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ZetaChessMapped

onexiv
Feb 20th, 2025 (edited)
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  1. White moves first:
  2.  
  3. Game starts: White moves first
  4. Tracking moves, t, and ζ(s)...
  5.  
  6. Turn 1:
  7. White Pawn: (0, 1) → (1, 2), Dist = 1.414214
  8. White Rook: (3, 0) → (2, 1), Dist = 1.414214
  9. White Bishop: (2, 0) → (5, 3), Dist = 4.242641
  10. White Queen: (4, 0) → (5, 1), Dist = 1.414214
  11. White Knight: (1, 0) → (2, 2), Dist = 2.236068
  12. White King: (5, 0) → (4, 1), Dist = 1.414214
  13. White: t = 12.135563, s = 0.5 + 12.135563i, ζ(s) = 0.943132 + -0.758047i, Mag = 1.210014
  14. Closest t = 14.134725, Off by = 1.999162
  15. Black King: (5, 7) → (4, 6), Dist = 1.414214
  16. Black Knight: (1, 7) → (3, 6), Dist = 2.236068
  17. Black Pawn: (0, 6) → (1, 5), Dist = 1.414214
  18. Black Rook: (3, 7) → (2, 6), Dist = 1.414214
  19. Black Bishop: (2, 7) → (7, 2), Dist = 7.071068
  20. Black Queen: (4, 7) → (0, 3), Dist = 5.656854
  21. Black: t = 19.206631, s = 0.5 + 19.206631i, ζ(s) = 1.376373 + -1.245712i, Mag = 1.856394
  22. Closest t = 21.02204, Off by = 1.815409
  23.  
  24. Turn 2:
  25. White Rook: (2, 1) → (3, 0), Dist = 1.414214
  26. White Pawn: (1, 2) → (2, 3), Dist = 1.414214
  27. White Bishop: (5, 3) → (4, 4), Dist = 1.414214
  28. White Queen: (5, 1) → (3, 3), Dist = 2.828427
  29. White King: (4, 1) → (5, 0), Dist = 1.414214
  30. White Knight: (2, 2) → (4, 1), Dist = 2.236068
  31. White: t = 22.856912, s = 0.5 + 22.856912i, ζ(s) = 1.403911 + 0.289555i, Mag = 1.433460
  32. Closest t = 21.02204, Off by = 1.834872
  33. Black Bishop: (7, 2) → (6, 3), Dist = 1.414214
  34. Black Rook: (2, 6) → (3, 7), Dist = 1.414214
  35. Black Queen: (0, 3) → (1, 4), Dist = 1.414214
  36. Black King: (4, 6) → (5, 5), Dist = 1.414214
  37. Black Pawn: (1, 5) → (2, 4), Dist = 1.414214
  38. Black Knight: (3, 6) → (5, 7), Dist = 2.236068
  39. Black: t = 28.513767, s = 0.5 + 28.513767i, ζ(s) = 2.033297 + -1.487623i, Mag = 2.519389
  40. Closest t = 25.010858, Off by = 3.502909
  41.  
  42. Turn 3:
  43. White Knight: (4, 1) → (5, 3), Dist = 2.236068
  44. White Queen: (3, 3) → (0, 0), Dist = 4.242641
  45. White Rook: (3, 0) → (4, 1), Dist = 1.414214
  46. White King: (5, 0) → (6, 1), Dist = 1.414214
  47. White Pawn: (2, 3) → (3, 4), Dist = 1.414214
  48. White Bishop: (4, 4) → (1, 7), Dist = 4.242641
  49. White: t = 37.820902, s = 0.5 + 37.820902i, ζ(s) = 0.213018 + 0.386058i, Mag = 0.440928
  50. Closest t = 25.010858, Off by = 12.810044
  51. Black King: (5, 5) → (6, 4), Dist = 1.414214
  52. Black Knight: (5, 7) → (3, 6), Dist = 2.236068
  53. Black Rook: (3, 7) → (2, 6), Dist = 1.414214
  54. Black Queen: (1, 4) → (4, 7), Dist = 4.242641
  55. Black Bishop: (6, 3) → (3, 0), Dist = 4.242641
  56. Black Pawn: (2, 4) → (1, 3), Dist = 1.414214
  57. Black: t = 43.477757, s = 0.5 + 43.477757i, ζ(s) = -0.138047 + 0.252474i, Mag = 0.287750
  58. Closest t = 25.010858, Off by = 18.466899
  59.  
