E1: Contract both arrays to a point. Choose y = 0 in the number field and shift the point of the quadratic array. Observe the periodic mapping to -∞ ≤ x≤ +∞ . The differing speeds in the planes corresponds to xu = tang xz
E2: Initialize. The quadratic array has size 1 and its lowest row is along the real axis. Shift it slowly along the real axis and observe the periodic mapping. You can do this automatically with play. How do parallels to the real and to the imaginary axis transform?
E3: Initialize and move the array with the y slider along the imaginary axis. Now you see the transformed curves at a greater distance to the origin. What happens for large positive and negative imaginary parts?
E4: Initialize, enlarge the quadratic array to 2 and choose y = -1. The array now is symmetric to the real axis. Shift it with Play or with the x- slider. Rotation around +i and -i will be nicely visible.
E5: Contract the quadratic array to a point and study the mapping of the circular array. Do that for different diameters.
E6: Try to analytically derive the formulas for the curves into which parallels to the axis are mapped. (Hint: set x or y constant).