Step 1: Make a thing. 
I went with a leaf shape.
Step 2: Effect > Distort & Transform > Transform. Make sure to preview, then make some copies of that leaf and scale ‘em down. Add a reflect X, scale dimensions down to 90%, and put some Move Vertical, and with some tweaking you should get a fern-looking thing. 
Why does this remind me of the geometric series elves?
Step 3: Object > Expand Appearance so that the effect becomes materialized. Select all, right-click and group that sucker. 
Step 4: Now for the fractal part: iterate! I rotated my tree-looking thing 90º clockwise so it resembled the initial leaf. Then I repeated the transformation to make a bunch of these tree things with a scale factor of 90%. 
With 50 copies of a shape made of 50 parts, you’ll notice your computer start to slow down a bit. I decided to stop while I was ahead… not a perfect fractal, but good enough for your Christmas card.
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