Simple Fractal Mug

In geometry, a fractal canopy, a type of fractal tree, is one of the easiest-to-create types of fractals. Each canopy is created by splitting a line segment into two smaller segments at the end (symmetric binary tree), and then splitting the two smaller segments as well, and so on, infinitely. Canopies are distinguished by the angle between concurrent adjacent segments and ratio between lengths of successive segments. A fractal canopy must have the following three properties: 1. The angle between any two neighboring line segments is the same throughout the fractal. 2. The ratio of lengths of any two consecutive line segments is constant. 3. Points all the way at the end of the smallest line segments are interconnected.