  60. Turn 4:
  61. White King: (6, 1) → (5, 0), Dist = 1.414214
  62. White Pawn: (3, 4) → (4, 5), Dist = 1.414214
  63. White Rook: (4, 1) → (3, 2), Dist = 1.414214
  64. White Knight: (5, 3) → (6, 5), Dist = 2.236068
  65. White Queen: (0, 0) → (3, 3), Dist = 4.242641
  66. White Bishop: (1, 7) → (7, 1), Dist = 8.485281
  67. White: t = 57.027533, s = 0.5 + 57.027533i, ζ(s) = 1.004452 + 0.646699i, Mag = 1.194631
  68. Closest t = 25.010858, Off by = 32.016675
  69. Black Rook: (2, 6) → (3, 5), Dist = 1.414214
  70. Black Queen: (4, 7) → (7, 4), Dist = 4.242641
  71. Black Pawn: (1, 3) → (0, 2), Dist = 1.414214
  72. Black Bishop: (3, 0) → (1, 2), Dist = 2.828427
  73. Black King: (6, 4) → (7, 3), Dist = 1.414214
  74. Black Knight: (3, 6) → (1, 7), Dist = 2.236068
  75. Black: t = 57.027533, s = 0.5 + 57.027533i, ζ(s) = 1.004452 + 0.646699i, Mag = 1.194631
  76. Closest t = 25.010858, Off by = 32.016675
  77.  
  78. Turn 5:
  79. White King: (5, 0) → (4, 1), Dist = 1.414214
  80. White Knight: (6, 5) → (5, 7), Dist = 2.236068
  81. White Pawn: (4, 5) → (3, 6), Dist = 1.414214
  82. White Queen: (3, 3) → (1, 5), Dist = 2.828427
  83. White Bishop: (7, 1) → (2, 6), Dist = 7.071068
  84. White Rook: (3, 2) → (4, 3), Dist = 1.414214
  85. White: t = 73.405737, s = 0.5 + 73.405737i, ζ(s) = 3.293817 + 0.954715i, Mag = 3.429390
  86. Closest t = 25.010858, Off by = 48.394879
  87. Black King: (7, 3) → (6, 4), Dist = 1.414214
  88. Black Queen: (7, 4) → (6, 5), Dist = 1.414214
  89. Black Bishop: (1, 2) → (2, 3), Dist = 1.414214
  90. Black Pawn: (0, 2) → (1, 1), Dist = 1.414214
  91. Black Rook: (3, 5) → (4, 4), Dist = 1.414214
  92. Black Knight: (1, 7) → (0, 5), Dist = 2.236068
  93. Black: t = 66.334669, s = 0.5 + 66.334669i, ζ(s) = 0.830671 + -0.603035i, Mag = 1.026482
  94. Closest t = 25.010858, Off by = 41.323811
  95.  
  96. Turn 6:
  97. White Rook: (4, 3) → (3, 2), Dist = 1.414214
  98. White Bishop: (2, 6) → (5, 3), Dist = 4.242641
  99. White Pawn: (3, 6) → (2, 7), Dist = 1.414214
  100. White Queen: (1, 5) → (3, 3), Dist = 2.828427
  101. White Knight: (5, 7) → (7, 6), Dist = 2.236068
  102. White King: (4, 1) → (5, 2), Dist = 1.414214
  103. White: t = 86.955513, s = 0.5 + 86.955513i, ζ(s) = 0.285304 + -0.868507i, Mag = 0.914168
  104. Closest t = 25.010858, Off by = 61.944655
  105. Black Bishop: (2, 3) → (3, 4), Dist = 1.414214
  106. Black Rook: (4, 4) → (3, 5), Dist = 1.414214
  107. Black King: (6, 4) → (5, 5), Dist = 1.414214
  108. Black Knight: (0, 5) → (2, 6), Dist = 2.236068
  109. Black Queen: (6, 5) → (5, 6), Dist = 1.414214
  110. Black Pawn: (1, 1) → (0, 0), Dist = 1.414214
  111. Black: t = 75.641805, s = 0.5 + 75.641805i, ζ(s) = -0.091802 + -0.071041i, Mag = 0.116080
  112. Closest t = 25.010858, Off by = 50.630947
  113.  
