Fractals


Models of this type are also automatically listed in: abstract, geometric, mathematical object More restrictive types: modular fractal, recursive non-tileable model, recursive and periodic tessellations, recursive tessellation

Fractals are a class of mathematical objects which are characterized by self-similarity: a part of the object resembles the whole. Such structures can be approximated in origami using iterative folding or using modular origami techniques.

This page lists models of a single type. You might be interested in folding instructions instead.
Fractalized CFW 91

Fractalized CFW 91

I found out that Shuzo Fujimoto’s molecule used in his CFW 91 star, can be changed into a fractal. By pulling some paper outside in the center, you can get a...

Origami in Shades of Gray

Origami in Shades of Gray

This is a collections of my origami tessellations that I framed and hung near the desk I use for folding. The models, all kept in neutral colors, are as foll...

Scissors Fractal

Scissors Fractal

This is a recursive version of Shuzo Fujimoto’s Scissors (CFW 87). I wanted to call it Biohazard Fractal since it resembles the biohazard symbol, but later d...

Scissors Fractal (alternating rotation)

Scissors Fractal (alternating rotation)

This is another fold of Scissors Fractal, a recursive model I derived from Shuzo Fujimoto’s Scissors (CFW 87). In this fold, the direction each level rotates...

Stacked Whirlwind Molecule

Stacked Whirlwind Molecule

This is a single molecule which can be tessellated. It is made from a molecule of Whirlwind Tessellation placed inside a larger one. More than the two levels...

Fortune Teller Christmas Tree

Fortune Teller Christmas Tree

You can assemble a simple Christmas tree from multiple Fortune Tellers (which you probably already know how to fold). Each Fortune Teller is smaller than the...

Hydrangea Tessellation

Hydrangea Tessellation

Believe it or not, over all these years of folding tessellations, I never folded a clean tiling of Fujimoto’s Hydrangea. I recently decided to make up for th...

Hydrangea (Tant)

Hydrangea (Tant)

Another fold of Shuzo Fujimoto’s Hydrangea. I’ve kept two outermost leaf layers free of unnecessary creases. For deeper layers, it becomes much harder.

Chrysanthemum

Chrysanthemum

This design is my modification of Shuzo Fujimoto’s Hydrangea. Despite the change being very minor, it allows the model to be shaped in a more three-dimension...

Lucky Star Fractals (10 different colors)

Lucky Star Fractals (10 different colors)

Ten level-3 Lucky Star Fractals, folded from metallic paper in different colors. This is just a small subset of how many times I have folded this model over ...

Hydrangea

Hydrangea

This is, along with Clover Folding, one of the oldest pictures of a tessellation folded by me (taken in June 2015).

Clover Folding

Clover Folding

Along with the Hydrangea, this is one of the oldest picture of a tessellation folded by me (taken in June 2015).

Clover Folding (blue)

Clover Folding (blue)

Along with the other Clover Folding model, this is the oldest picture of a tessellation folded by me (taken in June 2015).

Hydrangea (Prägo Kristall paper)

Hydrangea (Prägo Kristall paper)

This is just a simple Hydrangea, designed by Shuzo Fujimoto, but I think it looks really nice in back light. Folded from Grünperga Kristall Prägo, a kind of ...

Hydrangea from book wrapping foil

Hydrangea from book wrapping foil

Model folded from transparent book wrapping fold which shows the internal structure of the model in an interesting way. Have a look at the detailed review of...

Triangle Recursion

Triangle Recursion

This is the simplest recursive/fractal model I have come up with so far. It is folded from a square. Due to the very high shrinkage factor, which is almost 4...

Twisted Bird Base Fractal

Twisted Bird Base Fractal

This is a recursion of my Twisted Bird Base Tessellation. The recursive / fractal version looks interesting, but it’s rather hard to collapse.

Lucky Star Fractal Tessellation

Lucky Star Fractal Tessellation

This is a tessellation of the Lucky Star Fractal. The standalone star was designed independently by several people, starting with Shuzo Fujimoto. I don’t kno...

Lucky Star Fractal (Open Back)

Lucky Star Fractal (Open Back)

This model is a variant of the Lucky Star Fractal (aka Logarithmic Star), designed by myself and independently by many others before me, starting with Shuzo ...

Lucky Star Fractal (level 3)

Lucky Star Fractal (level 3)

A level-3 fold of Lucky Star Fractal, this time from gray metallic paper. I rarely fold a model multiple times, but this particular model is so nice I have f...

Lucky Star Fractal

Lucky Star Fractal

This is a recursive version of the Lucky Star molecule. Just like the non-recursive version, it can be tessellated or used for decorating a box. The back of ...

Rhombus Fractal

Rhombus Fractal

Rhombus Fractal, an origami tessellation designed by Endre Somos (and independently also by Joel Cooper and by Wei Fu), folded by me. You may also find inter...

