Length-encode a string

JavaScript (ES6), 61 bytes

f=(s,d=2)=>s?d>s.length?s[0]+f(s.slice(1),d-2):'*'+f(s,d*2):s

Recursive function that does the following:

• If d is less than or equal to remaining string length divided by 2:

  Append * to output and multiply d by 2

• Else:

  Shift the string and append to output, subtract 1 from d.

See it in action:

f=(s,d=2)=>s?d>s.length?s[0]+f(s.slice(1),d-2):'*'+f(s,d*2):s

input.oninput = e => output.innerHTML = f(input.value);

<input id="input" type="text"/>
<p id="output"></p>

Pyth, 29 27 (Noticed broken) 27 26 25 bytes

+*\*sKllzXJ-^2.EKlzz?J\*k

Explanation to come.

Test Suite

Pyth (36 27 bytes)

Thanks to Jakube for a 9 byte improvement! Currently not as good as muddyfish's answer, but whatever

KlzJ1VzWgKyJp\*=yJ)pN=tK=tJ

Test Suite

Translation to python:

                            | z=input() #occurs by default
Klz                         | K=len(z)
   J1                       | J=1
     Vz                     | for N in z:
       WgKyJ                |   while K >= J*2:
            p\*             |     print("*", end="")
               =yJ          |     J=J*2
                  )         |     #end inside while
                   pN       |   print(N, end="")
                     =tK    |   K=K-1
                        =tJ |   J=J-1