My library is now available. Here are some highlights:
Instantiation
morpion = Morpion2::Morpion.new
Random completion (from any state)
morpion.random_completion
Get the score:
morpion.score
Generating a dna array:
dna = morpion.generate_dna
Evaluating a dna array:
eval_morpion = Morpion2::Morpion.new
eval_morpion.eval_dna dna
For a basic demo take a look at the demo folder for basic.rb. This code will perform a naive search and reset every minute.
One way to compare two grids is by the positions of the made moves. Essentially we want to create a hash value to identify grids that have the same moves but could have different lines.
To demonstrate this effect I have put together a demonstration.
Use the left and right arrow keys to cycle between configurations.
Grids sharing points with different lines
Hashing
To achieve this we iterate over the taken moves on the grid. We form a collection of strings with their x and y values. The list is then sorted and joined together by a token.
@taken_moves.collect{|move| "#{move.x},#{move.y}"}.sort.join('|')
NOTE: To keep the string shorter I SHA1 encode the string.
This provides a very quick way to tell if this configuration of points has been seen after a dna modification.
This is a collection of my highest scoring grids. There are some duplicates in there.
Each move consists of two parts; a grid point where the move was made and a line that passes through the point.
Let’s consider the line universe of discourse. Each point on the grid can be the beginning of four possible lines. These possibilities per point encompass all the possible lines that can be formed.
Encoding
To store the possible lines for a 40×40 grid one would need an array of size 40x40x4.
The correspondence is defined by:
def dna_line_index (line)
line.x * 40 * 4 + line.y * 4 + DIRECTION_INDEX[line.dir]
end
The direction index is a consistent arbitrary ordering of the possible directions. I use:
DIRECTION_INDEX = {
:ne => 0,
:e => 1,
:se => 2,
:s => 3
}
Given a move’s line we can now get a corresponding value from the array.
The goal is to encode a completed grid into this array.
The array is initialized to a random real between 0 and 1 (needed for later).
dna = Array.new(40*40*4){rand}
We then run the following loop.
@taken_moves.each_with_index do |move, index|
dna[dna_line_index move.line] = (@taken_moves.length + 1) - index
end
Iterate over the taken moves of the grid and set the corresponding position in the array to a descending move numbering. For example if the completed grid has a score of 90 then the value stored in the array at the corresponding position of the first move’s line is 90. The second move’s line is 89 and so on.
Evaluation
The array can now be evaluated deterministically with the following method:
At each stage of the algorithm consider the set of possible moves. Rank each move using the value of the array index corresponding to the move’s line. Make that move. Continue the process until there are no possible moves.
This is a complete encoding. Evaluating the dna string will generate a consist grid.
Move Black Listing
The strength of this encoding is it’s resiliency to change. Consider the black listing of a move. A black listed move is a move that can only be made if it is the only possible move at an evaluation stage. This is accomplished quite easily with:
dna[morpion.dna_line_index morpion.taken_moves.sample.line] = -1
Since all the values in the array are positive this move will never be ranked higher than an available move. Also any undisturbed structures are preserved in their line preferences. A move that has been made will always be ranked higher than a move that was not made. If a situation occurs that all possible moves are not part of the original grid then a random move is taken. This is accomplished by initializing unused array indices to rand.
I find black listing three of the taken moves works really well.
Coming soon…
How to efficiently identify two grids that have the same move positions (could have different lines)
End Search: Using loose moves, random completions and move index timeouts to generate similar solutions (hopefully better ones!)
The penta constructor is a very versatile constructor capable of many different configurations. The shape consists of 20 magnets.
The Penta:
Two Dimensional Representation:
Some Shapes:
Could 178 be the upper limit of Morpion Solitaire? My 178 matches the world record set by Chris Rosin.
I have about 50 grids above above 150 that I will continue to test to see if a new record can be found.
Excellent article on determining if a point is in a triangle.
