Are you asking, "what is a fractal, anyway?!?"
According to Learnthat, "A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in)."
Here are two famous examples. See how the geometric forms are made of larger and smaller versions of the same shape? That's the basic concept.
Now look at a plain white version of my valentine. See that the hearts are the same, only varying in size, and that the smaller ones subdivide the larger ones. That makes it a fractal.
How to make a fractal valentine
My inspiration came from this book, a collection of pop up fractal patterns to cut. If you're interested in the math behind the design, it's there, but you don't need to understand it (or even read it) to make the cards.
Download and print the template. I printed it on the back of my paper.
Download this one if you want fewer lines printed on your paper. Refer to the white pattern for guidance in placing your folds.
Cut out the top of every heart (shown in solid black on the white pattern).
Deeply score the dotted lines. Many of the hearts need to fold diagonally across the grain of the paper. The paper will resist folding, especially at the points, if you do not score well.
Refer to the white pattern. Looking at the back side of the paper (assuming you printed on the back of your paper), green dotted lines are mountain folds. Red lines are valley folds.
Each heart is a simple v-fold.
As in Lesson 3, fold and pop forward the hearts in size order, largest to smallest. I used the point of a knitting needle (also my favorite scoring tool) to coax the smallest hearts foward.
Decorate as desired. I outlined the hearts to make them more visible.
Back the cutout with another piece of paper if you like. My paper was purple on one side and pink on the other, so I used the same paper (flipped over) as the backing.
Close the card. Make sure all the hearts remain popped forward as you close the card.
If you're really interested in fractals, check out these links.
Scissor Craft snowflake
Fractal teaching unit by Cynthia Lanius