Calculating the starting size of a length, when it grows per iteration and must remain within a limit

Calculating the starting size of a length, when it grows per iteration and
must remain within a limit

Ok so, obviously from the way I've worded my question; I'm no
mathematician. I'm currently experimenting with fractals, and this
specific question refers to the 'TSqare' fractal. (See bottom of question
for explanation).
Basically I want to calculate the size of the initial square, so the
resulting fractal of depth(n) never extends beyond the limit of the
drawing surface. I've tried to figure it out myself, but I'm getting no
where.
All I have figured out is the rate the square grows:
Assuming an initial size of 100, total length of fractal is as follows
Depth(0) = 100
Depth(1) = 150
Depth(2) = 175

Unfortunately I can't even figure out the formula for that, even though
the pattern is obvious. D:
TSquare Definition: An initial square S0 is drawn with size x2. Each
iteration 4 Squares half the size of the original (x2/2) are drawn with
their centers on the 4 vertices of the square before it. See
http://www.smokycogs.com/blog/t-square-fractals/ for more details.