Point in triangle test
I needed a javascript version of the Barycentric coordinate method. Here is the function:
function is_in_triangle (px,py,ax,ay,bx,by,cx,cy){
//credit: http://www.blackpawn.com/texts/pointinpoly/default.html
var v0 = [cx-ax,cy-ay];
var v1 = [bx-ax,by-ay];
var v2 = [px-ax,py-ay];
var dot00 = (v0[0]*v0[0]) + (v0[1]*v0[1]);
var dot01 = (v0[0]*v1[0]) + (v0[1]*v1[1]);
var dot02 = (v0[0]*v2[0]) + (v0[1]*v2[1]);
var dot11 = (v1[0]*v1[0]) + (v1[1]*v1[1]);
var dot12 = (v1[0]*v2[0]) + (v1[1]*v2[1]);
var invDenom = 1/ (dot00 * dot11 - dot01 * dot01);
var u = (dot11 * dot02 - dot01 * dot12) * invDenom;
var v = (dot00 * dot12 - dot01 * dot02) * invDenom;
return ((u >= 0) && (v >= 0) && (u + v < 1));
}
Chaos Game: http://koozdra.ca/chaosgame/main.html
Outer Pentagonal Coloring:
Inner Pentagonal Coloring:
The colors are determined by the source chosen point.
For this example I will use a very interesting 135 configuration. It appears to be a peak.
Our goal is encode these moves into a binary string.
Lets begin by considering the 28 possible moves that are available when starting a new game. Out of these initial 28 moves some are going to be used and some will be removed as a consequence of making some other moves. Taking the intersection of the possible moves and the taken moves from the configuration above we see that eight moves were made and 20 moves not made.
For each of the eight moves that were taken we are going to add a 1 to the binary encoding and a 0 for the moves not taken.
In order to be able to decode this binary encoding it is important to consistently order the possible moves. I chose [move.x, move.y, move.line.x, move.line.y, Morpion2::DIRECTION_INDEX[move.line.dir]]. Since all attributes are included I am guaranteed a unique ordering.
For the 20 moves that were not taken, we are explicitly stating that at no point should any of these moves be made. These are added to a list of ‘taboo’ moves. Also we no longer need to encode these moves if they appear as possible moves later on.
Okay, lets take a look at the first layer:
layer 0
1. -1, 3 – (-1,3,e): 0
2. -1, 6 – (-1,6,e): 0
3. 0, 2 – (0,2,s): 0
4. 0, 7 – (0,3,s): 0
5. 2, 0 – (2,0,e): 0
6. 2, 2 – (0,4,ne): 1
7. 2, 7 – (0,5,se): 0
8. 2, 9 – (2,9,e): 0
9. 3, -1 – (3,-1,s): 0
10. 3, 4 – (3,0,s): 0
11. 3, 5 – (3,5,s): 0
12. 3, 10 – (3,6,s): 1
13. 4, 3 – (0,3,e): 0
14. 4, 6 – (0,6,e): 1
15. 5, 3 – (5,3,e): 1
16. 5, 6 – (5,6,e): 0
17. 6, -1 – (6,-1,s): 0
18. 6, 4 – (6,0,s): 0
19. 6, 5 – (6,5,s): 1
20. 6, 10 – (6,6,s): 0
21. 7, 0 – (3,0,e): 1
22. 7, 2 – (5,0,se): 0
23. 7, 7 – (5,9,ne): 1
24. 7, 9 – (3,9,e): 0
25. 9, 2 – (9,2,s): 1
26. 9, 7 – (9,3,s): 0
27. 10, 3 – (6,3,e): 0
28. 10, 6 – (6,6,e): 0
We see the 28 possible moves sorted by the given criteria. The eight taken moves are marked with a 1. The moves that aren’t taken are marked with a 0 and added to a taboo list (this will come into play in the later layers).
We now make our first eight moves on a grid. After making the moves consider the set of possible moves available to us. There are 18 possible moves. Out of those 18 moves, 14 moves are in our taboo list. We have already stated that these moves will not be used. That means we can ignore them.
