You are an autistic, lonely, young sociopathic man, probably with multitude of other mental illnesses, browsing soyjak.party right now.

Broke my toenail in to by slamming it into the sitting room chair while playing with my dog; now it's (my toe) bleeding like hell.

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So i just found this thing,

Ok so lets just say you can only use the functions a(x) = 2x and b(x) = 2x-1 with x being any natural number,
And lets just say that you have to get the result of one of these 2 functions being applied to a number y, like
y>a(y_1)>y_1>b(y_2)>y_2>…a(y_n)>y_n>….
(The greater than are supposed to be arrows if the symbol change becuase obsessed formatting)
so, The minimum iterations for a number y to get to 1 is floor(log_4(y)) (things such as a/b(n) are ignored)
Example:
77>b(39)>39>b(20)>20>a(10)>10>a(5)>5>b(3)>3>b(2)>2>a(1)>1>a(1)>…
77>39>20>10>5>3>2>1>1….
What is this type of iterative function thing called doelbeit , has there been ANY paper on things like these (Collatz doesn't count)?
>OP why didn't you extend it to the rationals and integers?
For rationals It either Leads to either y diverging to infinity or converging to 0 for the example i gave,
And for integers the amount of steps is the same for negatives or something,
>OP what happens if i have a lot of possible functions to use
Either turns into a chaotic mess (like dynamical systems) or something similiar to what i posted (that is trivial btw)
>Have you tried doing things with complex numbers,irrationals,primes etc… Yet?
Not yet
Thoughts?

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I don’t watch a lot of tranime but I am enjoying this cardcaptor sakura. I started listening to one of the songs from the show and that got me to want to explore the show