Over on Facebook someone shared with me this video about the use of yarncrafts in mathematics:
https://www.facebook.com/mentalflossmagazine/videos/10154510337972365/

Here's the accompanying article:
http://mentalfloss.com/article/86016/6-math-concepts-explained-knitting-and-crochet

I've been collecting links about this subject for a while so I offered to do a linkspam.

Particularly rich sites to investigate:

Dr. Sarah-Marie Belcastro's mathematical knitting page.

http://www.toroidalsnark.net/mathknit.html

WoollyThoughts.com, the yarncraft home of mathematicians Pat Ashforth & Steve Plummer.

http://www.woollythoughts.com/

They also have a Ravelry group.

http://www.ravelry.com/groups/woolly-thoughts

In detail:

The original paper about crocheting and mounting the Lorenz manifold.

http://research-information.bristol.ac.uk/files/2988096/2004r03.pdf

Crochet your own Lorenz manifold

http://www.ravelry.com/patterns/library/lorenz-manifold

An interview with the people who designed and crocheted a hyperbolic plane.

http://www.cabinetmagazine.org/issues/16/crocheting.php

Mary Pat Campbell's fractal crochet

http://www.ravelry.com/patterns/library/crochet-sierpinski-fractal-triangle

http://www.marypat.org/stuff/nylife/020325.html

Gallery of sierpinski crochet

http://www.crochetgeek.net/crochet/sierpinski/gallery/index.html

Random stripe generator

http://www.biscuitsandjam.com/stripe_maker.php

Tessellated fish

http://www.ravelry.com/patterns/library/a-recipe-for-fish

A recipe for knitting a Klein bottle (which can be worn as a hat)

http://www.toroidalsnark.net/mkkb.html#kbinst

The Crochet Coral Reef, a project of the Institute for Figuring

(this isn't strictly mathematical, but a lot of the creatures depicted grow in ways that can be depicted using hyperbolic plane crochet)

http://crochetcoralreef.org/coral-reef-gallery.php

You can participate in this project. Some example patterns here:

http://guides.uflib.ufl.edu/crochetreef/crochetcoralreef/patterns

Cable knitting using random numbers

http://web.archive.org/web/20130707042959/http://www.fuzzygalore.biz/articles/probability.shtml

Knitting using cellular automata

http://www.knitting-and.com/knitting/tips/automaton.htm

Cellular Automaton pattern generator (uses Flash)

http://www.unikatissima.de/e/?page_id=2148

Cellular automaton pattern examples

http://mathworld.wolfram.com/ElementaryCellularAutomaton.html

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