We are left with four possible moves. Just like in the first layer we now want to take the intersection of the possible moves and the taken moves. This shows that three moves were taken and one not. Note: Moves shown in [] are tabooed.
layer 1
29. 4, 3 – (1,3,e): 1
30. 5, 6 – (4,6,e): 1
31. 5, 8 – (3,10,ne): 0
32. 6, 4 – (6,1,s): 1
[3, -1 – (3,-1,s)]
[6, -1 – (6,-1,s)]
[3, 4 – (3,0,s)]
[7, 2 – (5,0,se)]
[6, 4 – (6,0,s)]
[0, 2 – (0,2,s)]
[-1, 3 – (-1,3,e)]
[4, 3 – (0,3,e)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[5, 6 – (5,6,e)]
[10, 6 – (6,6,e)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
This process is continued until there are no possible moves left on the board.
layer 2
33. 5, 4 – (3,2,se): 0
34. 5, 5 – (3,7,ne): 1
35. 7, 4 – (5,6,ne): 1
[3, -1 – (3,-1,s)]
[3, 4 – (3,0,s)]
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
layer 3
36. 4, 4 – (2,2,se): 1
37. 4, 4 – (3,3,se): 0
38. 7, 5 – (7,3,s): 0
[3, -1 – (3,-1,s)]
[3, 4 – (3,0,s)]
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[5, 4 – (3,2,se)]
layer 4
39. 3, 5 – (2,6,ne): 1
[3, -1 – (3,-1,s)]
[3, 4 – (3,0,s)]
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[5, 4 – (3,2,se)]
[7, 5 – (7,3,s)]
layer 5
40. 3, 4 – (3,1,s): 0
41. 3, 4 – (3,2,s): 1
[3, -1 – (3,-1,s)]
[3, 4 – (3,0,s)]
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[5, 4 – (3,2,se)]
[7, 5 – (7,3,s)]
layer 6
42. 4, 5 – (2,3,se): 0
43. 5, 2 – (3,4,ne): 1
44. 5, 4 – (3,4,e): 0
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[5, 4 – (3,2,se)]
[7, 5 – (7,3,s)]
layer 7
45. 4, 1 – (3,0,se): 0
46. 4, 2 – (2,2,e): 1
47. 5, 4 – (5,2,s): 1
48. 8, 5 – (5,2,se): 0
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[5, 4 – (3,2,se)]
[7, 5 – (7,3,s)]
[5, 4 – (3,4,e)]
[4, 5 – (2,3,se)]
layer 8
49. 2, 0 – (2,0,se): 0
50. 2, 1 – (2,1,se): 0
51. 2, 4 – (2,4,e): 0
52. 4, 1 – (4,0,s): 0
53. 4, 5 – (4,2,s): 1
54. 7, 5 – (3,1,se): 0
55. 7, 5 – (4,2,se): 0
56. 8, 4 – (4,4,e): 1
57. 8, 4 – (5,4,e): 0
58. 8, 7 – (4,3,se): 0
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[7, 5 – (7,3,s)]
[4, 5 – (2,3,se)]
[4, 1 – (3,0,se)]
[8, 5 – (5,2,se)]
layer 9
59. 1, 2 – (1,2,se): 0
60. 2, 5 – (2,5,e): 1
61. 2, 7 – (2,7,ne): 0
62. 5, 1 – (4,0,se): 0
63. 5, 1 – (5,1,se): 0
64. 7, 2 – (3,6,ne): 1
65. 7, 5 – (3,5,e): 0
66. 7, 8 – (3,4,se): 0
67. 10, 6 – (6,2,se): 0
[7, 2 – (5,0,se)]
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[7, 5 – (7,3,s)]
[4, 1 – (3,0,se)]
[8, 5 – (5,2,se)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
layer 10
68. 2, 4 – (2,2,s): 1
69. 4, -1 – (4,-1,se): 0
70. 7, 1 – (7,0,s): 1
