Make text triangle waves

05AB1E, 13 12 bytes

1 byte saved thanks to Erik the Outgolfer

[¹ð.ø²Lû¨×€,

Try it online!

Run locally if you want the lines displayed 1 at a time.

Explanation

[              # start infinite loop
 ¹ð.ø          # surround the first input by a space on each side
     ²Lû¨      # construct the range [1 ... n ... 2]
         ×     # replace each number in the range by that many instances of the string
          €    # for each string in the list
           ,   # print it on a separate line

Haskell, 68 62 bytes

t#n=mapM putStrLn[[1..n-abs m]>>' ':t++" "|m<-[1-n..n-2]]>>t#n

Try it online! Example usage: "somestring" # 5.

Edit: Saved 6 bytes thanks to @Ørjan Johansen!

Given for example n=4, [1-n..n-2] constructs the list [-3,-2,-1,0,1,2]. For each element m in this list, [1..n-abs m] is a list of length n minus the absolute value of m, thus we get lists of length 4-3, 4-2, 4-1, 4-0, 4-1 and 4-2, that is 1, 2, 3, 4, 3 and 2. For each of this numbers >>' ':t++" " concatenates as many times the given string t with a space added to back and front.

This yields a list of strings with the first triangle. mapM putStrLn prints each of the strings in the list on a new line, then the function # calls itself again with the same arguments and starts over.

Java 7, 128 129 128 125 bytes

+1 byte: Missed the padding after each character

-1 byte: Changed k==1 to k<2

-3 byes thanks to Kevin Cruijssen

void a(String s,int i){s=" "+s;for(int j=-1,k=1,l;;k+=j){for(l=0;l<k;)System.out.print(s+(++l<k?" ":"\n"));j=k==i|k<2?-j:j;}}

First post here so let me know if I'm doing something wrong. Any golfing help is much appreciated.

Try it online! Note: this times out after 60 seconds and then prints the results, the actual code continually prints infinitely

Ungolfed

void a(String s,int i){
    s= " " + s;

    for(int j=-1, k=1, l;; k+=j){
        for(l=0; l<k;)
            System.out.print(s+ (++l < k ? " " : "\n"));
        
        j = (k == i | k < 2) ? -j : j;
    }
}

Prepends a space to the input string then starts an infinite loop. For each iteration it prints the string k times and then prints a new line. k is then incremented / decremented based on the sign of j