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Versor Algebra, Geometric Algebra, and Base Number System Patterns

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  • Versor Algebra, Geometric Algebra, and Base Number System Patterns

    Base Number Patterns 2-64 for multiplication by 2-9:

    The different color paths are the different patterns present in the base number system, the more colors present, the more unique patterns within that base number system. The patterns work like Marko Rodins base 10 number system patterns. The gif shows all the patterns for the multiplication operations of *2 to *9 for base numbers 2-64. I figured out this discovery after watching Rodins vortex math videos. His number patterns only apply to the base 10 number system, my base number pattern algorithm applies to ALL base number systems. I only show base number system patterns for base 2 (binary) to base 64 because all ascii alpha-numeric symbols only account for base 2-base 61 (then I added 3, I believe they were ^,|, and & to make it a even 64), but my algorithm can get the patterns for ANY base number system it just gets ugly looking when you can no longer use a single symbol to represent the base number.

    Some things I discovered by doing this were that every base number system has unique patterns. The number of unique base number patterns for even base number systems does not exceed 8(iirc) and the number of unique base number patterns for odd base number systems does not exceed the odd base number(so base 61 has less than 61 patterns). Some things I discovered since making the gif above are that the number '1' could be placed in the center to represent the ancient greek monad and/or to represent an electrical engineering copper wire. When I imagine each pattern operating independently and as a vortex around a center point (copper wire/monad) the entire concept of polyphase electrical systems becomes much easier to visualize. I also suspect these patterns have something to do with the basis of all elements...The yellow balls are the location in time, a physicist might call them the 'electron cloud valence levels' but physicists have invented nothing, ever, in history, soooo who cares what any of them think.

    IMO Eric Dollard's book 'Versor Algebra' could further simplify greater than 2nd order differential equation algebra by utilizing base number system patterns like shown. I believe Dollards book 'Versor Algebra' only scratches the surface for what is possible by using 'operators' to represent imaginary numbers within electrical phase calculations. I suspect the matrix math and complicated series mathematics can be completely abstracted out by the use of different base number system patterns. For the exact base number pattern tables email me, pm me, or ask me in the comments.
    Last edited by Spells Of Truth; 09-05-2019, 07:35 PM. Reason: Irrelevant extra info

  • #2
    1 = 1 2 = 2
    3 = 3 4 = 4
    5 = 5 6 = 6
    7 = 7 8 = 8
    9 = 9 a = 10
    b = 11 c = 12
    d = 13 e = 14
    f = 15 g = 16
    h = 17 i = 18
    j = 19 k = 20
    l = 21 m = 22
    n = 23 o = 24
    p = 25 q = 26
    r = 27 s = 28
    t = 29 u = 30
    v = 31 w = 32
    x = 33 y = 34
    z = 35 A = 36
    B = 37 C = 38
    D = 39 E = 40
    F = 41 G = 42
    H = 43 I = 44
    J = 45 K = 46
    L = 47 M = 48
    N = 49 O = 50
    P = 51 Q = 52
    R = 53 S = 54
    T = 55 U = 56
    V = 57 W = 58
    X = 59 Y = 60
    Z = 61 ^ = 62
    | = 63 & = 64

    Marko Rodin discovered universal patterns within the base 10 number system. He did so by reducing calculations to a single base 10 symbol. The example usually given by Rodin and his 'disciples' is the concept of 'doubling' which refers to doubling numbers and reducing them to a single symbol if they are larger than a single symbol. The largest single symbol in the base 10 number system according to modern number systems is the symbol '9'. To determine the *2 multiplication pattern you would start at 1 and *2 (1*2=2) then *2 (2*2=4) then *2 (4*2=8) then *2 (8*2=16 and since 16 is not a single digit symbol, it is reduced to one symbol through addition of 1 and 6 which results in 7) then *2 (7*2=14, 1+4=5 but lets say we didn't convert the last calculation and still had the number 16, so it becomes 16*2=32, 3+2=5, it results in 5 regardless if the previous calc was reduced or not) then *2 (5*2=10, 1+0=1 and the cycle repeats). Then the same process is repeated starting from the number 2(which results in the same repeating pattern), then starting with the number 3. 3*2=6, 6*2=12, 1+2=3, 3*2=6, 6*2=12, 1+2=3..... That pattern repeats forever. Then the pattern repeats until the operation 9*2 which always reduces into a 9.