71. 7, 5 – (7,2,s): 0
72. 10, 5 – (6,1,se): 0
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[7, 5 – (7,3,s)]
[4, 1 – (3,0,se)]
[8, 5 – (5,2,se)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
[1, 2 – (1,2,se)]
[7, 8 – (3,4,se)]
[5, 1 – (4,0,se)]
[5, 1 – (5,1,se)]
[10, 6 – (6,2,se)]
layer 11
73. 0, 2 – (0,2,se): 1
74. 1, 4 – (0,4,e): 0
75. 1, 5 – (0,6,ne): 0
76. 5, 1 – (2,4,ne): 1
77. 5, 7 – (1,3,se): 0
78. 5, 7 – (2,4,se): 0
[0, 2 – (0,2,s)]
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[4, 1 – (3,0,se)]
[8, 5 – (5,2,se)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
[1, 2 – (1,2,se)]
[7, 8 – (3,4,se)]
[5, 1 – (4,0,se)]
[5, 1 – (5,1,se)]
[10, 6 – (6,2,se)]
[4, -1 – (4,-1,se)]
[10, 5 – (6,1,se)]
layer 12
79. 0, 1 – (0,1,s): 1
80. 3, -1 – (3,-1,se): 1
81. 4, 1 – (3,1,e): 1
[0, 7 – (0,3,s)]
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[4, 1 – (3,0,se)]
[8, 5 – (5,2,se)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
[1, 2 – (1,2,se)]
[7, 8 – (3,4,se)]
[10, 6 – (6,2,se)]
[4, -1 – (4,-1,se)]
[10, 5 – (6,1,se)]
[1, 4 – (0,4,e)]
layer 13
82. 1, 2 – (0,1,se): 1
83. 1, 4 – (0,5,ne): 0
84. 1, 4 – (1,4,ne): 1
85. 2, -1 – (2,-1,se): 1
86. 3, -2 – (3,-2,s): 1
87. 6, -1 – (2,3,ne): 0
88. 8, 5 – (4,1,se): 0
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[8, 5 – (5,2,se)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
[1, 2 – (1,2,se)]
[7, 8 – (3,4,se)]
[4, -1 – (4,-1,se)]
[10, 5 – (6,1,se)]
[1, 4 – (0,4,e)]
layer 14
89. -1, 2 – (-1,2,se): 1
90. -1, 4 – (-1,4,e): 1
91. 1, 5 – (1,2,s): 1
92. 4, -1 – (3,-2,se): 1
93. 4, 7 – (0,3,se): 0
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
[4, -1 – (4,-1,se)]
[10, 5 – (6,1,se)]
layer 15
94. -2, 2 – (-2,2,e): 0
95. -1, 3 – (-1,3,se): 0
96. 1, 0 – (-1,2,ne): 1
97. 2, 1 – (-1,4,ne): 0
98. 2, 1 – (0,3,ne): 0
99. 2, 7 – (-1,4,se): 0
100. 4, -2 – (4,-2,s): 1
101. 4, 8 – (0,4,se): 0
102. 4, 8 – (1,5,se): 0
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
layer 16
103. 2, 1 – (1,0,se): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[2, 1 – (2,1,se)]
[8, 7 – (4,3,se)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[2, 1 – (-1,4,ne)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
[2, 1 – (0,3,ne)]
layer 17
104. -2, 5 – (-2,5,ne): 0
105. 5, -2 – (1,2,ne): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
layer 18
106. 5, -1 – (5,-2,s): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
layer 19
107. 1, -1 – (1,-1,e): 1
108. 3, -3 – (3,-3,se): 0
109. 6, -1 – (2,-1,e): 0
110. 8, 2 – (4,-2,se): 1
111. 8, 2 – (5,-1,se): 0
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
