Fibonacci Sequence: Back to Basics

Back to Basics




The Linear Algebra View of the Fibonacci Sequence | by Andrew Chamberlain, Ph.D. | Medium - https://medium.com/@andrew.chamberlain/the-linear-algebra-view-of-the-fibonacci-sequence-4e81f78935a3 Sent from my Galaxy

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Links Blogged: The Fibonacci Sequence, Spirals and The Golden Mean and More

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The Golden Ratio: How to derive it a+b/a=a/b=1.618.. How to Calculate the Golden Ratio - https://www.masterclass.com/articles/golden-ratio-explained#a-brief-history-of-the-golden-ratio  https://en.wikipedia.org/wiki/Golden_spiral : In geometry , a golden spiral is a logarithmic spiral whose growth factor is φ , the golden ratio . Graphically: https://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/GoldenSpiralLogarithmic_color_in.gif/440px-GoldenSpiralLogarithmic_color_in.gif   Fn = Fn-1 + Fn-2 where n>3 or n=3 http://jwilson.coe.uga.edu/EMT669/Student.Folders/Morris.Stephanie/EMT.669/Essay.3/Fibonacci.Essay.html Special feature of the Golden Number is it has a similar conjugate: Golden Ratio Conjugate: 0.618.. 1 / 0.618 = 1.618.. = 1 + 0.618   x2-x-1=0, x(x-1)=1, we get x=0 or x=1 unit circle 1.618 is one of the roots of x2-x-1=0  using formula x=-b+-sqrt..  https://www.tiger-algebra.com/drill/x2-x-1=0/   x2-x-1=0   x2-x...
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Interpretation of the Mandelbrot Set: Chaos is Mathematically Deterministic

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Chaos does not exist. The Mandelbrot set only gives the appearance of chaos when the spiral hits a deterministic number, in the above case, at iteration number 1019. Chaos is deterministically a function of iteration that has mathematically escaped out of the Mandelbrot set into the unstable area outside the Mandelbrot set.  The black area shows the Mandelbrot set while the series of green circles forms a stable spiral. In the picture, the spiral - which is a stable formation inside the Mandelbrot set - escapes out of the set at iteration 1019.  That is to say, the spiral has become unstable when it reaches 1019 iterations. Reference: https://www.youtube.com/watch?v=7MotVcGvFMg Addendum: The picture below shows the picture of the Mandelbrot set on a graph setting. Basic idea behind the cosmos is the unit circle which when iterated under x^2+x-1=0 gives rise to the Mandelbrot set.  Solutions to the equation have roots 0.16803 and -1.16803:  https://www.symbolab.com/...
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Spiral Source Code For the Beautiful Cosmos

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Both the universe and the blueprint that engenders its existence is rooted in the same single source. The universe is a geometrical phenomenon, not a physical phenomenon. In fact, physicality is an illusory manifestation of vibrating curved lines. Source Code of the Universe: The gorilla has been in the room for a very long time..     extracted from the matrix form..     The Fibonacci Matrix Equation engenders the infinite recurrence code 111011101110111011101110.. which is generated by repeating nibbles of 1110 from the coefficient matrix in the above matrix equation.   There exist correspondence between the universe and consciousness which is linked by the Fibonacci Sequence.    By adding up the source code above using the formula F n =F n-1 +F n-2  we generate Fibonacci numbers.. The Fibonacci numbers are generated by setting F0 = 0, F1 = 1, and then using the recursive formula Fn = Fn-1 + Fn-2 to get the rest. Thus the sequence begins...
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