10- Explain what it means to have a fractal dimension between 1 and 2.

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10- Explain what it means to have a fractal dimension between 1and 2.

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Students and teachers are often fascinated by the fact thatcertain geometric images have fractional dimension The Sierpinskitriangle provides an easy way to explain why this must be soTo explain the concept of fractal dimension it is necessary tounderstand what we mean by dimension in the first place Obviouslya line has dimension 1 a plane dimension 2 and a cube dimension3 But why is this It is interesting to see students struggle toenunciate why these facts are true And then What is the dimensionof the Sierpinski triangleThey often say that a line has dimension 1 because there is only1 way to move on a line Similarly the plane has dimension 2because there are 2 directions in which to move Of course therereally are 2 directions in a line backward and forward andinfinitely many in the plane What the students See Answer

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