Hi Daniel,
Yes, Alan Mackay is my father.
The sequence here is that several people in the early seventies managed to create aperiodic tilings, with relatively large numbers of rather abstruse tiles. In 1975, Penrose came up with his kites and darts tiling, with only two simple tiles. My father and I visited him that year, and were given a photocopy of the pattern. I wrote a computer program to draw the pattern on a Calcomp pen-plotter. My father, being a crystallographer, reduced the pattern to 35mm slide size and did a light diffraction pattern. This got published in about 1981. Dan Schectman discovered actual quasi-crystals in 1984, for which he received the Nobel prize for Chemistry in 2011. My father was not a chemist!
There was another thread earlier on using Grasshopper for this: Penrose Tiling, which has some of the pictures.
Escher died in 1972. He had been in correspondence with Penrose, and had attended crystallographic meetings with my father, but never lived to see aperiodic tilings. Sad! He would have loved this stuff!
The minimal surface work came much later. My father used PovRay and Mathematica to generate a variety of minimal surfaces. There are 3-D prints, which can be seen at: https://www.shapeways.com/designer/alan_l_mackay/creations.
The question as to whether these can be made from carbon remains for the future! Certainly buckminsterfullerenes and carbon nanotubules exist, even in nature, but creating more complex minimal surfaces at the atomic level remains to be seen.
Thank you so much for your grasshopper model above. I am going to have to play around with this.
Bob