First of all some other mathematical blogs which can be fun for the recreational or apprentice mathematician (I’m both):
https://solvemymaths.com/author/solvemymaths/
http://donsteward.blogspot.co.uk/
https://plus.maths.org/content/
… and finally, for now, a site supposedly dedicated to school-level maths teaching techniques, but often beyond Dave-level:
An obvious starting point for tilings is wikipedia: http://en.wikipedia.org/wiki/Tessellation. Just Googling tessellations will bring up a spectacular host of repeating patterns, otherwise known as tilings ( a term which I don’t employ because of its everyday use in association with ceramics and bathrooms). At the time of first blogging (November 2013), not one Lattice Labyrinth tessellation of higher than trivial order is to be found by searching for “images”
Another route into experimenting with tessellations is via the generalisation of the domino to polyominoes and, replacing squares with equilateral triangles, polyiamonds. See my book list or again be grateful to the compilers of wikipedia at: http://en.wikipedia.org/wiki/Polyomino. Consultation of the above article will convince you that even the most powerful computer would have no chance of finding the shape of the supertile of, say, Chinese Labyrinth (39,23), which design I had better post, by the not-so-simple process of running through all the possibilities, one by one, within….shall we say …. the estimated main-sequence lifetime of a sun-like star raised to a substantial positive power.
A good way to find books of artistic inspiration via mathematics ought to be to peruse the lists of specialist publishers. Rich pickings, especially with an educational slant can be found in the list of independent British publisher Tarquin , but I’m obviously biased. In Germany, Teubner appeared, only two years ago, to do a lighthearted maths series, but I’ve failed to find it tonight – their integration within Springer (whose London mathematics editor was very helpful to me) seems to have distributed such titles too thinly among their lists. Gibt es für Freizeit-Mathematik keine Sonderreihe mehr?
Based in the United States, Dover produce or republish many classics in the fields of mathematics, graphic design and historic art and crafts but, alas, their list does not recognise recreational mathematics as a category – bring back Martin Gardner! What about the erstwhile publishers of Gardner’s classic stomping ground, Scientific American, W.H.Freeman. Alas, searching their list for “recreational mathematics” and even “Gardner” bring up zero results, so I won’t bother with a link to them.
As usual, these days, someone’s probably charitable work on the Web saves the day. Lots of thanks to Eric W. Weisstein for his excellent list, of which my own list is largely a personal subset.
IF you do manage to produce some lovely Lattice Labyrinth designs of your own, you can have them digitally reproduced as designs on fabric or paper by Spoonflower, based in North Carolina, who will print a few copies off for you at an affordable (but several times above mass-produced) price, and can also put your designs on sale via their website. Be realistic. Give me a mention, or put in a link to this site – please.
LatticeLabyrinths 