  114. Turn 7:
  115. White Knight: (7, 6) → (6, 4), Dist = 2.236068
  116. White Bishop: (5, 3) → (1, 7), Dist = 5.656854
  117. White Rook: (3, 2) → (4, 1), Dist = 1.414214
  118. White Queen: (3, 3) → (4, 4), Dist = 1.414214
  119. White King: (5, 2) → (6, 1), Dist = 1.414214
  120. White: t = 99.091076, s = 0.5 + 99.091076i, ζ(s) = 0.283356 + 0.847070i, Mag = 0.893207
  121. Closest t = 25.010858, Off by = 74.080218
  122. Black King: (5, 5) → (6, 6), Dist = 1.414214
  123. Black Queen: (5, 6) → (1, 2), Dist = 5.656854
  124. Black Rook: (3, 5) → (4, 6), Dist = 1.414214
  125. Black Knight: (2, 6) → (0, 5), Dist = 2.236068
  126. Black Bishop: (3, 4) → (0, 7), Dist = 4.242641
  127. Black: t = 90.605795, s = 0.5 + 90.605795i, ζ(s) = 4.362554 + 0.868068i, Mag = 4.448080
  128. Closest t = 25.010858, Off by = 65.594937
  129.  
  130. Turn 8:
  131. White Knight: (6, 4) → (4, 3), Dist = 2.236068
  132. White King: (6, 1) → (5, 0), Dist = 1.414214
  133. White Bishop: (1, 7) → (0, 6), Dist = 1.414214
  134. White Rook: (4, 1) → (3, 2), Dist = 1.414214
  135. White Queen: (4, 4) → (5, 5), Dist = 1.414214
  136. White: t = 106.983998, s = 0.5 + 106.983998i, ζ(s) = 0.461903 + -0.176695i, Mag = 0.494545
  137. Closest t = 25.010858, Off by = 81.973140
  138. Black Queen: (1, 2) → (6, 7), Dist = 7.071068
  139. Black King: (6, 6) → (7, 5), Dist = 1.414214
  140. Black Rook: (4, 6) → (3, 5), Dist = 1.414214
  141. Black Knight: (0, 5) → (1, 3), Dist = 2.236068
  142. Black Bishop: (0, 7) → (1, 6), Dist = 1.414214
  143. Black: t = 104.155571, s = 0.5 + 104.155571i, ζ(s) = 0.674236 + 0.353757i, Mag = 0.761405
  144. Closest t = 25.010858, Off by = 79.144713
  145.  
  146. Turn 9:
  147. White Knight: (4, 3) → (2, 4), Dist = 2.236068
  148. White King: (5, 0) → (4, 1), Dist = 1.414214
  149. White Queen: (5, 5) → (7, 7), Dist = 2.828427
  150. White Rook: (3, 2) → (2, 1), Dist = 1.414214
  151. White Bishop: (0, 6) → (6, 0), Dist = 8.485281
  152. White: t = 123.362202, s = 0.5 + 123.362202i, ζ(s) = 0.318103 + 0.450356i, Mag = 0.551371
  153. Closest t = 25.010858, Off by = 98.351344
  154. Black Queen: (6, 7) → (0, 1), Dist = 8.485281
  155. Black Bishop: (1, 6) → (5, 2), Dist = 5.656854
  156. Black Rook: (3, 5) → (4, 6), Dist = 1.414214
  157. Black King: (7, 5) → (6, 4), Dist = 1.414214
  158. Black Knight: (1, 3) → (3, 4), Dist = 2.236068
  159. Black: t = 123.362202, s = 0.5 + 123.362202i, ζ(s) = 0.318103 + 0.450356i, Mag = 0.551371
  160. Closest t = 25.010858, Off by = 98.351344
  161.  
