Fibonacci Strings
December 13th, 2011 at 12:03:11 PM
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I don't know if these series of numbers have a correct mathematical name, but I dubbed them "Fibonacci Strings"...
0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0
0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0
0 5 5 0
1 3 4 7 1 8 9 7 6 3 9 2 1
2 6 8 4 2
In base 10 math, these are the digits found in the 1's place in a Fibonacci sequence. The bolded digits at the start/end of each string is where the it begins to repeat itself.
The BLACK string is the classic Fibonacci, starting with 0, 1. It has a period of 60 digits. Every 5th digit is 5, save for every 15th digit is a 0.
The BLUE string starts with 0, 2. It has a period of 20 digits. All digits are even, and every 5th digit is 0. If placed directly under the BLACK string and repeated, every BLUE digit is double that of the BLACK digit above (mod 10).
The RED string starts with 0, 5. It has a period of 3 digits. If placed directly under the BLACK string and repeated, the RED digit is "coded" to show if the BLACK digit above is even (RED zero) or odd (RED five).
The PURPLE string starts with 1, 3. It has a period of 12 digits. It seems to have no correlation to the BLACK string that I can see.
The GREEN string starts with 2, 6. It has a period of 4 digits. Like the relationship between the BLACK and BLUE strings, the GREEN digits are double that of the PURPLE digit above it.
Every two-digit pairing from 01-99 can be found exactly once, and it uses 104 digits total to do so.
Does anyone have any further information on these strings?
0 1 1 2 3 5 8 3 1 4 5 9 4 3 7 0 7 7 4 1 5 6 1 7 8 5 3 8 1 9 0 9 9 8 7 5 2 7 9 6 5 1 6 7 3 0 3 3 6 9 5 4 9 3 2 5 7 2 9 1 0
0 2 2 4 6 0 6 6 2 8 0 8 8 6 4 0 4 4 8 2 0
0 5 5 0
1 3 4 7 1 8 9 7 6 3 9 2 1
2 6 8 4 2
In base 10 math, these are the digits found in the 1's place in a Fibonacci sequence. The bolded digits at the start/end of each string is where the it begins to repeat itself.
The BLACK string is the classic Fibonacci, starting with 0, 1. It has a period of 60 digits. Every 5th digit is 5, save for every 15th digit is a 0.
The BLUE string starts with 0, 2. It has a period of 20 digits. All digits are even, and every 5th digit is 0. If placed directly under the BLACK string and repeated, every BLUE digit is double that of the BLACK digit above (mod 10).
The RED string starts with 0, 5. It has a period of 3 digits. If placed directly under the BLACK string and repeated, the RED digit is "coded" to show if the BLACK digit above is even (RED zero) or odd (RED five).
The PURPLE string starts with 1, 3. It has a period of 12 digits. It seems to have no correlation to the BLACK string that I can see.
The GREEN string starts with 2, 6. It has a period of 4 digits. Like the relationship between the BLACK and BLUE strings, the GREEN digits are double that of the PURPLE digit above it.
Every two-digit pairing from 01-99 can be found exactly once, and it uses 104 digits total to do so.
Does anyone have any further information on these strings?
-Dween!
December 13th, 2011 at 1:39:59 PM
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Quote: DweenDoes anyone have any further information on these strings?
Not really, but if you're a math nerd that also likes music you may think this is interesting:
http://en.wikipedia.org/wiki/Lateralus_%28song%29#Mathematical_significance
http://www.youtube.com/watch?v=EDlC7oG_2W4
Solo venimos, solo nos vamos. Y aqui nos juntamos, juntos que estamos.
