# Math Monday: Microscopic Fractals

By George Hart for the Museum of Mathematics

We have seen various ways to make the Sierpinski tetrahedron in a past Math Monday column, but here is a new one. A direct laser writing process was used to produce this polymer tetrahedron, which is just 100 microns tall—the thickness of a hair. This remarkable object and these electron microscope images were created and sent to me by Michael Thiel of Nanoscribe, using the STL file available here. In person, the whole tetrahedron can just barely be seen by the naked eye as a very tiny, featureless speck on the surface of a small glass disk. When you look at it with a magnifying glass, you can make out the overall tetrahedral shape and the larger openings.

In this higher-magnification view of just one corner, you can see more of the detailed structure within the speck.

I wonder if someday direct laser-writers will become household machines so we can all make our own personal specks–little Who-villes of our own imaginations. What speck would you want to create?

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### BY Gareth Branwyn

Gareth Branwyn is a freelancer writer and the former Editorial Director of Maker Media. He is the author or editor of a dozen books on technology, DIY, and geek culture, including the first book about the web (Mosaic Quick Tour) and the Absolute Beginner’s Guide to Building Robots. He is currently working on a best-of collection of his writing, called Borg Like Me.

### 2 Responses to Math Monday: Microscopic Fractals

1. I’d make little castles, leave them for a few months in a nonsterile place, and see what sort of microscopic tenants moved in. It’d be like Sea Monkeys, only smaller and more civilized.

I wonder if neighboring castles would have wars, swap daughters in marriage, that sort of thing…little microbe politics?

2. Where are the scale bars in the images? SEM fail.