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/*
* Handwritten data tables for the Spectre tiling.
*
* This file is used by both the final tiling generator in spectre.c,
* and by spectre-gen.c which auto-generates further tables to go with
* these.
*/
/*
* We generate the Spectre tiling based on the substitution system of
* 9 types of marked hexagon shown in the paper.
*
* The substitution expands each hexagon into 8 others, except for the
* G hex which expands to only seven. The layout, numbered with the
* indices we use in the arrays here, is as follows:
*
* 0 1
* 2 3
* 4 5 6
* 7
*
* That is: the hexes are oriented with a pair of vertical edges.
* Hexes 0 and 1 are horizontally adjacent; 2 and 3 are adjacent on
* the next row, with 3 nestling between 0 and 1; 4,5,6 are on the
* third row with 5 between 2 and 3; and 7 is by itself on a fourth
* row, between 5 and 6. In the expansion of the G hex, #7 is the
* missing one, so its indices are still consecutive from 0.
*
* These arrays list the type of each child hex. The hexes also have
* orientations, but those aren't listed here, because only
* spectre-gen needs to know them - by the time it's finished
* autogenerating transition tables, the orientations are baked into
* those and don't need to be consulted separately.
*/
static const Hex subhexes_G[] = {
HEX_F,
HEX_X,
HEX_G,
HEX_S,
HEX_P,
HEX_D,
HEX_J,
/* hex #7 is not present for this tile */
};
static const Hex subhexes_D[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_X,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_J[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_P,
};
static const Hex subhexes_L[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_X[] = {
HEX_F,
HEX_Y,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_P,
};
static const Hex subhexes_P[] = {
HEX_F,
HEX_Y,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_S[] = {
HEX_L,
HEX_P,
HEX_G,
HEX_S,
HEX_X,
HEX_D,
HEX_F,
HEX_X,
};
static const Hex subhexes_F[] = {
HEX_F,
HEX_P,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_Y,
};
static const Hex subhexes_Y[] = {
HEX_F,
HEX_Y,
HEX_G,
HEX_S,
HEX_Y,
HEX_D,
HEX_F,
HEX_Y,
};
/*
* Shape of the Spectre itself.
*
* Vertex 0 is taken to be at the top of the Spectre's "head"; vertex
* 1 is the adjacent vertex, in the direction of the shorter edge of
* its "cloak".
*
* This array indicates how far to turn at each vertex, in 1/12 turns.
* All edges are the same length (counting the double-edge as two
* edges, which we do).
*/
static const int spectre_angles[14] = {
-3, -2, 3, -2, -3, 2, -3, 2, -3, -2, 0, -2, 3, -2,
};
/*
* The relative probabilities of the nine hex types, in the limit, as
* the expansion process is iterated more and more times. Used to
* choose the initial hex coordinates as if the segment of tiling came
* from the limiting distribution across the whole plane.
*
* This is obtained by finding the matrix that says how many hexes of
* each type are expanded from each starting hex, and taking the
* eigenvector that goes with its limiting eigenvalue.
*/
#define PROB_G 10000000 /* 1 */
#define PROB_D 10000000 /* 1 */
#define PROB_J 1270167 /* 4 - sqrt(15) */
#define PROB_L 1270167 /* 4 - sqrt(15) */
#define PROB_X 7459667 /* 2 sqrt(15) - 7 */
#define PROB_P 7459667 /* 2 sqrt(15) - 7 */
#define PROB_S 10000000 /* 1 */
#define PROB_F 17459667 /* 2 sqrt(15) - 6 */
#define PROB_Y 13810500 /* 13 - 3 sqrt(15) */
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