    The base 10 number system has exactly 3 separate repeating reduction patterns when continuously multiplied by 2, they are 124875, 36, and 9. This occurs for multiplication by 3,4,5,6,7,8,9 etc usually up to the largest single symbol base number so for base 10 system the largest single symbol base number is 9, therefore a unique number of patterns are present for multiplication all the way up to 9 for all base 10 number systems. This discovery by Rodin was groundbreaking for its simplicity and despite being looked down upon by most scum 'academics', 'scholars', and 'intellectuals', was legitimately useful and influential in computer gaming graphics engines(which imo is the most math intensive subject in existence). Most 'scholars','academics' and 'intellectuals' agreed with Rodins methods but because Rodin is of 'common birth', aka he didn't get a piece of paper signed by a modern cattle farm aka university he is considered lesser by the geniuses that got 150,000 in debt to get a piece of paper that basically tells everyone else that they are docile 'ngiger cattle' dumb enough that they will believe anything they are told without question. My discovery expands on Rodins to show that the series and number of patterns he discovered for base 10 number systems are unique and present for every base number system not just base 10. Base 12 number system has 2 repeating patterns of reduction for the *2 operation and they are 12485a9736, and b(11), base 10 has 3 patterns for the *2 operation(see above). Here is a full list of all the unique base number patterns for the *2 operation up to base 63:
    base:2 operation:*2 pattern:['1']
    base:3 operation:*2 pattern:['12', '2']
    base:4 operation:*2 pattern:['12', '3']
    base:5 operation:*2 pattern:['124', '4']
    base:6 operation:*2 pattern:['1234', '5']
    base:7 operation:*2 pattern:['124', '24', '36', '6']
    base:8 operation:*2 pattern:['124', '356', '7']
    base:9 operation:*2 pattern:['1248', '2458', '3468', '8']
    base:10 operation:*2 pattern:['124578', '36', '9']*********************RODIN************************ ************
    base:11 operation:*2 pattern:['12468', '2468', '5a', 'a']
    base:12 operation:*2 pattern:['123456789a', 'b']
    base:13 operation:*2 pattern:['1248', '2478', '36c', '48', '48a', '69c', '6c', 'c']
    base:14 operation:*2 pattern:['123456789abc', 'd']
    base:15 operation:*2 pattern:['1248', '248', '248b', '36ac', '56ac', '6ac', '7e', 'e']
    base:16 operation:*2 pattern:['1248', '369c', '5a', '7bde', 'f']
    base:17 operation:*2 pattern:['1248g', '2489g', '368cg', '48adg', '48g', '68bcg', '68cg', '78ceg', 'g']
    base:18 operation:*2 pattern:['12489dfg', '3567abce', 'h']
    base:19 operation:*2 pattern:['1248aeg', '2478aeg', '248adeg', '248aeg', '36c', '6c', '6cf', '9i', 'i']
    base:20 operation:*2 pattern:['123456789abcdefghi', 'j']
    base:21 operation:*2 pattern:['1248cg', '248bcg', '3468cg', '468cg', '48cg', '5ak', 'afk', 'ak', 'k']
    base:22 operation:*2 pattern:['1248bg', '36c', '5adhjk', '7e', '9fi', 'l']
    base:23 operation:*2 pattern:['12468acegik', '2468acegik', 'bm', 'm']
    base:24 operation:*2 pattern:['1234689cdgi', '57abefhjklm', 'n']