  162. Turn 10:
  163. White King: (4, 1) → (3, 2), Dist = 1.414214
  164. White Knight: (2, 4) → (0, 3), Dist = 2.236068
  165. White Bishop: (6, 0) → (3, 3), Dist = 4.242641
  166. White Queen: (7, 7) → (5, 5), Dist = 2.828427
  167. White Rook: (2, 1) → (3, 0), Dist = 1.414214
  168. White: t = 135.497765, s = 0.5 + 135.497765i, ζ(s) = 0.330659 + 2.746725i, Mag = 2.766556
  169. Closest t = 25.010858, Off by = 110.486907
  170. Black Knight: (3, 4) → (2, 2), Dist = 2.236068
  171. Black King: (6, 4) → (7, 5), Dist = 1.414214
  172. Black Rook: (4, 6) → (3, 5), Dist = 1.414214
  173. Black Queen: (0, 1) → (2, 3), Dist = 2.828427
  174. Black Bishop: (5, 2) → (2, 5), Dist = 4.242641
  175. Black: t = 135.497765, s = 0.5 + 135.497765i, ζ(s) = 0.330659 + 2.746725i, Mag = 2.766556
  176. Closest t = 25.010858, Off by = 110.486907
  177.  
  178. Turn 11:
  179. White Knight: (0, 3) → (2, 4), Dist = 2.236068
  180. White King: (3, 2) → (4, 3), Dist = 1.414214
  181. White Queen: (5, 5) → (4, 6), Dist = 1.414214
  182. White Rook: (3, 0) → (2, 1), Dist = 1.414214
  183. White Bishop: (3, 3) → (1, 5), Dist = 2.828427
  184. White: t = 144.804901, s = 0.5 + 144.804901i, ζ(s) = 3.611080 + -1.657800i, Mag = 3.973437
  185. Closest t = 25.010858, Off by = 119.794043
  186. Black King: (7, 5) → (6, 4), Dist = 1.414214
  187. Black Bishop: (2, 5) → (3, 4), Dist = 1.414214
  188. Black Rook: (3, 5) → (4, 4), Dist = 1.414214
  189. Black Knight: (2, 2) → (4, 1), Dist = 2.236068
  190. Black Queen: (2, 3) → (0, 5), Dist = 2.828427
  191. Black: t = 144.804901, s = 0.5 + 144.804901i, ζ(s) = 3.611080 + -1.657800i, Mag = 3.973437
  192. Closest t = 25.010858, Off by = 119.794043
  193.  
  194. Turn 12:
  195. White Knight: (2, 4) → (4, 5), Dist = 2.236068
  196. White Queen: (4, 6) → (3, 7), Dist = 1.414214
  197. White King: (4, 3) → (5, 4), Dist = 1.414214
  198. White Bishop: (1, 5) → (3, 3), Dist = 2.828427
  199. White Rook: (2, 1) → (3, 2), Dist = 1.414214
  200. White: t = 154.112036, s = 0.5 + 154.112036i, ζ(s) = 3.931968 + 2.306577i, Mag = 4.558582
  201. Closest t = 25.010858, Off by = 129.101178
  202. Black Bishop: (3, 4) → (2, 5), Dist = 1.414214
  203. Black King: (6, 4) → (7, 3), Dist = 1.414214
  204. Black Knight: (4, 1) → (6, 2), Dist = 2.236068
  205. Black Rook: (4, 4) → (5, 3), Dist = 1.414214
  206. Black Queen: (0, 5) → (1, 6), Dist = 1.414214
  207. Black: t = 152.697823, s = 0.5 + 152.697823i, ζ(s) = 1.115739 + -0.409455i, Mag = 1.188498
  208. Closest t = 25.010858, Off by = 127.686965
  209.  
  210. Turn 13:
  211. White Queen: (3, 7) → (0, 4), Dist = 4.242641
  212. White Rook: (3, 2) → (2, 1), Dist = 1.414214
  213. White Bishop: (3, 3) → (7, 7), Dist = 5.656854
  214. White Knight: (4, 5) → (6, 6), Dist = 2.236068
  215. White King: (5, 4) → (4, 5), Dist = 1.414214
  216. White: t = 169.076026, s = 0.5 + 169.076026i, ζ(s) = -0.005725 + -0.028176i, Mag = 0.028752
  217. --> White hits a zeta zero!
  218.  
  219. Game Over: White wins!
  220.  
  221. Zeta Chess Python Code:
  222. import math
  223. from mpmath import mp, zeta
  224. import random
  225. import plotly.graph_objects as go
  226. from plotly.subplots import make_subplots
  227.  
  228. # Precision
  229. mp.dps = 20
  230.  
