue to dedicate valuable land area to this, especially when so many natural ecosystems are threatened by​ human changes. An environment which does offer an extremely large amount of space would be the ocean for a floating installation. A floating assembly of tiled flashers would have no practical limitation to available space.

    • The area between the tropics mostly open ocean, and sees the most consistent direct sunlight. The primary concern of an ocean assembly would be withstanding the forces of hurricanes and ocean storms.

      • The way to withstand a hurricane is to not be near the hurricane.

      • Hurricanes travel across the surface of the ocean, but 30m below hurricans there are significantly less forces.

    • Ocean arrays could stow entire assemblies of units and pull them to a safe depth to wait out the storm. When the danger has passed, the installation could return to the calm surface, open, and return its solar collection.

What's Next?

This is an ongoing project. While I will complete my Masters Thesis Project in April 2020, I am continuing to develop this project and solve remaining issues. It is my hope that a future employer sees the potential of this, so it can be further developed with improved resources.

bottom of page