    base:25 operation:*2 pattern:['1248g', '248dg', '36co', '478eg', '48egj', '48g', '58agk', '6cfo', '6co', '8agk', '8g', '8gkm', '9cio', 'cilo', 'cio', 'co', 'o']
    base:26 operation:*2 pattern:['12346789bcdeghijlmno', '5afk', 'p']
    base:27 operation:*2 pattern:['12468acegikmo', '2468acegikmo', 'dq', 'q']
    base:28 operation:*2 pattern:['124578abdeghjkmnpq', '36cflo', '9i', 'r']
    base:29 operation:*2 pattern:['1248g', '248fg', '36cko', '48bgm', '48g', '48gi', '48gm', '48gmp', '5acko', '6chko', '6cko', '7es', 'acjko', 'acko', 'cko', 'ckoq', 'els', 'es', 's']
    base:30 operation:*2 pattern:['123456789abcdefghijklmnopqrs', 't']
    base:31 operation:*2 pattern:['1248g', '248g', '248gj', '248gn', '36cio', '5ak', '69cio', '6cilo', '6cio', '6cior', '7emqs', 'ak', 'akp', 'bemqs', 'demqs', 'emqs', 'fu', 'u']
    base:32 operation:*2 pattern:['1248g', '36cho', '59aik', '7ejps', 'bdlmq', 'fnrtu', 'v']
    base:33 operation:*2 pattern:['1248gw', '248ghw', '36cgow', '489giw', '48gipw', '48gw', '58agkw', '6cgjow', '6cgow', '7egosw', '8dgkqw', '8gkqtw', '8gkw', '8gw', 'bcgmow', 'cgmorw', 'cgmow', 'egnosw', 'egosw', 'fgosuw', 'w']
    base:34 operation:*2 pattern:['1248ghptvw', '369cfiloru', '57adejknqs', 'bm', 'x']
    base:35 operation:*2 pattern:['1248giquw', '248dgiquw', '248fgiquw', '248gilquw', '248gipquw', '248giquw', '36acekmos', '56acekmos', '6acekmors', '6acekmos', '6acekmosv', 'hy', 'y']
    base:36 operation:*2 pattern:['12489bgimntw', '36cdhjoqrvxy', '5ak', '7els', 'fpu', 'z']
    base:37 operation:*2 pattern:['1248gksw', '248gjksw', '36co', '478egksw', '48agksw', '48dgkqsw', '48egkpsw', '48gkmsw', '48gkqsvw', '48gksw', '48gkswy', '6clo', '6co', '9Ai', 'A', 'Ai', 'Air', 'cfou', 'co', 'cou', 'coux']
    base:38 operation:*2 pattern:['123456789Aabcdefghijklmnopqrstuvwxyz', 'B']
    base:39 operation:*2 pattern:['12468Aacegikmoqsuwy', '2468Aacegikmoqsuwy', 'C', 'Cj']
    base:40 operation:*2 pattern:['12458abgkmpw', '369Acfilorux', '7BCehjnstvyz', 'D', 'dq']
    base:41 operation:*2 pattern:['1248gow', '248glow', '368cgow', '48bgmow', '48gmovw', '48gow', '5Eak', '68cgnow', '68cgow', '78egosw', '8Agow', '8cgoqw', '8gow', 'E', 'Eak', 'Eakp', 'Efku', 'Ek', 'Eku', 'Ekuz']
    base:42 operation:*2 pattern:['124589ABDEagiklnpvwx', '367Cbcdefhjmoqrstuyz', 'F']
    base:43 operation:*2 pattern:['1248gmw', '248Bgmw', '248bgmw', '248gmpw', '248gmtw', '248gmw', '36co', '5CEakqy', '6co', '6cor', '6cox', '7es', '9Aiu', 'ADiu', 'Afiu', 'Aiu', 'CEadkqy', 'CEahkqy', 'CEajkqy', 'CEakqvy', 'CEakqy', 'G', 'Gl', 'es', 'esz']
    base:44 operation:*2 pattern:['1248DFGbglmrwz', '356BCEacjknovx', '79Adefhipqstuy', 'H']
    base:45 operation:*2 pattern:['1248AEcgkosw', '248AEcgknosw', '3468AEcgkosw', '48AEcgkosw', '48AEcgkoswy', 'I', 'Ibm', 'Im', 'Imx']
    base:46 operation:*2 pattern:['1248Cghjnvwy', '36co', '5Eakpz', '7BFHIbdemqst', '9Air', 'DGlx', 'J', 'fu']
    base:47 operation:*2 pattern:['12468Acgioqw', '2468ADcgioqw', '2468AFcgioqw', '2468Acgioqtw', '2468Acgioqvw', '2468Acgioqw', '2468Acgioqwz', '5CEGIaekmsuy', '7CEGIaekmsuy', 'BCEGIaekmsuy', 'CEGIaehkmsuy', 'CEGIaejkmsuy', 'CEGIaekmsuxy', 'CEGIaekmsuy', 'K', 'Kn']
    base:48 operation:*2 pattern:['12346789ABGceghiloprswy', '5CDEFHIJKabdfjkmnqtuvxz', 'L']
