RSF: multi-valued function example: the infinite sheets of the logarithm

The complex logarithm has a branch point of infinite order at 0, around which the sheets appear like a spiral staircase. As the complex value on the left changes in the imaginary direction, the exponential repeats itself again and again. Viewed in the other direction, there are an infinite number of values for the complex logarithm, depending on which sheet you consider the number whose logarithm is being taken to lie on.
The Riemann Project: Non-Quantitative Change