Morphing

Ascending

Imagine a piece of graph paper with an x-axis and a y-axis. If a sine curve was drawn on the x-axis, its period would start and end on the x-axis. Plotting a sine curve is much like plotting a horizontal line, with undulations of a specific amplitude and frequency. Adding a u-parameter outside the trigonometric function [for example, u+sin(u)] is much like plotting a diagonal line at an angle to the horizontal. For every cycle the function completes, it incrementally moves vertically. The centre of the sine curve would no longer follow the x-axis; instead, it would follow the newly plotted diagonal line. Adding an integer to a function would give a linear translation, while adding a u-parameter would shift the shape and produce a diagonal ...