One of Alan Turing's most impressive contributions was a 1951 paper called "The Chemical Basis of Morphogenesis," in which he described a theory for how complex biological patterns, like those found on skin, fur, and shells, could arise from simple chemicals diffusing through a tissue. This theory can be expressed mathematically, and these reaction-diffusion simulations can make images of incredible beauty. I've wanted to play around with applying these Turing patterns to various media for a while, but they really look best with precise, mechanical treatment.
Enter the Epilog laser cutter at FabLab Tacoma, which permitted cutting and engraving Turing patterns into various synthetic fabrics.
To generate the original pattern, I used this handy simulation from the supplementary material of Kondo and Miura (2010). If you run it yourself, you'll see that you can tune each of the parameters in the equations by clicking on them. It's really worth playing with!
The simulation will output a bitmap which can be mirrored, tiled, and thresholded with GIMP, then imported to Inkscape, where the Trace Bitmap command will vectorize it.
Each fabric (synthetics work best as they can be melted and cauterized) does require a bit of playing around to get the laser power within the range between "etch" and "immolate." And, by utilizing two different modes of image interpretation, the Epilog can either draw vectors, cutting cleanly through fabric (such as the brown rayon in the first image) or raster across filled patterns, marking the leggings below.
Up next: making complex fabrics out of layers of cut polyester.