ref: 6fb890e0ea20a3c366ffd2de45d26a0c1c454dd6
parent: 71cf891fdc3ab237ecf0e5d1aae39b6c9fe97a4d
author: Simon Tatham <anakin@pobox.com>
date: Mon Apr 10 10:56:34 EDT 2023
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.
--- a/auxiliary/hatgen.c
+++ b/auxiliary/hatgen.c
@@ -1330,6 +1330,26 @@
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)
@@ -1452,6 +1472,31 @@
sfree(h);
} else {draw_metatile_set_svg(tiles, tiles->vertices, false);
+ }
+
+ metatile_free_set(tiles);
+
+ 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);
--- a/hat.c
+++ b/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
--- a/penrose.c
+++ b/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>
--
⑨