Stacked Propellers Tessellation

Stacked Propellers Tessellation

A refold of my older design, Stacked Propellers Tessellation, this time as a complete tessellation rather than a single molecule. 64×64 grid.

Phantasma Fractal Variant

Phantasma Fractal Variant

This is my variant of Edward Mistretta’s model, Phantasma Fractal. It’s a nice design which can be folded as a single molecule, or tessellated.

Clover Folding Lookalike

Clover Folding Lookalike

This is my design which at first glance looks very similar to Shuzo Fujimoto’s Clover Folding but has a completely different crease pattern and design.

Clover Folding (22×22 grid)

Clover Folding (22×22 grid)

I hadn’t folded Shuzo Fujimoto’s Clover Folding for at least two years when I decided to fold one again after seeing some examples beautifully folded by John...

Hydrangea Cube (Harmony paper)

Hydrangea Cube (Harmony paper)

Shuzo Fujimoto’s Hydrangea can be used as a modular unit. The method was first published by Meenakshi Mukerji and then reinvented independently by myself. I ...

Hydrangea Heart

Hydrangea Heart

My modification of Shuzo Fujimoto’s Hydrangea into a heart shape. I found on flickr a similar model, designed by Francis Ow.

Hydrangea with Leaves

Hydrangea with Leaves

A color-change variant of Shuzo Fujimoto’s Hydrangea, designed by Meenakshi Mukerji. Test fold based on unpublished diagrams, kindly provided by Meenakshi [u...

Stacked Hearts

Stacked Hearts

Stacked molecules of my Hearts Tessellation. This model is a fractal, and you can go on stacking heart upon heart indefinitely, each twice as large as the pr...

Leafless Hydrangea

Leafless Hydrangea

This Leafless Hydrangea model is a simple modification of Shuzo Fujimoto’s Hydrangea. It’s interesting how a simple change can modify a model’s appearance. J...

Cube from Recursive Four-Sink Base

Cube from Recursive Four-Sink Base

This cube is made from six units, each of which is a recursive four-sink base modified for use as a module.

Fractal Pinwheel Cube

Fractal Pinwheel Cube

This is an example of using my Fractal Pinwheel as a modular unit. Due to small size, there’s only one level so the fractalness is not so clearly visible.

Fractal Pinwheel

Fractal Pinwheel

This pinwheel displays a fractal pattern with smaller pinwheels embedded inside larger ones, a series which can be continued indefinitely with thin enough pa...

Fenced Tiling of Clover Folding

Fenced Tiling of Clover Folding

I designed this tiling of Shuzo Fujimoto’s Clover Folding after I saw the tiling by Peter Budai and thought it would be better to make the borders between mo...

The Tower of Babel

The Tower of Babel

This rendition of the Tower of Babel consists of a series of square platforms placed one on top of another and rotated by 45 degrees at each level. This frac...

Down the Rabbit Hole

Down the Rabbit Hole

This tessellation consists of concentric square twists of growing size. The medium is self-adhesive holographic foil glued onto tracing paper. The spiral is ...

Hydrangea Picture Frame

Hydrangea Picture Frame

This picture frame can hold a standard 15×10 cm photograph. It consists of four molecules of the Hydrangea Tessellation (designed by Shuzo Fujimoto), spaced ...

Hydrangea Icosahedron

Hydrangea Icosahedron

After I made a Hydrangea Cube, Hydrangea Icosahedron was the next logical step. Just as in the cube, the Hydrangea Tessellation by Shuzo Fujimoto is used as ...

Hydrangea Cube

Hydrangea Cube

I came up with the idea of connecting Hydrangeas to form a modular origami design independently, then found out Meenakshi Mukerji had published it in her boo...

Menger Sponge, level 1½ (StEM)

Menger Sponge, level 1½ (StEM)

The modules’ shape makes this level 1 model look even closer to a level 2 model than the Penultimate Module version. The hole in each small square is exactly...

Menger Sponge (level 2)

Menger Sponge (level 2)

This is a labor-intensive, but very satisfying to fold model. Some people have managed to go as far as level 3 but even level 2 was quite challenging. About ...

Ticket Menger Sponge

Ticket Menger Sponge

Model folded from Warsaw public transport tickets (back side with magnetic strip visible). 192 modules: 120 for the body and 72 for coating.

Menger Sponge, level 1½ (Penultimate unit)

Menger Sponge, level 1½ (Penultimate unit)

Thanks to the modules’ shape and the holes created in the spaces between them, this model looks almost like a level 2 Menger sponge even though it is actuall...

Koch Snowflake, level 1 (Trimodule)

Koch Snowflake, level 1 (Trimodule)

A level-1 Koch snowflake is just a simple hexagonal star, and this is the way of connecting the Trimodule units originally suggested in Nick Robinson’s instr...

3D Koch Snowflake (Trimodule)

3D Koch Snowflake (Trimodule)

This fractal is an analogue of the standard Koch snowflake. Level 0 is a tetrahedron. In each iteration, a tetrahedron with half the edge length is placed in...