layer 20
112. 2, 0 – (1,-1,se): 1
113. 8, 5 – (8,2,s): 1
114. 10, 2 – (6,2,e): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[2, 0 – (2,0,se)]
[7, 5 – (3,1,se)]
[7, 5 – (4,2,se)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
layer 21
115. 1, 1 – (0,2,ne): 0
116. 2, -2 – (2,-2,s): 1
117. 5, 8 – (4,9,ne): 0
118. 5, 8 – (5,8,ne): 1
119. 7, 5 – (6,6,ne): 1
120. 10, 3 – (6,7,ne): 0
121. 10, 7 – (6,3,se): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[5, 8 – (3,10,ne)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
layer 22
122. 1, -2 – (1,-2,e): 1
123. 6, -2 – (2,-2,e): 0
124. 7, 8 – (7,4,s): 1
125. 9, 7 – (5,3,se): 1
126. 10, 5 – (6,5,e): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
[1, 1 – (0,2,ne)]
layer 23
127. 1, 1 – (1,-2,s): 1
128. 4, 8 – (3,8,e): 0
129. 8, 7 – (6,7,e): 0
130. 8, 7 – (6,9,ne): 1
131. 8, 9 – (4,5,se): 1
132. 11, 6 – (7,2,se): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
[1, 1 – (0,2,ne)]
layer 24
133. -1, 1 – (-1,1,e): 1
134. -1, 3 – (-1,3,ne): 1
135. 5, -3 – (1,1,ne): 0
136. 5, 7 – (5,7,e): 0
137. 7, 9 – (4,9,e): 0
138. 9, 8 – (5,4,se): 1
139. 11, 7 – (7,7,e): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[-1, 3 – (-1,3,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
[4, 8 – (3,8,e)]
layer 25
140. -2, 2 – (-2,2,se): 1
141. -1, 0 – (-1,0,s): 0
142. -1, 5 – (-1,1,s): 1
143. 7, 10 – (7,10,ne): 1
144. 8, 8 – (5,8,e): 1
145. 10, 6 – (7,3,se): 1
146. 12, 5 – (8,9,ne): 0
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[-2, 2 – (-2,2,e)]
[2, 7 – (-1,4,se)]
[4, 8 – (0,4,se)]
[4, 8 – (1,5,se)]
[4, 8 – (3,8,e)]
[7, 9 – (4,9,e)]
layer 26
147. -3, 2 – (-3,2,e): 1
148. -2, 5 – (-2,5,e): 1
149. 0, 0 – (-2,2,ne): 1
150. 4, 7 – (3,6,se): 1
151. 8, 10 – (8,6,s): 1
152. 12, 6 – (8,6,e): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[2, 7 – (-1,4,se)]
[7, 9 – (4,9,e)]
layer 27
153. -3, 6 – (-3,6,ne): 1
154. -2, 3 – (-3,2,se): 1
155. -1, 0 – (-1,0,e): 1
156. 5, 7 – (3,7,e): 1
[2, 7 – (0,5,se)]
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[2, 7 – (-1,4,se)]
[7, 9 – (4,9,e)]
layer 28
157. -3, 3 – (-3,3,e): 1
158. 5, 10 – (5,6,s): 0
159. 7, 9 – (4,6,se): 1
[2, 9 – (2,9,e)]
[7, 9 – (3,9,e)]
[7, 9 – (4,9,e)]
layer 29
160. 6, 10 – (6,10,ne): 1
161. 9, 9 – (5,9,e): 1
162. 11, 5 – (7,9,ne): 0
[2, 9 – (2,9,e)]
[5, 10 – (5,6,s)]
layer 30
163. 4, 8 – (2,6,se): 1
164. 9, 10 – (9,6,s): 1
165. 10, 8 – (8,10,ne): 1
166. 10, 10 – (6,6,se): 1
[5, 10 – (5,6,s)]
layer 31
167. 2, 10 – (2,10,ne): 1
168. 4, 10 – (4,6,s): 1
169. 5, 10 – (5,10,e): 1
170. 10, 4 – (10,4,s): 1
171. 10, 9 – (10,5,s): 0
