# 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.

## Fractalized CFW 85 (consistent fold direction)

I developed Shuzo Fujimoto’s design, Petals (CFW 85) into a fractal. I don’t have direct proof if Fujimoto was aware of this possibility, but I think it’s li...

## Fractalized CFW 85 (alternating fold direction)

I developed Shuzo Fujimoto’s design, Petals (CFW 85) into a fractal. I don’t have direct proof if Fujimoto was aware of this possibility, but I think it’s li...

## 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

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

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)

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...

## Comparison of Scissors Fractal Variants — alternating and consistent rotation direction

A comparison of two variants of Scissors Fractal: one with consistent rotation direction for all levels and one with alternating rotation directions.

## 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...

## Lucky Star Fractal Box (Simplified) Variant B

When you fold variants of my Lucky Star Box, you can extend the star to its fractal form. This particular variant emerges when you apply that procedure to th...

## 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

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)

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

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)

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

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

## 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)

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)

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

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...

## Fractal Mountains Reflecting in a Lake

A minimalistic self-similar origami design, in the style of Edward Mistretta’s recent works.

## 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

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 (level 7)

This is a level-7 Lucky Star Fractal, the largest number of levels I folded so far.

## 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)

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)

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

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, 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

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

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 (Fujimoto) and Lookalike (Kosmulski) side by side

A side-by-side comparison of Shuzo Fujimoto’s Clover Folding (left) and my own Clover Folding Lookalike (right). Front and back sides are shown (top and bott...

## 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)

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)

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

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

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 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

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...

Happy New Year!

## Stacked Propellers Tessellation (single molecule)

This is a fractalized version of my Propellers Tessellation. Stacked Propellers Tessellation is folded from a 16×16 grid per molecule in this case but you ca...

## 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

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

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

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

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

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

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

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

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 (BBU)

Model uses 192 modules: 120 × A1, 72 × A2

## 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)

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

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

## Sierpiński Tetrahedron, level 3 (Trimodule)

This model uses 128 Trimodules, forming 64 2-unit tetrahedra, and 126 links that connect them, for a total of 254 units. The links were made from narrow rec...

## 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 2 (Trimodule)

Compare also with level-1 version of the same fractal.

## 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)

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...