Parametric Mobius Strip

One-sided Mobius surface from parametric equations

Category: MathematicalLevel: Intermediate28 components · 33 wires

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The Mobius strip is built straight from its equations: x = (R + v cos(k u/2)) cos u, y = (R + v cos(k u/2)) sin u, z = v sin(k u/2), with u running around the circle and v across the strip width. A grafted data tree forms the u x v point grid made into Surface From Points. The Half Twists slider changes k so the strip can be twisted half a turn (classic Mobius) or more. The strip edges are piped to emphasise the form.

Grasshopper definition with wires

The real Grasshopper canvas: 28 components joined by 33 wires.

Parametric Mobius Strip: Grasshopper canvas with components and wires

The result in Rhino

Parametric Mobius Strip: result in Rhino

Project info

CategoryMathematical
LevelIntermediate
ToolGrasshopper · Rhino 8
Price (one price)US$133
Components28
Wires33

The project file you can download

The real project file is available. It is not just the pictures on this page: you get the working definition with every component and wire in place. It can be downloaded after payment, and we send the download link by WhatsApp or email.

ZIP: .gh + .ghx + baked .3dm + images

What is inside the file

The original Grasshopper definition (.gh and .ghx) with every component and wire in place, ready to open and tweak
The geometry baked to Rhino (.3dm)
Canvas and result images
A BACA-DULU.txt file listing the plugins required, the version and how to use it
All packed in one ZIP file

Project file: The actual project file (not just the picture) is available to download once payment is complete; we send the download link by WhatsApp or email
Payment: One price per project, paid in full upfront; the file is sent once payment is received
Tax: Prices exclude 11% VAT
Customisation: Adapting it to your own size or design can be ordered separately via WhatsApp

Components and plugins

Components used

Range
Surface From Points
List Item
Interpolate
Pipe
Pi

Plugins required

None. It uses only the components built into Grasshopper.

Parameters you can change

Radius (3 to 20): core circle radius
Strip Width (1 to 10): half strip width
Half Twists (1 to 7): half turns (1 = Mobius)

How the definition works

1Set the sliders in the Parameters group (Radius, Strip Width, Half Twists).
2u, v parameters: Range u around the circle (grafted) and Range v across the strip; twist angle a = k u / 2.
3Equations: Cosines and sines of the twist and circle angles are combined per the Mobius equations.
4Surface: The point grid becomes Surface From Points; the first and last edge points of each branch (List Item) are interpolated into one continuous edge and piped.

Price and ordering

US$133

One price for the whole project file, excl. 11% VAT

Order the file via WhatsApp

Frequently asked questions

Do I get the real file?

Yes. The pictures on this page are only previews. After payment we send the download link of the real project file (a ZIP containing the .gh and .ghx definition, the baked .3dm, images and a BACA-DULU.txt note) by WhatsApp or email.

Which Grasshopper version do I need?

The file was made in Rhino 8 with Grasshopper (Rhino 8). Newer versions open it too.

Can you adapt it to my design?

Yes, as a separate order. Message us on WhatsApp with a short description of the size and shape you want.

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Images are real captures of Rhino 8 and Grasshopper taken from the project files. Rhino and Grasshopper are trademarks of Robert McNeel & Associates.

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The project file you can download

ZIP: .gh + .ghx + baked .3dm + images

What is inside the file

The original Grasshopper definition (.gh and .ghx) with every component and wire in place, ready to open and tweak

The geometry baked to Rhino (.3dm)

Canvas and result images

A BACA-DULU.txt file listing the plugins required, the version and how to use it

All packed in one ZIP file

Project file: The actual project file (not just the picture) is available to download once payment is complete; we send the download link by WhatsApp or email

Payment: One price per project, paid in full upfront; the file is sent once payment is received

Tax: Prices exclude 11% VAT

Customisation: Adapting it to your own size or design can be ordered separately via WhatsApp

How the definition works

1Set the sliders in the Parameters group (Radius, Strip Width, Half Twists).

2u, v parameters: Range u around the circle (grafted) and Range v across the strip; twist angle a = k u / 2.

3Equations: Cosines and sines of the twist and circle angles are combined per the Mobius equations.

4Surface: The point grid becomes Surface From Points; the first and last edge points of each branch (List Item) are interpolated into one continuous edge and piped.