Part a
Define the fractal construction process by describing how a fractal is built from an initial geometric shape through iteration. In your explanation, specify the role of the scaling factor \(r\) and the replication number \(N\) generated in each iteration.
Part b
Let \(M_0\) be the initial measure. Assume that at each iteration, the measure is scaled by a factor of \(N r^d\), where \(d\) is the Euclidean dimension of the space (e.g., \(d=1\) for length, \(d=2\) for area, \(d=3\) for volume). Derive the sum of the infinite geometric series for the total measure. State the condition […]