4.0 CLOCKS AND BAR CHARTS

Clocks are used here not for time but to mark out the progression of digits in number series and to help reveal the patterns thus formed [including those series generated by natural phenomena]. The use of clocks [particularly 9, 12 and 24 hour clocks] to explore series as events proved to be very rewarding - see games with Prime Numbers 4.1 and the Fibonacci and Albarn Series 4.2.Bar Charts are made from some of the series and manipulated by rotation to reveal patterns of behaviour and something of the resulting character of the digits thus amplifying the nature of their relationship and the forms and concepts they tend to represent.

4.1 Primes reduced - Some patterns revealed

4.1.1 The digits array around a 24 hr. clock [including the reduced prime numbers - on white] demonstrate the symmetrical grouping of 147, 258 and 369

4.1.2 The sum of numbers opposite is 6

4.1.3 The sum of numbers opposite is 2

4.1.4 The full set of opposite numbers in colour

4.1.5 Prime numbers have stubbornly resisted attempts to reveal any meaningful order, hence their use in codes

4.1.6 The position of Primes on the One o' Clock ray

4.1.7 The array of reduced Primes shows a constant 1,7,4 repeat ...... after [-1]. [see digits clock] And a repeat of 174.471,174.471,etc. for the primes! [K.A. after Plichta see 4.1.5].

4.2 Clocks and Series - The use of clocks to model series generates some further insights

4.2.1 Sample Clocks - The digits 1 - 9 around faces of 3, 6, 9, 12, 15, 21 and 24 hour clocks

4.2.2 A 24 hr. clock array, or 3x octave array of the nos. 1 - 24, 25 - 48, 49 - 72,etc.,all reduced to show the 147, 258 and 369 groupings

4.2.3 A 24 hr. clock array or 3x octave array of the nos. 1 - 24, 25 - 48,49 - 72,etc.all reduced to show the 147 group

4.2.4 A 24 hr. clock array or 3x octave array of the nos. 1 - 24, 25 - 48,49 - 72,etc.all reduced to show the 258 group

4.2.5 A 24 hr. clock array or 3x octave array of the nos. 1 - 24, 25 - 48,49 - 72,etc.all reduced to show the 369 group

4.2.6 The Digits to the powers of 1 - 9, as an array on 24 hour clock

4.2.7 The Multiplication Tables [reduced] as an array on the 24 hour clock

4.2.8 The Fibonacci Series [1 - 4] as an array on the 24 hour clock

4.2.9 The pattern of 1, 4 and 7 in the Fibonacci Series as an array on the 24 hour clock

4.2.10 The pattern of 2, 5 and 8 in the Fibonacci Series as an array on the 24 hour clock

4.2.11 The pattern of 3, 6 and 9 in the Fibonacci Series as an array on the 24 hour clock

4.2.12 The pattern of 1 and 8 in the Fibonacci Series as an array on the 24 hour clock

4.2.13 The pattern of 2 and 7 in the Fibonacci Series as an array on the 24 hour clock

4.2.14 The pattern of 3 and 6 in the Fibonacci Series as an array on the 24 hour clock

4.2.15 The pattern of 4 and 5 in the Fibonacci Series as an array on the 24 hour clock

4.2.16 The Albarn Series [1 - 4] as an array on the 24 hour clock

4.2.17 The pattern of 1 and 8 in the Albarn Series as an array on the 24 hour clock

4.2.17a The Albarn Series on the 9 hour clock with 1s and 8s joined

4.2.18 The pattern of 2 and 7 in the Albarn Series as an array on the 24 hour clock

4.2.18a The Albarn Series on the 9 hour clock with 2s and 7s joined

4.2.19 The pattern of 3 and 6 in the Albarn Series as an array on the 24 hour clock

4.2.19aThe Albarn Series on the 9 hour clock with 3s and 6s joined

4.2.20 The pattern of 4 and 5 in the Albarn Series as an array on the 24 hour clock

4.2.20a The Albarn Series on the 9 hour clock with 4s and 5s joined

4.2.21 The pattern of 1, 4 and 7 in the Albarn Seriesas an array on the 24 hour clock

4.2.22 The pattern of 2, 5 and 8 in the Albarn Series as an array on the 24 hour clock

4.2.23 The pattern of 3, 6 and 9 in the Albarn Series as an array on the 24 hour clock

4.2.24 The digits 1 - 4 connected on the Albarn Series as a string array on the 24 hour clock

4.2.25 The digits 1 - 4 connected on the Fibonacci Series as a string array on the 24 hour clock

4.2.26 Albarn and Fibonacci series as strings compared

4.2.27 More examples of strings

4.3 Bar Charts [an introduction]Manipulation of colour coded bar charts of series etc. produces diagrams which are later used to generate images and sounds

4.3.1 Series including the Fibonacci and Albarn Series and their parts are then translated into bar charts in which each bar is rotated Firstly, by 90degs; Secondly, placed in order to form a spiral [90degs] which either folds into itself [full series] or if the 9s are omitted, creates a spiralling linear pattern; Thirdly, to form spirals with each successive bar rotated at another angle e.g. 60degs [see later sections]

4.3.2 A stage one bar chart and rotation using the Tetrahedral Series [after Buckminster Fuller]

4.3.3 A stage two bar chart and rotation using the Tetrahedral Series [after Buckminster Fuller]

4.3.4 A stage three bar chart, rotation and spiral rotation using the Tetrahedral Series [after Buckminster Fuller]

4.3.5 The M [multiplication] Series minus 3, 6 and 9 is tested

4.3.6 The M [multiplication] Series minus 3, 6 and 9 is tested with spiral rotation

4.3.7 Series derived from Nuclear Sphere packing is also explored

4.3.8 A set of spiral rotations placed on the nine colours used to code the digits 1 - 9

4.4 Reduced Fibonacci Series [and as bar charts]

4.4.1 Fibonacci Series - reduced,bar chart+reflection and each bar rotated through 90 degrees

4.4.2 Alternate numbers of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.4.3 Every third number of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.4.4 Every fourth number of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.4.5 Every fifth number of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.4.6 Every sixth number of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degreesĘ

4.4.7 Every seventh number of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.4.8 Every eighth number of the Fibonacci Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.4.9 The No.1s from each of the eight series are compared

4.4.10 The No. 2s from each of the eight series are compared

4.4.11 The No. 3s from each of the eight series are compared

4.4.12 The No. 4s from each of the eight series are compared

4.5 Reduced Albarn Series [as bar charts]

4.5.2 Alternate numbers of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.3 Every third number of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.4 Every fourth number of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.5 Every fifth number of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.6 Every sixth number of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.7 Every seventh number of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.8 Every eighth number of the Albarn Series - reduced,reassembled,bar chart+reflection and each bar rotated through 90 degrees

4.5.9 The No.1s from each of the eight series are compared

4.5.10 The No. 2s from each of the eight series are compared

4.5.11 The No. 3s from each of the eight series are compared

4.5.12 The No. 4s from each of the eight series are compared

4.5.13 Full Albarn Series followed by the series minus 147, then minus 258 and finally minus 369

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