172. 10, 9 – (10,6,s): 0
173. 11, 10 – (7,10,e): 0
[5, 10 – (5,6,s)]
layer 32
174. 1, 10 – (1,10,e): 1
175. 2, 7 – (1,6,se): 1
176. 5, 11 – (5,7,s): 1
177. 11, 5 – (8,2,se): 1
layer 33
178. 2, 9 – (1,10,ne): 1
layer 34
179. 1, 9 – (1,9,e): 1
180. 2, 8 – (2,6,s): 1
layer 35
181. 1, 7 – (-1,5,se): 0
182. 1, 7 – (0,6,se): 0
183. 1, 7 – (1,7,se): 1
184. 1, 8 – (1,8,e): 0
185. 6, 12 – (2,8,se): 0
layer 36
186. -2, 4 – (-3,3,se): 1
187. 1, 8 – (1,6,s): 1
[1, 8 – (1,8,e)]
layer 37
188. -2, 1 – (-2,1,s): 0
189. -2, 6 – (-2,2,s): 1
190. 0, 8 – (0,8,e): 1
layer 38
191. -1, 7 – (-2,6,se): 1
layer 39
192. -2, 8 – (-2,8,ne): 1
193. 0, 7 – (-1,7,e): 1
layer 40
194. -1, 6 – (-2,5,se): 0
195. -1, 6 – (-1,6,se): 1
196. -1, 8 – (-1,8,ne): 1
197. 0, 9 – (0,5,s): 1
198. 4, 11 – (0,7,se): 0
layer 41
199. -4, 6 – (-4,6,e): 0
200. -2, 7 – (-3,6,se): 1
201. -1, 9 – (-1,5,s): 0
202. -1, 10 – (-1,10,ne): 1
layer 42
203. -3, 8 – (-3,8,ne): 1
204. -1, 9 – (-1,6,s): 1
[-4, 6 – (-4,6,e)]
[-1, 9 – (-1,5,s)]
layer 43
205. -4, 8 – (-4,8,e): 1
206. -2, 10 – (-2,10,ne): 1
[-4, 6 – (-4,6,e)]
layer 44
207. -3, 7 – (-4,8,ne): 1
208. -2, 9 – (-2,6,s): 1
[-4, 6 – (-4,6,e)]
layer 45
209. -3, 9 – (-3,9,e): 1
[-4, 6 – (-4,6,e)]
layer 46
210. -3, 5 – (-3,5,s): 0
211. -3, 10 – (-3,6,s): 1
[-4, 6 – (-4,6,e)]
layer 47
212. 0, 10 – (-3,10,e): 1
[-4, 6 – (-4,6,e)]
layer 48
213. -4, 6 – (-4,6,se): 1
214. -1, 11 – (-1,11,ne): 1
215. 1, 11 – (-3,7,se): 0
[-4, 6 – (-4,6,e)]
layer 49
216. -5, 6 – (-5,6,e): 1
217. -5, 7 – (-5,7,se): 0
218. 0, 12 – (-4,8,se): 0
layer 50
219. -4, 7 – (-5,6,se): 1
[-5, 7 – (-5,7,se)]
[0, 12 – (-4,8,se)]
layer 51
220. -5, 7 – (-5,7,e): 1
[-5, 7 – (-5,7,se)]
[0, 12 – (-4,8,se)]
layer 52
221. -6, 6 – (-6,6,se): 1
222. -3, 5 – (-5,7,ne): 1
[0, 12 – (-4,8,se)]
layer 53
223. -3, 4 – (-3,2,s): 1
layer 54
224. -4, 5 – (-5,6,ne): 1
layer 55
225. -4, 4 – (-4,4,s): 1
226. -4, 9 – (-4,5,s): 0
layer 56
227. -5, 4 – (-5,4,e): 1
228. -5, 5 – (-6,6,ne): 1
layer 57
229. -6, 5 – (-6,5,e): 1
230. -5, 3 – (-5,3,s): 1
231. -5, 8 – (-5,4,s): 0
layer 58
232. -6, 2 – (-6,2,se): 1
Our binary encoding now looks like:
0000010000010110001010101000110101110010101001100000100100010001000101001001001111011100111100010001001011100101110101101101111001111100011101111011111111111011101111111100011111110010011011111011100101111111101111010011111110111101
I then base64 encode this string to:
BBYqjXKmCREUk9zxEuXW3nx3v/u/x/JvuX+9P70
In summary each successive layer is just the moves that were created from the layer below.
Please let me know if any part requires further explanation.
Descent into Mathness 