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Internet Message Format  |  1992-11-09  |  11.3 KB
  1. Path: sparky!uunet!ornl!utkcs2!darwin.sura.net!zaphod.mps.ohio-state.edu!moe.ksu.ksu.edu!crcnis1.unl.edu!unlinfo!dfowler
  2. From: dfowler@unlinfo.unl.edu (david fowler)
  3. Newsgroups: sci.math
  4. Subject: Picture of Allan Turing
  5. Date: 9 Nov 1992 20:13:38 GMT
  6. Organization: University of Nebraska--Lincoln    
  7. Lines: 66
  8. Distribution: world
  9. Message-ID: <1dmgpiINNmd1@crcnis1.unl.edu>
  10. NNTP-Posting-Host: unlinfo.unl.edu
  11. Summary: Mma density plot of A Turing
  12. Keywords: recreational math graphics
  13.  
  14. at={15,15,15,7,6,5,7,5,6,4,6,6,4,3,5,5,5,3,4,4,3,3,1,2,6,5,13,14,15,14,13,15,13,12,10,9,9,7,7,5,4,6,8,12,13,15,11,10,15,12,7,10,12,12,12,9,9,7,9,11,9,14,13,13,
  15. 15,15,15,8,6,6,7,5,5,6,5,5,4,5,4,6,4,4,5,2,2,4,2,5,5,8,13,15,14,14,14,12,12,11,8,9,5,6,7,4,3,5,7,10,13,14,15,7,13,12,8,11,11,12,11,9,9,9,11,12,14,14,15,15,
  16. 15,15,15,11,9,8,6,5,8,4,6,5,6,7,5,3,4,7,3,3,3,6,2,5,7,12,15,13,14,14,12,9,11,9,6,7,5,5,5,3,3,3,4,7,11,13,14,13,6,15,10,12,12,8,11,11,12,14,14,15,15,15,15,15,
  17. 15,15,15,15,15,15,13,8,8,11,6,6,7,4,6,6,4,5,4,1,4,4,5,5,12,13,13,15,14,11,10,10,8,6,7,5,5,2,4,2,2,5,2,3,7,10,14,15,4,15,13,12,11,13,14,15,15,15,15,15,15,15,15,15,
  18. 15,15,15,15,15,15,15,15,14,10,9,9,6,7,8,4,6,5,2,3,6,5,4,10,13,14,15,12,12,10,10,7,7,4,3,5,2,2,2,2,3,3,4,2,2,5,11,15,8,15,13,15,15,15,15,15,15,15,15,15,15,15,15,15,
  19. 15,15,15,15,15,15,15,15,15,15,14,12,9,8,7,6,4,5,5,4,3,3,6,13,14,14,13,11,9,9,8,4,5,4,2,2,3,2,3,4,3,4,3,4,4,4,4,10,8,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
  20. 15,15,15,15,15,15,15,15,15,15,15,15,14,10,10,6,4,4,6,1,5,5,11,14,13,13,10,10,8,9,4,3,3,2,3,3,2,3,3,3,5,5,4,4,5,1,2,2,2,4,4,8,10,14,15,15,15,15,15,15,15,15,15,15,
  21. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,13,9,5,6,5,4,4,8,14,13,13,10,11,10,8,6,3,4,3,1,2,2,4,4,4,3,3,7,4,5,5,3,6,5,5,6,6,5,6,7,10,15,15,15,15,15,15,15,15,15,
  22. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,8,5,1,5,5,11,14,13,11,12,8,8,6,4,4,2,5,7,4,8,6,6,6,6,6,7,6,7,9,8,8,9,8,9,10,9,12,10,10,12,15,15,15,15,15,15,15,15,
  23. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,5,3,5,7,12,13,11,10,9,9,7,5,5,4,5,5,8,7,8,8,7,8,7,7,9,7,9,9,9,11,10,10,11,12,13,12,13,13,12,15,15,15,15,15,15,15,15,
  24. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,10,4,4,7,13,11,11,9,9,8,6,5,7,6,8,8,8,7,9,7,10,9,8,8,7,8,9,9,11,12,12,13,13,14,14,14,14,15,15,15,15,15,15,15,15,15,15,
  25. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,4,7,11,9,9,8,7,6,5,6,8,8,7,8,8,10,9,8,10,8,9,8,9,8,9,11,11,12,13,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
  26. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,11,3,7,10,9,10,7,7,7,7,7,8,8,10,10,9,9,9,9,10,9,8,10,7,9,10,10,12,12,14,15,15,14,15,15,15,15,15,15,15,15,15,15,15,15,15,
  27. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,8,6,7,10,8,7,8,7,8,8,9,10,8,9,10,9,10,10,9,10,9,9,10,8,9,11,12,14,12,11,11,13,14,14,15,15,15,15,15,15,15,15,15,15,15,
