A Rigorous Derivation of the Bubble Sort Curve
linesthatconnect.github.io
linesthatconnect.github.io
y ≤ (x+t) / x
Thats an hiperbole, with the vertical asintote in -t (at the left, outside the graphic), and the horizontal asintote in 1 (the top of the graphic). It would be nice to add the "whole" hiperbole to the graph at the bottom.
y ≤ x / (x+t)
This equation only fits the first part of the curve, i.e. x ≤ 1-t. Here t is a time parameter, ranging from 0 at the start to 1 when everything is fully sorted.
The other videos created by the same author are equally impressive, beginning with straightforward explanations and gradually advancing to complex topics such as gamma and digamma functions [0]. These videos fully grasp the capabilities of Grant Sanderson's Manim library to enhance their visual appeal and educational value [1].
[0]: https://www.youtube.com/watch?v=v_HeaeUUOnc [1]: https://github.com/ManimCommunity/manim