i found a interesting pattern in the fibbonachi sequences one digit,when graphed with the next ones digit.any suggestions as to why it looks like this?
tip:move m to the end
What is the rule for sequence of points?
(0,1),(1,1),(1,2),(2,3),(3,5),(5,8),(8,3),(3,1),(1,4),(4,5),(5,9),(9,4),(4,3)
its the fibbonachi sequence but only the ones digits
(a,b)->(b,a+b)->(a+b,(a+b)+b)
ah ok, only the last digit in the fibonacci numbers … I get it …
let me try to understand why they do that …
so, the sequence can be easily generated by applying mod10 to the standard Fibnoacci sequence …
https://www.desmos.com/calculator/yzxjqkejdc
I’m still looking for a simple explanation for the pattern …
this may help to think about it:
https://www.desmos.com/geometry/llvuplhgda
Of course the slope of the points (f(n), f(n+1)) tends to the golden ratio …
wow i have like 0 idea how you figure this stuff out but good job (guzman)
maybe its about the slope of the golden ratio
Well, you would get some repetitive pattern also with other slopes …
the idea is that the line wraps around the square and gives rise to a pattern … but the details are not clear to me.
It’s like drawing a line on the surface of a torus. But we are only plotting some points of the line and they get increasingly sparser.
Also, observe that the sequence repeats itself after 60 elements …
Also, I noticed that finding the distance between (f(n), f(n+1)) and (f(n+1), f(n+2)), then applying an exponential regression to it results in y=0.32492*1.61803^x:
that one is actually easy to explain …
consider that you can get the fibonacci numbers by this explicit formula:
https://www.desmos.com/calculator/blzpqyx1ry
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yes the fibbonachi pattern is my dream college
this has “spiraled” out of control
just realized: the pattern actually when sideways, then put in in morse code spells out “gullible”
dude stop delete that,lets get back on track
i have no clue, and i dont think anybody else does
TLDR;
we dont know
Oh dear I’m so gullible!
yall,so i put the sequence in desmos and asked for a linear equation ,and it gave me one thats
has a common denominator of 37.idk if its helpfull,just saying