  28. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,9,7,8,9,8,8,9,7,9,9,8,11,10,10,9,9,10,10,10,10,9,9,8,9,10,13,11,9,6,5,6,6,10,11,14,15,15,15,15,15,15,15,15,15,
  29. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,12,7,9,8,8,9,9,8,10,9,9,11,10,8,11,10,9,10,9,10,11,8,6,7,10,11,9,9,7,7,4,6,7,7,12,15,15,15,15,15,15,15,15,15,
  30. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,10,7,7,6,8,9,8,9,9,10,10,9,11,10,9,10,10,10,9,11,10,10,9,5,4,7,11,10,10,10,11,14,13,12,11,15,14,15,15,15,15,15,15,15,
  31. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,11,5,6,3,8,10,10,8,10,11,10,10,9,10,9,10,8,10,11,9,11,10,10,8,3,3,3,4,4,8,8,10,14,15,15,13,12,15,15,15,15,15,15,15,
  32. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,8,6,9,7,7,11,9,11,10,11,10,11,11,10,10,9,11,10,10,10,11,11,11,11,8,7,9,9,9,8,6,7,7,8,12,6,10,15,15,15,15,15,15,15,
  33. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,9,12,12,14,11,11,9,10,10,12,11,12,11,10,10,10,10,11,10,10,11,12,13,12,12,12,11,10,11,12,14,13,14,15,13,13,14,15,15,15,15,15,15,15,
  34. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,12,12,14,13,15,13,11,11,11,11,11,12,11,10,11,11,11,11,11,12,10,12,10,13,13,12,14,13,13,13,12,13,15,14,14,15,15,15,15,15,15,15,15,15,15,
  35. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,11,12,13,12,12,13,13,12,11,11,11,11,11,11,12,11,11,11,12,13,13,12,12,10,13,14,14,13,13,13,14,14,14,13,15,14,14,15,15,15,15,15,15,15,15,15,
  36. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,11,10,9,12,13,14,13,12,12,11,11,10,10,10,11,11,11,11,13,12,12,12,13,13,14,12,13,14,14,15,14,13,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,
  37. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,12,11,8,11,13,14,12,12,12,12,10,10,11,10,11,11,11,11,12,11,12,12,13,13,13,14,12,13,13,15,14,14,14,12,11,10,12,13,15,15,15,15,15,15,15,15,15,15,
  38. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,11,9,11,13,12,12,12,14,13,10,11,10,10,11,9,10,12,11,11,12,13,14,14,15,15,14,14,13,13,14,15,9,7,4,7,5,4,5,13,15,15,15,15,15,15,15,15,15,
  39. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,11,11,12,10,13,14,9,14,15,12,11,10,11,11,9,11,11,11,12,12,13,14,14,15,15,15,15,14,15,14,13,14,12,11,10,3,6,3,6,8,13,15,15,15,15,15,15,15,15,
  40. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,11,11,10,13,9,11,10,9,15,14,12,10,11,10,11,11,10,10,11,12,14,12,13,14,14,15,15,15,15,15,14,14,14,14,14,14,13,11,9,8,11,13,15,15,15,15,15,15,15,15,
  41. 15,15,15,15,15,15,15,15,15,15,15,15,15,13,13,12,14,14,8,6,6,7,14,14,11,11,10,11,12,12,12,12,14,12,14,14,13,14,15,15,14,15,15,15,15,15,14,14,14,15,13,14,13,14,15,15,15,15,15,15,15,15,15,15,
  42. 15,15,15,15,15,15,15,15,15,15,15,15,15,11,11,12,12,14,12,7,3,9,11,12,12,12,13,13,12,13,12,13,12,14,13,15,14,15,15,15,15,15,15,15,15,14,15,15,14,14,13,13,15,15,15,15,15,15,15,15,15,15,15,15,
  43. 15,15,15,15,15,15,15,15,15,15,15,15,15,11,11,14,13,15,13,13,8,12,12,12,11,10,12,13,14,12,13,12,14,14,14,14,15,15,14,14,15,13,14,15,14,15,15,14,14,14,13,15,15,15,15,15,15,15,15,15,15,15,15,15,
