Wolfram Cloud Document

To celebrate the Fibonacci Day 2023, lets compute some numbers...

Getting a definition from a prompt chat robot:

In[]:=

ChatEvaluate[ChatObject[],"Define Fibonacci number"]

Out[]=

ChatObject

	Define Fibonacci number
	A Fibonacci number is a number in the sequence created by adding the two previous numbers together to form the next number. The sequence starts with 0 and 1, so the Fibonacci sequence is: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. Each number in the sequence is called a Fibonacci number.

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Fibonacci Day meme, unknown author:

https://www.facebook.com/groups/2692404370981189/permalink/3706309316257351/

List the first 100 Fibonacci numbers, the Fibonacci integer numbers can get large very fast:

In[]:=

fibonacci100=Table[Fibonacci[n],{n,0,100,1}]

Out[]=

{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,1134903170,1836311903,2971215073,4807526976,7778742049,12586269025,20365011074,32951280099,53316291173,86267571272,139583862445,225851433717,365435296162,591286729879,956722026041,1548008755920,2504730781961,4052739537881,6557470319842,10610209857723,17167680177565,27777890035288,44945570212853,72723460248141,117669030460994,190392490709135,308061521170129,498454011879264,806515533049393,1304969544928657,2111485077978050,3416454622906707,5527939700884757,8944394323791464,14472334024676221,23416728348467685,37889062373143906,61305790721611591,99194853094755497,160500643816367088,259695496911122585,420196140727489673,679891637638612258,1100087778366101931,1779979416004714189,2880067194370816120,4660046610375530309,7540113804746346429,12200160415121876738,19740274219868223167,31940434634990099905,51680708854858323072,83621143489848422977,135301852344706746049,218922995834555169026,354224848179261915075}

List plot the values:

In[]:=

ListPlot[fibonacci100,ColorFunction->Hue]

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List plot the values in log:

In[]:=

ListLogPlot[fibonacci100,ColorFunction->Hue]

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Calculate and visualize the gabs between Fibonacci digits:

In[]:=

{Most[#],Rest[#]}&[fibonacci100]{#[[1]]->#[[2]],#[[2]]-#[[1]]}&/@Partition[Riffle[%[[1]],%[[2]]],2]ListPlot[Last/@%,ColorFunction->"Rainbow",ImageSize->Medium]->ListLogPlot[Last/@%,ColorFunction->"Rainbow",ImageSize->Medium](*ListPlot[%,ColorFunction->"Rainbow"]->ListLogPlot[%%,ColorFunction->"Rainbow"]*)

Out[]=

{{0,1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,1134903170,1836311903,2971215073,4807526976,7778742049,12586269025,20365011074,32951280099,53316291173,86267571272,139583862445,225851433717,365435296162,591286729879,956722026041,1548008755920,2504730781961,4052739537881,6557470319842,10610209857723,17167680177565,27777890035288,44945570212853,72723460248141,117669030460994,190392490709135,308061521170129,498454011879264,806515533049393,1304969544928657,2111485077978050,3416454622906707,5527939700884757,8944394323791464,14472334024676221,23416728348467685,37889062373143906,61305790721611591,99194853094755497,160500643816367088,259695496911122585,420196140727489673,679891637638612258,1100087778366101931,1779979416004714189,2880067194370816120,4660046610375530309,7540113804746346429,12200160415121876738,19740274219868223167,31940434634990099905,51680708854858323072,83621143489848422977,135301852344706746049,218922995834555169026},{1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4181,6765,10946,17711,28657,46368,75025,121393,196418,317811,514229,832040,1346269,2178309,3524578,5702887,9227465,14930352,24157817,39088169,63245986,102334155,165580141,267914296,433494437,701408733,1134903170,1836311903,2971215073,4807526976,7778742049,12586269025,20365011074,32951280099,53316291173,86267571272,139583862445,225851433717,365435296162,591286729879,956722026041,1548008755920,2504730781961,4052739537881,6557470319842,10610209857723,17167680177565,27777890035288,44945570212853,72723460248141,117669030460994,190392490709135,308061521170129,498454011879264,806515533049393,1304969544928657,2111485077978050,3416454622906707,5527939700884757,8944394323791464,14472334024676221,23416728348467685,37889062373143906,61305790721611591,99194853094755497,160500643816367088,259695496911122585,420196140727489673,679891637638612258,1100087778366101931,1779979416004714189,2880067194370816120,4660046610375530309,7540113804746346429,12200160415121876738,19740274219868223167,31940434634990099905,51680708854858323072,83621143489848422977,135301852344706746049,218922995834555169026,354224848179261915075}}

