For example, this image, which happens to be like the logo of the old Crocker Bank, takes a 'seed' shape, a hexagon, and simply places the same triangle shape along each side of the hexagon.
That's neat! But it gets better. If you place simple Pretzangles next to each other a bit of magic occurs - you get an instant interlaced knot pattern:
It was when I spotted Steve Abbott's 3D Celtic Knot website that I saw how there was a relationship between Pretzangles and Celtic Knots.
Steve became enthusiastic about the amazing possibilities of the Pretzangles method and kindly produced for me the Pretzangles program.
Pretzangles in 3D
Pretzangles work when you put seed shapes side-by-side. You can do this in 2D, but you can equally do it in 3D. Here's a Buckminsterfullerene created in a few seconds' work in the Pretzangles program:
If you have a VRML add-in in your web browser, you can look at the Fullerene in full interactive 3D by clicking on fullerene.wrl
The program comes full of goodies. It contains all the Archimedean tilings of the plane (all the ways that you can fill your screen with regular geometrical patterns), all the 3D Platonic and Archimedean solids, and lots of examples of Pretzangles to give you ideas for creating your own designs.
The program lets you save your 2D and 3D designs as images, and it's very easy to save your designs as small .prz files which you can re-use, share with your friends, modify later. The download comes with a large selection of .prz files to get you started.
And best of all, Pretzangles is completely free. Of course there is the hope that you will e-mail your suggestions, corrections, interjections and observations. I've been working on Pretzangles since 1975, and it's about time to start sharing the idea.
Click here to download the 3MB install version. This use the Microsoft Windows Installer to install itself. If you have an old version of Windows you might need to find a copy of InstallMSI.exe to install the Windows installer!
Click here to download for those who have previously installed Pretzangles - 512K. If you have run Steve's Celtic knots program or a previous version of Pretzangles then this one will work fine.
For a fuller explanation about Pretzangles click on More on Pretzangles
For a gallery of Pretzangles art click on Pretzangles Art Gallery
There's an extensive Tutorial on Pretzangles available. You can go view the online version of the Tutorial
or get it as a ~800KB Word file. If you click on the link it will open live in Word within your browser, which most of us don't like. If you right click on the link (the preferred approach) it will let you download the Word file to a convenient folder so you can read it at your leisure. Tutorial.doc
The Pretzangles concept, this software implementation of it and the accompanying Tutorial texts are all Copyright © 1975-2002 Matthew Kells