Rectangular pseudo-fractal
APL, 25 chars/bytes*

{⍉⍣⍵⊃{a,⍺⍴⍨⍴a←⍉⍪⍵}/⌽⍵↑⎕A}


Exploded view

{                   ⍵↑⎕A}   ⍝ take the first ⍵ letters
    ⊃{           }/⌽        ⍝ fold over them, using the first one as initial accum. value
            a←⍉⍪⍵           ⍝    ensure the accum. is a table, transpose it and call it 'a'
        ⍺⍴⍨⍴                ⍝    make a table as large as 'a' filled with the next letter
      a,                    ⍝    append it to the right of 'a' and loop as new accumulator
 ⍉⍣⍵                        ⍝ transpose the result as many times as the original ⍵ number


Examples

      {⍉⍣⍵⊃{a,⍺⍴⍨⍴a←⍉⍪⍵}/⌽⍵↑⎕A}¨⍳8
A AB  AB  ABDD  ABDD  ABDDFFFF  ABDDFFFF  ABDDFFFFHHHHHHHH
      CC  CCDD  CCDD  CCDDFFFF  CCDDFFFF  CCDDFFFFHHHHHHHH
                EEEE  EEEEFFFF  EEEEFFFF  EEEEFFFFHHHHHHHH
                EEEE  EEEEFFFF  EEEEFFFF  EEEEFFFFHHHHHHHH
                                GGGGGGGG  GGGGGGGGHHHHHHHH
                                GGGGGGGG  GGGGGGGGHHHHHHHH
                                GGGGGGGG  GGGGGGGGHHHHHHHH
                                GGGGGGGG  GGGGGGGGHHHHHHHH


⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
*: APL can be written in its own (legacy) single-byte charset that maps APL symbols to the upper 128 byte values. Therefore, for the purpose of scoring, a program of N chars that only uses ASCII characters and APL symbols can be considered to be N bytes long.