Fractals are still cheating IMO, because fractals have infinitely small features. Whenever you use infinity you can get all kinds of crazy results. It's like the geometric proof that pi=4:

Draw a circle of diameter 1

Draw a square touching it on all sides, perimeter 4

Cutting at right angles to the existing edges, cut smaller squares out of all the corners so they touch the circle

Perimeter remains 4

Repeat this corner cutting infinity times

Perimeter of the cut square (4) matches the circumference of the circle (pi)

pi = 4

Unlike traditional geometry, it's just abstract symbol manipulation with no relevance to real shapes.