Out[]=

{{01,1},{11,0},{12,1},{23,1},{35,2},{58,3},{813,5},{1321,8},{2134,13},{3455,21},{5589,34},{89144,55},{144233,89},{233377,144},{377610,233},{610987,377},{9871597,610},{15972584,987},{25844181,1597},{41816765,2584},{676510946,4181},{1094617711,6765},{1771128657,10946},{2865746368,17711},{4636875025,28657},{75025121393,46368},{121393196418,75025},{196418317811,121393},{317811514229,196418},{514229832040,317811},{8320401346269,514229},{13462692178309,832040},{21783093524578,1346269},{35245785702887,2178309},{57028879227465,3524578},{922746514930352,5702887},{1493035224157817,9227465},{2415781739088169,14930352},{3908816963245986,24157817},{63245986102334155,39088169},{102334155165580141,63245986},{165580141267914296,102334155},{267914296433494437,165580141},{433494437701408733,267914296},{7014087331134903170,433494437},{11349031701836311903,701408733},{18363119032971215073,1134903170},{29712150734807526976,1836311903},{48075269767778742049,2971215073},{777874204912586269025,4807526976},{1258626902520365011074,7778742049},{2036501107432951280099,12586269025},{3295128009953316291173,20365011074},{5331629117386267571272,32951280099},{86267571272139583862445,53316291173},{139583862445225851433717,86267571272},{225851433717365435296162,139583862445},{365435296162591286729879,225851433717},{591286729879956722026041,365435296162},{9567220260411548008755920,591286729879},{15480087559202504730781961,956722026041},{25047307819614052739537881,1548008755920},{40527395378816557470319842,2504730781961},{655747031984210610209857723,4052739537881},{1061020985772317167680177565,6557470319842},{1716768017756527777890035288,10610209857723},{2777789003528844945570212853,17167680177565},{4494557021285372723460248141,27777890035288},{72723460248141117669030460994,44945570212853},{117669030460994190392490709135,72723460248141},{190392490709135308061521170129,117669030460994},{308061521170129498454011879264,190392490709135},{498454011879264806515533049393,308061521170129},{8065155330493931304969544928657,498454011879264},{13049695449286572111485077978050,806515533049393},{21114850779780503416454622906707,1304969544928657},{34164546229067075527939700884757,2111485077978050},{55279397008847578944394323791464,3416454622906707},{894439432379146414472334024676221,5527939700884757},{1447233402467622123416728348467685,8944394323791464},{2341672834846768537889062373143906,14472334024676221},{3788906237314390661305790721611591,23416728348467685},{6130579072161159199194853094755497,37889062373143906},{99194853094755497160500643816367088,61305790721611591},{160500643816367088259695496911122585,99194853094755497},{259695496911122585420196140727489673,160500643816367088},{420196140727489673679891637638612258,259695496911122585},{6798916376386122581100087778366101931,420196140727489673},{11000877783661019311779979416004714189,679891637638612258},{17799794160047141892880067194370816120,1100087778366101931},{28800671943708161204660046610375530309,1779979416004714189},{46600466103755303097540113804746346429,2880067194370816120},{754011380474634642912200160415121876738,4660046610375530309},{1220016041512187673819740274219868223167,7540113804746346429},{1974027421986822316731940434634990099905,12200160415121876738},{3194043463499009990551680708854858323072,19740274219868223167},{5168070885485832307283621143489848422977,31940434634990099905},{83621143489848422977135301852344706746049,51680708854858323072},{135301852344706746049218922995834555169026,83621143489848422977},{218922995834555169026354224848179261915075,135301852344706746049}}

View the fourier of the 100 first digits of Fibonacci: absolute, complex and real values:

Visualize the wavelet scalogram from the 100 digits of Fibonacci numbers...

Break up the digits and get then in a simple list:

Visualize the first 100 Fibonacci numbers digits in a graph:

Visualize the first 100 Fibonacci number in a pie chart:

And in a bar chart too:

Visualize the 100 Fibonacci number as a binary...

Visualize the 100 Fibonacci number as a binary, just the odds...

Visualize the 100 Fibonacci number as a binary, just the even...

Visualize the 100 Fibonacci number as a binary, just the primes...

Visualize the 100 Fibonacci number as a binary, just the composite...

Visualize the 100 Fibonacci number as a binary, just the prime power...

With other creative data visualization of Fibonacci numbers you can build with Wolfram Language??

CITE THIS NOTEBOOK

Fibonacci Day 2023: Computing and visualizing the first 100 digits
by Daniel Carvalho
Wolfram Community, STAFF PICKS, November 23, 2023
https://community.wolfram.com/groups/-/m/t/3070628