Une période unique fait résonner toutes les fractions de n/157 en base 6.  

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

1/157=0,001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015...

2/157=0,002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034...

3/157=0,004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053...

4/157=0,005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112...

5/157=0,010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131...

6/157=0,012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150...

7/157=0,013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205...

8/157=0,015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224...

9/157=0,020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243...

10/157=0,021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302...

11/157=0,023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321...

12/157=0,024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340...

13/157=0,025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355...

14/157=0,031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414...

15/157=0,032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433...

16/157=0,034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452...

17/157=0,035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511...

18/157=0,040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530...

19/157=0,042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545...

20/157=0,043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004...

21/157=0,044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023...

22/157=0,050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042...

23/157=0,051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101...

24/157=0,053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120...

25/157=0,054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135...

26/157=0,055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154...

27/157=0,101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213...

28/157=0,102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232...

29/157=0,103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251...

30/157=0,105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310...

31/157=0,110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325...

32/157=0,112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344...

33/157=0,113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403...

34/157=0,114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422...

35/157=0,120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441...

36/157=0,121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500...

37/157=0,122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515...

38/157=0,124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534...

39/157=0,125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553...

40/157=0,131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012...

41/157=0,132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031...

42/157=0,133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050...

43/157=0,135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105...

44/157=0,140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124...

45/157=0,141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143...

46/157=0,143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202...

47/157=0,144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221...

48/157=0,150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240...

49/157=0,151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255...

50/157=0,152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314...

51/157=0,154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333...

52/157=0,155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352...

53/157=0,200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411...

54/157=0,202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430...

55/157=0,203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445...

56/157=0,205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504...

57/157=0,210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523...

58/157=0,211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542...

59/157=0,213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001...

60/157=0,214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020...

61/157=0,215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035...

62/157=0,221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054...

63/157=0,222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113...

64/157=0,224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132...

65/157=0,225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151...

66/157=0,230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210...

67/157=0,232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225...

68/157=0,233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244...

69/157=0,234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303...

70/157=0,240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322...

71/157=0,241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341...

72/157=0,243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400...

73/157=0,244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415...

74/157=0,245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434...

75/157=0,251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453...

76/157=0,252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512...

77/157=0,253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531...

78/157=0,255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550...

79/157=0,300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005...

80/157=0,302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024...

81/157=0,303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043...

82/157=0,304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102...

83/157=0,310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121...

84/157=0,311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140...

85/157=0,312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155...

86/157=0,314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214...

87/157=0,315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233...

88/157=0,321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252...

89/157=0,322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311...

90/157=0,323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330...

91/157=0,325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345...

92/157=0,330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404...

93/157=0,331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423...

94/157=0,333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442...

95/157=0,334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501...

96/157=0,340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520...

97/157=0,341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535...

98/157=0,342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554...

99/157=0,344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013...

100/157=0,345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032...

101/157=0,350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051...

102/157=0,352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110...

103/157=0,353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125...

104/157=0,355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144...

105/157=0,400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203...

106/157=0,401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222...

107/157=0,403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241...

108/157=0,404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300...

109/157=0,405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315...

110/157=0,411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334...

111/157=0,412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353...

112/157=0,414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412...

113/157=0,415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431...

114/157=0,420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450...

115/157=0,422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505...

116/157=0,423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524...

117/157=0,424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543...

118/157=0,430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002...

119/157=0,431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021...

120/157=0,433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040...

121/157=0,434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055...

122/157=0,435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114...

123/157=0,441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133...

124/157=0,442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152...

125/157=0,443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211...

126/157=0,445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230...

127/157=0,450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245...

128/157=0,452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304...

129/157=0,453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323...

130/157=0,454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342...

131/157=0,500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401...

132/157=0,501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420...

133/157=0,502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435...

134/157=0,504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454...

135/157=0,505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513...

136/157=0,511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532...

137/157=0,512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551...

138/157=0,513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010...

139/157=0,515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025...

140/157=0,520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044...

141/157=0,521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103...

142/157=0,523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312535341241403113222401500121310105135054221144355025515122...

143/157=0,524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141...

144/157=0,530040433032345325110352155312535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200...

145/157=0,531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215...

146/157=0,532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234...

147/157=0,534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253...

148/157=0,535341241403113222401500121310105135054221144355025515122523210230445203400243020214314152442333154055434245450420501334411200530040433032345325110352155312...

149/157=0,540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331...

150/157=0,542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350...

151/157=0,543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405...

152/157=0,545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502551512252321023044520340024302021431415244233315405543424...

153/157=0,550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443...

154/157=0,551512252321023044520340024302021431415244233315405543424545042050133441120053004043303234532511035215531253534124140311322240150012131010513505422114435502...

155/157=0,553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540554342454504205013344112005300404330323453251103521...

156/157=0,554342454504205013344112005300404330323453251103521553125353412414031132224015001213101051350542211443550255151225232102304452034002430202143141524423331540...