  231. # Chessboard: 8x8
  232. def is_valid(x, y):
  233. return 0 <= x <= 7 and 0 <= y <= 7
  234.  
  235. # Distance
  236. def distance(x1, y1, x2, y2):
  237. return math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
  238.  
  239. # Piece class
  240. class Piece:
  241. def __init__(self, name, x, y, color):
  242. self.name = name
  243. self.x = x
  244. self.y = y
  245. self.color = color
  246.  
  247. def get_sloped_moves(self, occupied):
  248. moves = []
  249. if self.name == "Pawn":
  250. dy = 1 if self.color == "White" else -1
  251. for dx in [-1, 1]:
  252. nx, ny = self.x + dx, self.y + dy
  253. if is_valid(nx, ny) and (nx, ny) not in occupied:
  254. moves.append((nx, ny))
  255. elif self.name == "Knight":
  256. deltas = [(-2, -1), (-2, 1), (-1, -2), (-1, 2), (1, -2), (1, 2), (2, -1), (2, 1)]
  257. moves = [(self.x + dx, self.y + dy) for dx, dy in deltas if is_valid(self.x + dx, self.y + dy) and (self.x + dx, self.y + dy) not in occupied]
  258. elif self.name == "Bishop" or self.name == "Queen":
  259. for d in range(-7, 8):
  260. if d != 0:
  261. if is_valid(self.x + d, self.y + d) and (self.x + d, self.y + d) not in occupied:
  262. moves.append((self.x + d, self.y + d))
  263. if is_valid(self.x + d, self.y - d) and (self.x + d, self.y - d) not in occupied:
  264. moves.append((self.x + d, self.y - d))
  265. elif self.name == "Rook":
  266. for dx in [-1, 1]:
  267. for dy in [-1, 1]:
  268. nx, ny = self.x + dx, self.y + dy
  269. if is_valid(nx, ny) and (nx, ny) not in occupied:
  270. moves.append((nx, ny))
  271. elif self.name == "King":
  272. deltas = [(-1, -1), (-1, 1), (1, -1), (1, 1)]
  273. moves = [(self.x + dx, self.y + dy) for dx, dy in deltas if is_valid(self.x + dx, self.y + dy) and (self.x + dx, self.y + dy) not in occupied]
  274. return moves
  275.  
  276. def is_checkmated(self, occupied):
  277. return len(self.get_sloped_moves(occupied)) == 0
  278.  
  279. # Test zeta
  280. def test_zeta(t):
  281. sigma = 0.5
  282. s = mp.mpc(real=str(sigma), imag=str(t))
  283. z = zeta(s)
  284. mag = abs(z)
  285. return s, z, mag < 0.05
  286.  
  287. # Chess-zeta game with data collection
  288. def chess_zeta_game(first_player="White"):
  289. white_pieces = [
  290. Piece("Pawn", 0, 1, "White"), Piece("Knight", 1, 0, "White"), Piece("Bishop", 2, 0, "White"),
  291. Piece("Rook", 3, 0, "White"), Piece("Queen", 4, 0, "White"), Piece("King", 5, 0, "White")
  292. ]
  293. black_pieces = [
  294. Piece("Pawn", 0, 6, "Black"), Piece("Knight", 1, 7, "Black"), Piece("Bishop", 2, 7, "Black"),
  295. Piece("Rook", 3, 7, "Black"), Piece("Queen", 4, 7, "Black"), Piece("King", 5, 7, "Black")
  296. ]
  297.  
  298. players = [("White", white_pieces, "Red"), ("Black", black_pieces, "Blue")]
  299. if first_player == "Black":
  300. players.reverse()
  301.  
  302. white_t, black_t = 0.0, 0.0
  303. all_occupied = {(p.x, p.y) for p in white_pieces + black_pieces}
  304. turn = 0
  305.  
  306. # Data storage
  307. data = {"White": {"turns": [], "t_values": [], "s_values": [], "zeta_values": [], "mags": [], "tooltips": []},
  308. "Black": {"turns": [], "t_values": [], "s_values": [], "zeta_values": [], "mags": [], "tooltips": []}}
  309.  
  310. print(f"\nGame starts: {first_player} moves first")
  311.  