  44. 15,15,15,15,15,15,15,15,15,15,15,15,15,13,7,10,14,15,11,5,12,13,11,11,11,11,13,13,12,14,12,13,13,13,13,15,14,14,14,14,14,14,15,14,13,13,15,13,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
  45. 15,15,15,15,15,15,15,15,15,15,15,15,15,14,7,6,8,7,7,10,13,15,10,11,10,11,13,11,13,12,13,12,12,13,12,11,12,12,12,11,10,11,13,15,12,12,14,14,14,14,13,15,15,15,15,15,15,15,15,15,15,15,15,15,
  46. 15,15,15,15,15,15,15,15,15,15,15,15,15,13,9,10,9,9,12,14,15,11,10,10,10,11,12,11,12,11,12,10,10,10,9,8,7,5,5,7,10,8,12,12,9,10,8,12,14,14,13,15,15,15,15,15,15,15,15,15,15,15,15,15,
  47. 15,15,15,15,15,15,15,15,15,15,15,15,15,8,5,9,12,14,13,11,11,10,10,10,10,11,12,11,12,11,11,9,10,7,7,7,7,2,4,1,2,3,4,6,2,6,5,8,10,13,15,15,14,12,14,13,12,15,15,15,15,15,15,15,
  48. 15,15,15,15,15,15,15,15,15,15,15,15,14,4,2,3,3,4,6,9,9,9,9,8,10,11,10,12,10,11,11,11,9,9,5,6,5,5,3,6,2,2,2,2,1,1,0,5,9,14,15,15,5,4,4,8,7,15,15,15,15,15,15,15,
  49. 15,15,15,15,15,15,15,15,15,15,15,15,11,3,3,3,4,4,7,8,9,9,9,7,9,10,11,10,12,11,10,11,9,8,7,4,6,4,4,2,0,2,3,0,1,2,2,2,7,11,15,14,7,2,7,3,3,11,15,15,15,15,15,15,
  50. 15,15,15,15,15,15,15,15,15,15,15,15,9,4,1,3,2,4,6,8,5,8,8,7,8,8,9,11,11,12,10,11,11,11,8,7,4,2,4,1,2,1,0,0,1,1,0,2,5,10,13,13,6,5,2,3,4,9,15,15,15,15,15,15,
  51. 15,15,15,15,15,15,15,15,15,15,15,15,7,2,3,3,1,4,6,5,5,7,4,7,8,7,7,11,9,11,11,10,10,9,10,8,7,3,5,3,3,3,1,1,1,2,2,2,8,10,12,13,11,6,2,4,4,5,13,15,15,15,15,15,
  52. 15,15,15,15,15,15,15,15,15,15,15,14,4,3,4,2,5,2,5,3,4,5,4,5,8,7,7,10,9,11,9,11,10,11,9,12,9,9,6,5,7,6,5,6,6,7,6,9,11,14,13,13,13,13,9,8,7,7,10,15,15,15,15,15,
  53. 15,15,15,15,15,15,15,15,15,15,15,13,4,2,3,2,3,5,1,2,3,5,1,6,4,5,8,7,9,9,9,10,11,11,10,11,11,10,10,8,7,7,8,7,9,10,12,14,13,15,14,15,15,15,15,13,10,11,13,15,15,15,15,15,
  54. 15,15,15,15,15,15,15,15,15,15,15,11,2,1,1,4,1,1,1,0,3,3,1,5,5,4,7,10,8,9,10,12,11,12,11,12,11,11,11,10,11,10,10,11,10,12,13,14,15,15,15,15,15,15,15,15,14,13,15,15,15,15,15,15,
  55. 15,15,15,15,15,15,15,15,15,15,15,11,2,1,2,2,0,1,0,1,1,3,1,3,5,4,6,8,9,10,10,11,11,12,12,12,11,12,11,12,11,11,12,11,13,12,14,14,15,15,15,15,15,15,15,15,15,14,13,15,15,15,15,15,
  56. 15,15,15,15,15,15,15,15,15,15,15,9,2,1,2,1,0,1,1,1,1,1,2,4,1,5,6,6,8,9,10,12,12,12,11,12,13,11,12,11,11,12,13,13,14,14,14,15,15,15,15,15,15,15,15,15,15,9,14,15,15,15,15,15,
  57. 15,15,15,15,15,15,15,15,15,15,15,11,2,1,3,1,1,1,1,1,2,2,0,3,2,2,5,4,9,11,10,12,12,13,12,11,12,11,12,11,12,11,12,13,13,15,14,15,15,15,15,15,15,15,15,15,14,7,14,15,15,15,15,15,
  58. 15,15,15,15,15,15,15,15,15,15,15,10,4,2,3,2,2,2,1,1,4,0,2,1,2,2,3,5,9,11,13,13,11,13,13,13,12,13,12,13,11,12,14,13,14,14,14,15,15,15,15,15,15,15,15,15,12,3,14,15,15,15,15,15,
  59. 15,15,15,15,15,15,15,15,15,15,15,13,3,1,5,1,0,2,2,0,3,2,2,2,0,1,5,8,10,12,13,12,13,13,13,12,13,13,12,12,12,14,13,13,14,14,14,15,15,14,15,15,15,15,15,15,7,2,10,15,15,15,15,15,
  60. 15,15,15,15,15,15,15,15,15,15,15,14,4,2,3,3,2,1,2,1,3,2,0,1,1,1,5,6,12,13,14,13,13,13,13,13,14,12,12,13,12,13,12,14,14,14,15,14,15,15,15,15,15,15,15,11,2,2,9,15,15,15,15,15,