    base:49 operation:*2 pattern:['1248gw', '248gpw', '36Mco', '48Bgqw', '48dgqw', '48gw', '5Eagkw', '6Mco', '6Mcor', '78egsw', '8CHgsw', '8Cgjsw', '8egsvw', '8gsw', '9AMio', 'AGJMo', 'AGMlo', 'AGMo', 'AMio', 'AMiox', 'AMo', 'DMcou', 'EIKgw', 'EIgmw', 'EIgw', 'Eagktw', 'Eagkw', 'Eghkwy', 'Egkw', 'Egkwy', 'Egw', 'M', 'Mcfou', 'Mco', 'Mcou', 'Mo', 'gw']
    base:50 operation:*2 pattern:['12489ABDHIKbfgimnptuw', '356CEFJLMacdhjkoqrvxy', '7es', 'Glz', 'N']
    base:51 operation:*2 pattern:['12468ACGIKMcegimoqswy', '2468ACFGIKMcegimoqswy', '2468ACGIKMbcegimoqswy', '2468ACGIKMcegilmoqswy', '2468ACGIKMcegimoqsvwy', '2468ACGIKMcegimoqswy', '5Eaku', 'EJaku', 'Eafku', 'Eaku', 'Eakuz', 'O', 'Op']
    base:52 operation:*2 pattern:['1248dgqw', '36DJMcor', '57Eaekst', '9AGfilux', 'BFIKbmnv', 'CHLNOjpz', 'P', 'hy']
    base:53 operation:*2 pattern:['1248AEIMcgkosw', '248AEIMcgkorsw', '3468AEIMcgkosw', '48AEIMcegkosw', '48AEIMcgkosw', 'DQq', 'Q', 'Qdq', 'Qq']
    base:54 operation:*2 pattern:['123456789ABCDEFGHIJKLMNOPQabcdefghijklmnopqrstuvw xyz', 'R']
    base:55 operation:*2 pattern:['1248CEIKOQaegkmqswy', '2478CEIKOQaegkmqswy', '248BCEIKOQaegkmqswy', '248CEHIKOQaegkmqswy', '248CEIKNOQaegkmqswy', '248CEIKOQadegkmqswy', '248CEIKOQaegjkmqswy', '248CEIKOQaegkmpqswy', '248CEIKOQaegkmqsvwy', '248CEIKOQaegkmqswy', '36GMcou', '6DGMcou', '6GMPcou', '6GMcfou', '6GMclou', '6GMcou', '6GMcoux', '9Ai', 'AJi', 'Ai', 'S', 'Sr']
    base:56 operation:*2 pattern:['124789AHNQdeghiqsvwy', '36BCDFGKLMPRScjlnort', '5EJOafkpuz', 'Ibmx', 'T']
    base:57 operation:*2 pattern:['1248gw', '248gtw', '36EMco', '48Hguw', '48fguw', '48gw', '5EMako', '6EMco', '6EMcov', '7Ues', '8AKgw', '8Agiw', '8Agw', '8DIgmw', '8IORgw', '8IOgpw', '8IOgw', '8Ibgmw', '8Igmw', '8gw', 'CELMko', 'CEMjko', 'CEMko', 'EJMcoy', 'EMQSo', 'EMQo', 'EMQoq', 'EMako', 'EMakox', 'EMchoy', 'EMco', 'EMo', 'GNUs', 'GUls', 'GUs', 'U', 'Ues', 'Uesz', 'Us']
    base:58 operation:*2 pattern:['12478FHNORTUegpstw', '369ADGJMPScfilorux', '5BEIKLQabdhkmnqvyz', 'Cj', 'V']
    base:59 operation:*2 pattern:['12468ACEGIKMOQSUacegikmoqsuwy', '2468ACEGIKMOQSUacegikmoqsuwy', 'W', 'Wt']
    base:60 operation:*2 pattern:['123456789ABCDEFGHIJKLMNOPQRSTUVWabcdefghijklmnopq rstuvwxyz', 'X']
    base:61 operation:*2 pattern:['1248gw', '248gvw', '36AMco', '48CNgw', '48Cgjw', '48Cgw', '48KRgw', '48Kgnw', '48Kgw', '48gw', '48gwy', '5Eak', '6AMco', '6AMcox', '7IQUes', '9AMcio', 'ADMcio', 'AGMPco', 'AGMclo', 'AGMco', 'AMSVco', 'AMSco', 'AMScor', 'AMcio', 'AMco', 'BIQUes', 'EOTk', 'EOk', 'EOkp', 'Eak', 'Eakz', 'Ek', 'FIQUms', 'HIQUqs', 'IQUWs', 'IQUbms', 'IQUdqs', 'IQUms', 'IQUqs', 'IQUs', 'JYu', 'Y', 'Yfu', 'Yu']
    base:62 operation:*2 pattern:['123456789ABCDEFGHIJKLMNOPQRSTUVWXYabcdefghijklmno pqrstuvwxyz', 'Z']
    base:63 operation:*2 pattern:['1248gw', '248Dgw', '248Lgw', '248gw', '248gwz', '36Mcoy', '5AEaik', '6BMcoy', '6HMcoy', '6MTcoy', '6Mchoy', '6Mcoy', '7COUes', '9AEaik', 'AENaik', 'AEPaik', 'AEaik', 'CJOUes', 'COUXes', 'COUejs', 'COUeps', 'COUes', 'GIQVmq', 'GIQbmq', 'GIQdmq', 'GIQlmq', 'GIQmq', 'KSWYfu', 'KSWYnu', 'KSWYru', 'KSWYtu', 'KSWYu', '^', '^v']

    Here are the patterns for *2-*9, /1-/9, and +1/+9: