# What is this geometric pattern called and how to construct it?

I am wondering if the design in this image has a name? Also does anyone know a mathematical way to construct this with circles, arc etc?

I am interested in 2d construction technique although 3d would be interesting to know as well.

• What program are you using? – WELZ Feb 25 '19 at 19:16
• Isn't it just four crescent moons each one 90 degrees off from the last? – Aaron Brick Feb 25 '19 at 20:18
• @WELZ I am interested in high level description of construction method – Numan Feb 25 '19 at 23:45
• @AaronBrick I can see that but I want a precise way to construct this so there is no guessing and tweaking. – Numan Feb 25 '19 at 23:47
• You should decide which one you want - 2d or 3d - and even then your question is still too broad. Perhaps you should try to construct it and come back with a question related to your issues then. – Luciano Feb 26 '19 at 9:14

This resembles a knot, as already said by others. You have not a better description of it than your screenshot. Without knowing any math relations of the seen image it's possible only to make a visual copy.

Of course someone can guess or know a math description of the shapes in your screenshot, for ex. the original creator. I guess it has 4 otherwise equal shapes, but rotated with 90 degrees steps. In addition a cusp node is placed on a certain point of the preceding shape.

I do not try to guess algebraic formulas of the shapes and a rule for exact placement

Visual copying starts by tracing one crescent-like shape:

Note: There's as few nodes as possible, one node is for placement the cusp node of the next shape.

The shapes resemble also ellipses, so as well I can guess it's made of ellipses. It's tried later.

Let's continue! Three 90, 180 and 270 degrees rotated copies has been made and placed so that the placement help node snaps:

A background has been inserted with the same color as the stroke color of the shapes.

The idea of using ellipses:

Unfortunately I haven't a formula for the sizes and placements for the ellipses to make an exact copy of your screenshot. I simply made two intersecting identical ellipses and then duplicated the pair, but as 90 degrees rotated.

The coloring is made in Illustrator with the Shape Builder. It hopefully gives an idea that in 3D it can be two loops braided together.

It can, but as well it can be something else. A flat pattern without any light effects can be in 3D created in infinite different ways. One example:

A common name for this kind of image is a "knot" or even a "torus knot." Celtic knots are good example of this idea taken to the extreme. There are many different techniques used to make them, so the question is a bit too general to answer as it stands. Do you have a specific question about how to make them?

• This really should be a comment unless you are planning on giving a method on how to construct it. – Ovaryraptor Feb 25 '19 at 22:44
• Thanks. I can see how it is related. Maybe a 2d projecction of a torus knot? It would be interested to know to construct this in 3d or 2d although I had 2d in mind in my initial question. – Numan Feb 25 '19 at 23:50
• @Ovaryraptor Unless the op has a specific question about the "how," a valid answer could be something as simple as "Trace it." That seemed self-evident and unhelpful, so instead I answered the "what" part of the question and asked for elaboration on the other part. He has responded, so now I will. – 13ruce Feb 26 '19 at 13:12
• @Numan A lot of 3D software has the ability to construct torus knots. A quick Google search for "3d torus knot tutorial" will give you everything you need there. For a 2D version, I would recommend using Illustrator or some other vector-based illustration software, like Inkscape. Your post doesn't list any specific software. I would recommend against software like Photoshop or GIMP for this type of design. Are you familiar with any specific art software that we could use as a way to show potential methods? – 13ruce Feb 26 '19 at 13:26
• I could show you how I would do it, but if you don't have the same software, it may not be very useful. – 13ruce Feb 26 '19 at 13:27

This appears to be two interlocking mobius rings. Basically, a mobius ring is created by this analogy: If you were to take a flat strip of ribbon, and while holding the two ends, add a twist, then reconnect the ends. The result will be a mobius ring. It's a paradoxical shape in that should you place your fingertip on any surface and move your fingertip across the surface in any direction, you would eventually touch both the surfaces (top and bottom) of the original, without having to lift your finger.

Building this shape geometrically is more involved and confusing than it might immediately appear. If 2D, I'd use Adobe Illustrator and its "Live Paint" tool. Create a single base shape, including a stroke that is the weight of the desired gap space. Copy the original and paste directly on top. Rotate the copy the desired degrees to achieve the desired offset from the original. Use live paint to achieve the desired "over/under" appearance (not unlike the interlocking Olympic rings). Expand the end result and delete unnecessary elements.