  312. while True:
  313. turn += 1
  314. print(f"\nTurn {turn}:")
  315. for player, pieces, color in players:
  316. random.shuffle(pieces)
  317. king = next(p for p in pieces if p.name == "King")
  318. total_dist = 0.0
  319. move_log = []
  320.  
  321. for piece in pieces:
  322. moves = piece.get_sloped_moves(all_occupied)
  323. if not moves:
  324. continue
  325. nx, ny = random.choice(moves)
  326. dist = distance(piece.x, piece.y, nx, ny)
  327. total_dist += dist
  328. move_log.append(f"{piece.name}: ({piece.x},{piece.y})→({nx},{ny}), Dist={dist:.4f}")
  329. all_occupied.remove((piece.x, piece.y))
  330. all_occupied.add((nx, ny))
  331. piece.x, piece.y = nx, ny
  332.  
  333. if player == "White":
  334. white_t += total_dist
  335. t_value = white_t
  336. else:
  337. black_t += total_dist
  338. t_value = black_t
  339.  
  340. s, z, near_zero = test_zeta(t_value)
  341. mag = float(abs(z))
  342. s_str = f"0.5 + {float(t_value):.6f}i"
  343. z_str = f"{float(z.real):.6f} + {float(z.imag):.6f}i"
  344. closest_t = min([14.134725, 21.022040, 25.010858], key=lambda z: abs(z - t_value))
  345. dist_to_zero = abs(t_value - closest_t)
  346.  
  347. # Store data
  348. tooltip = (f"Turn: {turn}<br>Player: {player} ({color})<br>t: {t_value:.6f}<br>"
  349. f"s: {s_str}<br>ζ(s): {z_str}<br>Mag: {mag:.6f}<br>"
  350. f"Nearest Zero t: {closest_t}<br>Dist to Zero: {dist_to_zero:.6f}<br>"
  351. f"Moves:<br>{'<br>'.join(move_log)}")
  352. data[player]["turns"].append(turn)
  353. data[player]["t_values"].append(float(t_value))
  354. data[player]["s_values"].append(s_str)
  355. data[player]["zeta_values"].append(z_str)
  356. data[player]["mags"].append(mag)
  357. data[player]["tooltips"].append(tooltip)
  358.  
  359. print(f"{player}: t = {t_value:.6f}, Mag = {mag:.6f}")
  360. if near_zero:
  361. print(f"--> {player} hits a zeta zero!")
  362. plot_game(data, first_player)
  363. return player
  364. elif king.is_checkmated(all_occupied):
  365. print(f"--> {player}'s King checkmated!")
  366. plot_game(data, first_player)
  367. return "White" if player == "Black" else "Black"
  368.  
  369. # Plotting function
  370. def plot_game(data, first_player):
  371. fig = go.Figure()
  372.  
  373. # Red (White)
  374. fig.add_trace(go.Scatter(
  375. x=data["White"]["turns"], y=data["White"]["t_values"],
  376. mode="lines+markers", name="White (Red)", line=dict(color="red"),
  377. text=data["White"]["tooltips"], hoverinfo="text"
  378. ))
  379.  
  380. # Blue (Black)
  381. fig.add_trace(go.Scatter(
  382. x=data["Black"]["turns"], y=data["Black"]["t_values"],
  383. mode="lines+markers", name="Black (Blue)", line=dict(color="blue"),
  384. text=data["Black"]["tooltips"], hoverinfo="text"
  385. ))
  386.  
  387. # Known zeros
  388. for t in [14.134725, 21.022040, 25.010858]:
  389. fig.add_hline(y=t, line_dash="dash", line_color="green", annotation_text=f"Zero at {t}")
  390.  
  391. fig.update_layout(
  392. title=f"Chess-Zeta Game: {first_player} Moves First",
  393. xaxis_title="Turn Number",
  394. yaxis_title="t (Imaginary Part)",
  395. hovermode="closest"
  396. )
  397.  
  398. fig.write_html(f"chess_zeta_{first_player}_first.html")
  399. print(f"Plot saved as 'chess_zeta_{first_player}_first.html'")
  400.  
  401. # Run
  402. for first in ["White", "Black"]:
  403. print(f"\n{first} moves first:")
  404. winner = chess_zeta_game(first)
  405. print(f"\nGame Over: {winner} wins!")
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