Coherence: A Hyperbolic Crochet Pattern

For Beginners

I am diving deep into the mathematical rabbit hole of Hyperbolic Crochet these days. If you landed on this page, I'm guessing you have an idea about this concept, but if you'd like to know more about it, you can have a look at this article I wrote comparing Euclidean, Spherical and Hyperbolic crochet. It's called The Ultimate Beginner's Guide to Hyperbolic Crochet

You might be wondering why I chose the name "Coherence" for this particular pattern.

Well, at its core, coherence means that parts of something fit together in a consistent, meaningful way. There’s a sense of order, even if the overall result looks complex.

So how does "Coherence" connect to hyperbolic crochet?

When we crochet a hyperbolic piece, we're doing something very simple and consistent:

• repeating the same stitches
• increasing at a steady rate
• following a clear rule

There’s no randomness in the process.

And yet… the result looks wild, organic, almost chaotic. It ruffles, folds, and expands in unexpected ways.

That contrast is exactly where coherence lives.

It's order creating complexity.

Every stitch we add follows the same logic. The pattern is coherent.
But because we're adding more stitches than a flat surface can hold, the fabric has to bend and curve.

So instead of lying flat, it forms a hyperbolic surface.

I think it's beautiful because:

• nothing is out of place
• nothing is accidental
• every ruffle is a direct result of the same simple rule.

This is complexity emerging from consistency.

And here's a deeper way to think about it:

You can think of your crochet piece as a system where:

• local actions (each stitch) follow a rule
• global structure (the final shape) emerges from those rules

Even though the shape looks irregular, it is completely coherent mathematically and structurally.

I might be overanalyzing this whole concept, but you get the picture, right?

Anyway, I'm pretty sure you want to find out the actual "rule" for this pattern.
Simply put, to create this particular hyperbolic plane we will use the formula

"x=n+1"

I started this project by choosing the number "4" (n=4 in the formula above), and working in continuous rounds using a 3mm hook and single crochet.

I sent out a "Call for Testers" on Facebook and have several testers taking part in this Crochet Experiment. Each tester will replace the "n" with a different number, which will lead to different shapes. I'll be adding photos of their makes at the bottom of this page as Testers submit them.

So to create this particular shape, you can follow the instructions below.

Disclaimer: This post contains affiliate links, which means I receive a small commission, at no extra cost to you, if you make a purchase using the Start Crochet links. Please see my disclosure for more details.

Materials Needed

• DK weight yarn in (cotton, acrylic, or blends)
• Size 3.0 mm crochet hook
• Yarn needle
• Scissors

Abbreviations Used in Pattern

• MC = magic circle
• sc = single crochet
• inc = increase = 2 sc into the same stitch
• st = stitch
• sts = stitches
• fo = fasten off

Skill Level

Beginner

Measurements/Size

Approximate finished size: 20 cm ( 8 ")

Gauge

Not important for this project.

Notes

• This hyperbolic plane is worked in continuous rounds.
• Please note that I use US crochet terms.

Coherence: A Hyperbolic Crochet Pattern Instructions

R1: Work 6 sc into a Magic Circle. (6)
Note: If you don't know how to work a Magic Circle, then ch 4, sl st to join and form a circle. Then work 6 sc into that circle.

Pull your magic circle closed. Do not join. Continue to R 2.

R2- 20 : [3 sc, increase]. Repeat [ ] in continuous rounds.

Note: You will find that for your beginning rounds, your piece looks more like a cone. It will gradually start to ruffle as you exponentially increase your stitches in subsequent rounds.

You can continue with more rounds if you like. You'll get even more fascinating shapes!

Once you feel that you've finished your piece, sl st to join to the next stitch. Leave a 4" tail, cut your yarn and fasten off.

Using your yarn needle, weave in your ends. You may want to keep the center yarn tail if you'd like to hang your project.

And that's all there is to it!

I hope you enjoyed making this project. Why not try experimenting with variations of the mathematical formula? Choose a new number, a new stitch, combine increase numbers or stitches, experiment with different yarn materials, hook sizes, you name it! Go for it and please do send me photos of your finished work so I can add them to this blog post 🙂

Thanks for stopping by and let me know if you have any questions in the comments section below.

Happy hooking!

May

Related Posts

Want to see even more Hyperbolic Crochet patterns? Have a look at these:

Worry Worm Crochet Patterns

Wind Spinner Crochet Patterns

Scrunchie Crochet Patterns

Ruffled Granny Square Hat Crochet Pattern