  61. 15,15,15,15,15,15,15,15,15,15,15,15,7,3,4,1,2,3,0,2,2,3,2,4,2,1,5,6,12,13,14,13,12,14,14,12,13,13,13,13,13,13,14,14,14,14,13,15,15,15,15,15,15,15,14,5,1,2,10,15,15,15,15,15,
  62. 15,15,15,15,15,15,15,15,15,15,15,15,10,4,5,3,1,2,2,2,2,3,2,3,3,3,2,4,10,13,13,14,14,13,14,13,14,13,13,13,14,14,14,14,15,15,15,15,15,15,15,15,15,15,11,2,3,2,10,15,15,15,15,15,
  63. 15,15,15,15,15,15,15,15,15,15,15,15,15,6,2,5,5,3,2,3,3,3,4,4,3,2,4,3,7,14,14,13,13,13,13,13,13,14,15,15,14,13,15,15,14,15,15,15,15,15,15,15,14,12,1,1,0,3,14,15,15,15,15,15,
  64. 15,15,15,15,15,15,15,15,15,15,15,15,15,10,6,4,6,6,3,3,4,2,3,4,3,3,2,2,7,11,14,15,14,15,14,13,15,13,13,14,14,15,14,15,15,15,14,15,15,15,14,13,9,3,0,5,2,6,15,15,15,15,15,15,
  65. 15,15,15,15,15,15,15,15,15,15,15,15,15,14,6,4,7,6,2,3,3,2,3,4,3,4,5,3,6,10,12,14,14,14,14,14,13,13,14,13,12,10,12,15,14,14,15,14,12,11,8,5,3,0,1,4,1,13,15,15,15,15,15,15,
  66. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,4,4,4,3,4,3,5,5,4,3,5,6,7,9,11,10,9,9,9,11,9,9,8,8,8,6,8,6,7,7,11,8,7,3,2,0,0,0,2,6,1,4,15,15,15,15,15,15,15,
  67. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,6,3,4,3,3,5,3,5,8,6,8,8,8,8,7,1,1,1,1,3,2,2,1,2,1,2,3,2,4,4,1,2,1,1,1,0,3,3,5,2,3,7,15,15,15,15,15,15,15,
  68. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,3,2,3,4,6,7,8,9,6,8,5,0,2,1,0,1,0,0,1,1,0,1,1,1,2,1,0,1,1,1,0,0,0,0,1,1,3,4,2,4,13,15,15,15,15,15,15,15,
  69. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,9,4,1,2,1,2,2,1,0,2,1,2,1,1,0,1,0,1,1,1,2,1,0,0,1,1,1,0,1,1,2,0,4,1,1,0,4,4,6,7,15,15,15,15,15,15,15,15,
  70. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,6,2,3,1,1,2,1,1,2,2,0,1,0,2,1,0,0,2,1,1,1,1,0,3,0,0,2,2,1,3,0,1,2,1,5,3,4,5,14,15,15,15,15,15,15,15,15,
  71. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,6,5,3,3,3,2,3,5,3,4,4,2,2,1,0,2,1,2,0,1,2,4,2,2,3,4,1,2,1,4,5,7,7,4,6,6,13,15,15,15,15,15,15,15,15,15,
  72. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,13,7,6,3,5,3,1,5,2,3,5,3,4,3,3,2,3,1,2,1,3,3,3,4,1,1,2,1,4,4,7,7,5,8,11,14,15,15,15,15,15,15,15,15,15,15,
  73. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,8,6,7,4,4,4,3,4,5,2,3,5,3,4,4,2,2,3,1,3,5,2,2,3,2,6,8,10,11,9,9,12,15,15,15,15,15,15,15,15,15,15,15,15,
  74. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,10,6,6,6,4,5,5,4,4,4,6,4,6,6,4,5,6,4,5,4,2,6,7,9,10,11,13,10,10,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
  75. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,8,6,7,4,5,5,4,5,6,5,6,6,5,6,6,6,7,8,10,11,12,14,15,15,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
  76. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,11,10,6,8,7,4,6,7,6,6,8,5,8,8,7,9,11,10,13,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,
  77. 15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,14,11,11,8,8,8,6,9,8,10,10,13,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15};
  78. atP=Partition[at,64];
  79. ListDensityPlot[atP,Mesh->False]
  80.