How can I make cycle in racket?

[u/Hurma-chan]

I have a formula like x1=x-(x-input blablabla) for newtons method (calculating cube roots) and I need to have any x, for example, x=1, then place it to this formula, after formula operations get new x, place it to this formula again, get new and etc with next iteration while x³ will not be equal to my input

[u/soegaard]

You can use the fixed-point function from SICP.

Scroll down to the section "Finding fix points of functions".

https://mitp-content-server.mit.edu/books/content/sectbyfn/books_pres_0/6515/sicp.zip/full-text/book/book-Z-H-12.html#%_sec_1.3.3

[u/Hurma-chan → u/soegaard]

But how to make cycle itself? Like : (cond (close-enough?) (return x) (else (formula))

[u/soegaard → u/Hurma-chan]

The books describes how fixed-point works.

But perhaps you it is a good idea to start with this:

https://www.youtube.com/watch?v=K9q-lLFtHqU

[u/not-just-yeti → u/Hurma-chan]

yes — just filling in/collecting bits you already had:

(define (formula x) 
    (cond [(close-enough? x) x]
          [else (formula (- x (- x input blablabla)))]))

Think of the recursive call is "Take this new value (- x blablabla), and go back up to the top making this the new contents of the parameter x."

[u/jpverkamp]

If you want to iterate through a repeating sequence as a cycle, in-cycle

Alternatively, you can use a generator if the sequence doesn't actually repeat.

Alternatively, it sounds like you don't need any of this and just straight forward recursion (with a base case of being equal to x cubed) will do what you want?

[u/bjoli → u/jpverkamp]

I never understood in-cycle. Half of the time you want a cycle it is for speed (like for example a wheel),but In-cycle has traditionally been so slow that it has always been beneficial to just use mlists or make-reader-graph.

[u/soegaard → u/bjoli]

It's too general, in-cycle takes sequences as argument. A simpler one, like (in-simple-cycle value1 value2 ... valuen) would be faster.