Une période unique fait résonner toutes les fractions de n/113 en base 5.  

Le microscope numérique permet alors d'en observer le graphe. 

1/113=0,0010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243...

2/113=0,0021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041...

3/113=0,0031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334...

4/113=0,0042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132...

5/113=0,0102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430...

6/113=0,0113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223...

7/113=0,0123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021...

8/113=0,0134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314...

9/113=0,0144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112...

10/113=0,0210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410...

11/113=0,0220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203...

12/113=0,0231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001...

13/113=0,0241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244...

14/113=0,0302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042...

15/113=0,0312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340...

16/113=0,0323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133...

17/113=0,0334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431...

18/113=0,0344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224...

19/113=0,0410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022...

20/113=0,0420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320...

21/113=0,0431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113...

22/113=0,0441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411...

23/113=0,1002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204...

24/113=0,1012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002...

25/113=0,1023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300...

26/113=0,1033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043...

27/113=0,1044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341...

28/113=0,1104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134...

29/113=0,1120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432...

30/113=0,1130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230...

31/113=0,1141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023...

32/113=0,1201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321...

33/113=0,1212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114...

34/113=0,1223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412...

35/113=0,1233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210...

36/113=0,1244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003...

37/113=0,1304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301...

38/113=0,1320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044...

39/113=0,1330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342...

40/113=0,1341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140...

41/113=0,1401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433...

42/113=0,1412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231...

43/113=0,1422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024...

44/113=0,1433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322...

45/113=0,1443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120...

46/113=0,2004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413...

47/113=0,2014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211...

48/113=0,2030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004...

49/113=0,2041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302...

50/113=0,2101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100...

51/113=0,2112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343...

52/113=0,2122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141...

53/113=0,2133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434...

54/113=0,2143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232...

55/113=0,2204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030...

56/113=0,2214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323...

57/113=0,2230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121...

58/113=0,2240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414...

59/113=0,2301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212...

60/113=0,2311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010...

61/113=0,2322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303...

62/113=0,2332430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101...

63/113=0,2343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344...

64/113=0,2403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142...

65/113=0,2414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440...

66/113=0,2430010231141212230113043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233...

67/113=0,2440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031...

68/113=0,3001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324...

69/113=0,3011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122...

70/113=0,3022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420...

71/113=0,3032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213...

72/113=0,3043103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011...

73/113=0,3103340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304...

74/113=0,3114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102...

75/113=0,3124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400...

76/113=0,3140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143...

77/113=0,3200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441...

78/113=0,3211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234...

79/113=0,3221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032...

80/113=0,3232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330...

81/113=0,3243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123...

82/113=0,3303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421...

83/113=0,3314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214...

84/113=0,3324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012...

85/113=0,3340031244024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310...

86/113=0,3400312440241422403442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103...

87/113=0,3411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401...

88/113=0,3421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144...

89/113=0,3432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442...

90/113=0,3442343211201443421330323221433140134110441320042030220410021012332430010231141212230113043103340031244024142240...

91/113=0,4003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033...

92/113=0,4013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331...

93/113=0,4024142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124...

94/113=0,4034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422...

95/113=0,4100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220...

96/113=0,4110441320042030220410021012332430010231141212230113043103340031244024142240344234321120144342133032322143314013...

97/113=0,4121223011304310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311...

98/113=0,4132004203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104...

99/113=0,4142240344234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402...

100/113=0,4203022041002101233243001023114121223011304310334003124402414224034423432112014434213303232214331401341104413200...

101/113=0,4213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443...

102/113=0,4224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241...

103/113=0,4234321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034...

104/113=0,4300102311412122301130431033400312440241422403442343211201443421330323221433140134110441320042030220410021012332...

105/113=0,4310334003124402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130...

106/113=0,4321120144342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423...

107/113=0,4331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221...

108/113=0,4342133032322143314013411044132004203022041002101233243001023114121223011304310334003124402414224034423432112014...

109/113=0,4402414224034423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312...

110/113=0,4413200420302204100210123324300102311412122301130431033400312440241422403442343211201443421330323221433140134110...

111/113=0,4423432112014434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403...

112/113=0,4434213303232214331401341104413200420302204100210123324300102311412122301130431033400312440241422403442343211201...