Exponentially Slimy Programming: Stacking Minecraft Slimes
MATL, 77 76 74 bytes
:&quot;')^.,9&amp;Xze`}+.E=p'F3ZaQ8e@qWt3$Y&quot;G@-W1X&quot;]&amp;h[OOO;11 17E]5*29 7U24hhE&amp;vEYG

The code works in this commit, which is earlier than the challenge.
You can try it in MATL online. This interpreter is still experimental. If it doesn't work, try refreshing the page and pressing &quot;Run&quot; again.
Here's an example run in the offline interpreter:

Explanation
:                     % Input N implicitly. Generate range [1 2 ... N]
&quot;                     % For each k in [1 2 ... N]
  ')^.,9&amp;Xze`}+.E=p'  %   Compressed string
  F3Za                %   Decompress with target alphabet [0 1 2]
  Q                   %   Add 1
  8e                  %   Reshape into 8×8 array containing values 1, 2, 3
  @qW                 %   Push 2 raised to k-1
  t                   %   Duplicate
  3$Y&quot;                %   Repelem: interpolate image by factor 2 raised to k-1
  G@-W                %   Push 2 raised to N-k
  1X&quot;                 %   Repmat: repeat the array vertically. Gives a vertical strip
                      %   of repeated subimages
]                     % End for each
&amp;h                    % Concatenate all vertical strips horizontally. This gives a big
                      % 2D array containing 1, 2, 3, which represent the three colors
[OOO;11 17E]5*        % Push array [0 0 0; 11 17 9] and multiply by 5
29 7U24hhE            % Push array [29 49 24] and multiply by 2
&amp;vE                   % Concatenate the two arrays vertically and multiply by 2.
                      % This gives the colormap [0 0 0; 110 170 90; 116 196 96]
YG                    % Take the array and the colormap and display as an image