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Sierpinski Triangle

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

Squareflake

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

How Many Elements Are There in the Cantor Set?

This article gives a proof of the uncountability of the Cantor set.

Von Koch Curve

Age 16 to 18
Challenge Level
It helps to consider the area added to ONE edge first. You have to sum an infinite geometrical series.