Reference my just-published article about aperiodic tilings.

In commit 8d6647548f7d005 I added the Hats grid type to Loopy, and
mentioned in the commit message that I was very pleased with the
algorithm I came up with.

In fact, I was so pleased with it that I've decided it deserves a
proper public writeup. So I've spent the Easter weekend producing one:

  https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-tilings/

In this commit I adjust the header comments in both penrose.c and
hat.c to refer to the article (replacing a previous comment in
penrose.c to a much less polished page containing a copy of my
jotting-grade personal notes that I sent James Harvey once). Also,
added some code to hatgen.c to output Python hat descriptions in a
similar style to hat-test, which I used to generate a couple of the
more difficult diagrams in the new article, and didn't want to lose.

auxiliary/hatgen.c

@@ -1330,6 +1330,26 @@ static void draw_hats_svg(const Hat *hats, size_t n,
     printf("</svg>\n");
 }
 
+static void draw_hats_python(const Hat *hats, size_t n)
+{
+    size_t i, j;
+
+    printf("def hats(hat):\n");
+    for (i = 0; i < n; i++) {
+        const Hat *hat = &hats[i];
+        Point vertices[HAT_NVERT];
+        size_t nv = hat_vertices(*hat, vertices);
+
+        printf("    hat('%c', %d, None, [",
+               "HTPF"[hat->parent->type], hat->index);
+        for (j = 0; j < nv; j++) {
+            Point v = vertices[j];
+            printf("%s(%d,%d)", j ? ", " : "", (v.x * 2 + v.y) / 3, v.y);
+        }
+        printf("])\n");
+    }
+}
+
 typedef enum KiteStep { KS_LEFT, KS_RIGHT, KS_F_LEFT, KS_F_RIGHT } KiteStep;
 
 static inline Point kite_step(Point k, KiteStep step)
@@ -1459,6 +1479,31 @@ int main(int argc, char **argv)
         return 0;
     }
 
+    if (argv[1][0] == 'P' && argv[1][1] && strchr("HTPF", argv[1][1])) {
+        int niter = atoi(argv[1] + 2);
+        MetatileType type = (argv[1][1] == 'H' ? MT_H :
+                             argv[1][1] == 'T' ? MT_T :
+                             argv[1][1] == 'P' ? MT_P : MT_F);
+        MetatileSet *tiles = metatile_initial_set(type);
+
+        while (niter-- > 0) {
+            MetatileSet *t2 = metatile_set_expand(tiles);
+            metatile_free_set(tiles);
+            tiles = t2;
+        }
+
+        {
+            size_t nh;
+            Hat *h = metatile_set_to_hats(tiles, &nh, NULL);
+            draw_hats_python(h, nh);
+            sfree(h);
+        }
+
+        metatile_free_set(tiles);
+
+        return 0;
+    }
+
     if (!strcmp(argv[1], "--tables")) {
         size_t i, j, k;
 

hat.c

@@ -2,10 +2,17 @@
  * Code to generate patches of the aperiodic 'hat' tiling discovered
  * in 2023.
  *
- * auxiliary/doc/hats.html contains an explanation of the basic ideas
- * of this algorithm, which can't really be put in a source file
- * because it just has too many complicated diagrams. So read that
- * first, because the comments in here will refer to it.
+ * This uses the 'combinatorial coordinates' system documented in my
+ * public article
+ * https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-tilings/
+ *
+ * The internal document auxiliary/doc/hats.html also contains an
+ * explanation of the basic ideas of this algorithm (less polished but
+ * containing more detail).
+ *
+ * Neither of those documents can really be put in a source file,
+ * because they just have too many complicated diagrams. So read at
+ * least one of those first; the comments in here will refer to it.
  *
  * Discoverers' website: https://cs.uwaterloo.ca/~csk/hat/
  * Preprint of paper:    https://arxiv.org/abs/2303.10798

penrose.c

@@ -2,9 +2,10 @@
  *
  * Penrose tile generator.
  *
- * Uses half-tile technique outlined on:
+ * Works by choosing a small patch from a recursively expanded large
+ * region of tiling, using one of the two algorithms described at
  *
- * http://tartarus.org/simon/20110412-penrose/penrose.xhtml
+ * https://www.chiark.greenend.org.uk/~sgtatham/quasiblog/aperiodic-tilings/
  */
 
 #include <assert.h>