Socolar 12-fold by teundenouden on DeviantArt (original) (raw)

Published: Apr 29, 2018

Description

I struggled getting this done, but I finally got it YES!
This is a 12-fold quasistructure substitution-tiling found by Joshua E. S. Socolar. This particular tiling was a pain to built in apophysis as an IFS because it has a lot of shapes of which a lot had to be cropped in really weird ways to get rid of the fractal boundaries. When I got the tile done, I decided to make an supertile out of it which was just as hard. First I had to make a pattern of 3 connected hexagons and then tile that along the x-axis which I would then rotate by 60° and tile on the x-axis again so that the pattern repeated on x and y.
There occured something weird concerning the cropped pieces too so I've spent a few days to figure that out and fix it properly.
I've used the following transformations: linear, post_crop, smartcrop, split_rot, tile and mobius to get this done and it was a neat challenge!

Find the substitution rules in socolar's publication: Simple octagonal and dodecagonal quasicrystals

Built with apophysis 7x and rendered with chaotica 1.5.8

Image size

7000x3937px 19.15 MB