E1:  Contract the quadratic array to a point. Set y = 0 and shift the point along the real axis in positive direction. You will recognize the logarithmic shrinking in the u-plane. The different speed of movement of the points in the two planes mirrors the real function xu = ln xz.

E2: Shift the point carefully towards x = 0 and beyond. Choose small deviations from 0 in the number field. Analyze the observations.

E3: Initialize. The array has size 2 and starts at the origin. Shift it along the real axis and observe the shrinking along both axes. Use the play button for the shift. Interpret your observation by the formulas for real and imaginary part.

E4: Initialize and move the array with the y slider parallel to the imaginary axis. What do you see? To get larger values of y, input numbers into the y number field. Adjust the scale in the planes.

E5: Initialize and move the array in the negative x direction. Remember that the array may now contain real values below and beyond 0. You had better divide the experiments into three classes: x > 1, x < -1, -1 < x < 1 . Move the array swiftly along the x axis. Do that for different y edge positions and for different array sizes.

E6: Activate the option visible. You will see the green mapping curve for x = 1 and the yellow mapping curve for y = 1. Shift the array swiftly in x and y direction and analyze your observations.

E7: Initialize, contract the quadratic array to a point and study the mapping of the circular array. Why do you see a straight line as mapping of the circle. Change the circle diameter and analyze your observations.

E8: Shift the circle by drawing its center point. Use different diameters. Consider that the array may contain points with different mapping characteristics.

E9: Try to derive analytically why the mapped strip has finite extension in the y direction, and calculate the formula for the limiting curves, which you see when the check box visible is activated.

E7: Initialize and set k = 1, -1, 2... What changes? (Use proper scale in the u-plane). Where lies the deeper cause of the periodicity?