We saw the Sierpinski Triangle pop up in a surprising place today, arising from bending a single line segment in the same manner as FractaSketch does. How can it be, then, that the same image can arise from an obviously 1D structure as it did from an obviously 2D structure, as we saw before? What is the dimension of the Sierpinski Triangle?
To help us answer this question, we need a clear idea on what we mean by dimension. When we say something is “two dimensional,” what does that mean, exactly? Think about this and try to have some ideas to share on Wednesday.