The Golden Fibonacci Sequence

The Golden String, the infinite Fibonacci Word, or the Rabbit Sequence is a fractal sequence of 1's and 0's that is closely related to the golden ratio (phi) and the Fibonacci numbers. It can be generated by starting with the binary strings: S0='0', and S1='1'. Then
S2 = (s1 & s0) = '10'
S3 = (s2 & s1) = '101'
S4 = (s3 & s2) = '10110'
...
This animation depicts 27 iterations of the construction. Each successive Sn is displayed per frame. The least signifigant bit is closest to the center. Blue pixels correspond to bits that are equal to 0. Any blue pixels that form continuous horizontal or vertical lines are shaded yellow. The binary expansion of the sequence has been proven transcendental and is nonperiodic. Even so, a striking spiral structure can be observed. Music by: cloudtalk Austin, Tx

Category:

Science & Technology

Tags:

• golden
• ratio
• string
• number
• theory
• Fibonacci
• numbers
• rabbit
• sequence
• mathemtaics
• binary
• fractal
• ulam
• spiral
• animation
• visualization
• cloudtalk
• math
• mathart
• Austin
• Texas
• paske

[TechXMarine]

@snafutube he never stats that god exists in anyway shape or form

this is just a quick demonstration of the sequence in no way relating to god (in this video anyway)

[nickharvey7]

unusual video!!

[hossrex]

@pxaialexi

Well done. You've found a subtle and innocent mistake, and your reaction was to be snotty about it. You're wonderful.

[pxaialexi]

@hossrex I never said that was addition. i was stating that 13 + 21 does NOT = 44

[hossrex]

@pxaialexi

Determining whether or not a number is odd or even isn't addition.

[pxaialexi]

@hossrex no, basic addition isnt something to be proud of.

[hossrex]

@pxaialexi

lol... a smart ass reply to a year old comment that wasn't anything deeper than an idle observation. Your mother must be so proud of you.

[pxaialexi]

@hossrex your doing it wrong...

[snafutube]

ok, this proves god exists? in what way exactly?