The Web of Chaos #2

"The Web of Chaos" by S. Liu stems from the cardioid curves, generated by a point on a circle rolling around a fixed circle of the same radius. By changing the rolling speed, we can discover novel symmetries resembling petals on flowers. To inject chaos into a given cardioid curve, we first shuffle x and y coordinates of each point on the curve and connect them using straight lines. We then rotate and translate the lines collectively to transform the interconnected bundle into a intriguing pattern. Finally, we animate the emergence of symmetric pattern by controlling speed and direction of the line rotations in order to give the audience the sense of time passing and the vivid elegance of dynamics on mathematical constructions.