Articles and Tutorials

A Whole Lot of 3   Sometimes it can be hard to tell what's 3 and what's 6. Now this may sound confusing - how can you not know the difference between 3 and 6? But when there's 6 things, with alternation between each one, is it 3 or is it 6? In terms of rotational symmetry, the answer is 3. In terms of twists in a loop, the answer is 6. And to make matters worse, you can't look for 3-fold symmetries around the point in question to decide - they're all going to be 3-fold in either case!...

Managing many pleats at once is one of the harder things about tessellations, but using these three-way intersections one at a time lets us minimize the difficulty and focus on the steps.

These three-way intersections can be put together in a huge variety of ways, from rotational to mirrored to combinations of both.

When we start folding tessellations we're presented with a couple grid options - all of which are aligned with the edge of the paper in some way.

This fact is invisible in the way we talk about grids too.

We don't say "square grid aligned with the edges of the paper" - it's just "a square grid".

Many folders would like to start learning tessellations, but aren't sure where to start. In this video I introduced the four major grid types that every tessellation folder needs to know and clarified the distinction between twist-based tessellations, corrugations, and tessellations that require an all-at-once collapse. You see, there are easier and harder ways to fold tessellations and when many folders see a crease pattern for the first time they think that they need to precrease everything and then collapse all at once. That's actually the hardest way to learn tessellations - you have more work at the beginning, more...

Backlighting Surprise!   As the name implies, Knotted Web Tight is a close relative of Knotted Web - everything's just one spacing closer together. Interestingly, the donut shape that's somewhat visible in Knotted Web is much more pronounced in Knotted Web Tight and shows up as overlapping circles in the backlighting. This was a huge surprise to me when I first saw it while I was folding! No part of this pattern is actually curved, and yet the backlighting seems to show only curves! What's more, since this is an isoarea pattern the same backlighting is seen on both sides....