Ever wondered why every dollar bill contains this cool looking geometrical grid? Is it just because it looks cool?

It’s not just the dollar bill. This pattern is called a Guilloché pattern and it can be seen on any kind of printed material that we want to protect from counterfeiting.

It can be seen on stamps, alcohol and tobacco seals, paper currency etc. I bet you’ve seen one in the wild, but you never even thought about it. This is one of those design & engineering masterpieces you never think of but plays an amazing role in our everyday lives.

How can this stop counterfeiters?

Guilloché patterns are really complex pieces of artwork that cannot be scanned and reprinted using even the most advanced technologies. Scanners simply can’t catch all of the intricate details of the pattern at the size it is printed. Regular printers can’t reproduce them without getting blurry. They are often engraved or stamped on materials to provide an impeccable structure of the print.

Guilloché patterns act similar to hash functions but in physical form. Drawing one from a set of parameters is easy, but trying to guess those parameters from a drawing is nearly impossible. This means that this pattern cannot be recreated digitally.

Including this pattern on physical objects makes them impossible to scan perfectly. Recreating them digitally is also nearly impossible because of their complexity. Did I mention this is one of the cheapest print security measures to implement? This makes them an invaluable tool for print security.

How are they designed?

The Guilloché patterns are created by applying a curve in a repetitive way on a surface. One way of doing this is using a spirograph. Spirograph is basically plotting a curve across a path of a different curve.

This approach allows you to change many parameters of how the pattern is created. We can modify the shapes of both curves, the color of the plotted shapes, how densely is the curve being drawn and the rotation speed of the curve. If you think about the infinite amount of curves we can use instead of the two in the example, along with all parameters mentioned above, you can get the idea of all possibilities.

This insane amount of variation is why I said these patterns act kinda like hash functions. It’s easy to draw one, but to guess all of the parameters used to draw a printed pattern is near impossible.

This is not the only way to design a Guilloché, but it will give you attractive looking results that offer all security benefits.

Example

As a fun Easter weekend project, I created a Swift Playground book that allows you to understand and interactively draw your own Guilloché patterns. The animation you saw just a moment ago is a recording from that playground.

I used the superformula to define the functions of both curves. Superformula curves are closed curves by definition which makes my approach possible. They can also produce very different results by changing their parameters. This makes them a good choice for a pattern that should have a lot of variation.

Next time you have any valuable piece of paper in your hands – examine it and admire the tiny printed pattern that protects us from counterfeiters.