
A fractal is a geometric object that has an complicated boundary and is selfsimilar at all scales. One property of fractals is that, as the complexity of the shape increases, the area or volume approaches a finite value and the length of the boundary approaches infinity. Manipulative 1 is a representation of a Sierpinski triangle. A Sierpinski triangle starts as a equilateral triangle. At each iteration, an area in the shape of an upsidedown equilateral triangle 1/4 the size of the triangle is removed from each triangle. At each iteration, the area decreases by 1/4 and the length of the boundary increases by 1/3. 
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