Creating Art with Never-Ending Self-Similar Spirals Using Mathematics

The power of a complex number, when the power varies, can be visualized as a never-ending spiral which is self-similar across different scales in the complex plane. It continues to infinity on one end and spirals inward to zero on the other end. Mobius transformations act on these spirals by projecting them onto a sphere called the Riemann Sphere, shifting and rotating this sphere, and then projecting them back onto the complex plane. With these transformations, one can create even more interesting forms and patterns that still maintain the infinite property of repetition and gradual curvature that naturally occurs with these spirals. In our project, we generate art formed entirely within these mathematical properties, and the results are shown on the complex plane in conjunction with its (stereographic) projection onto the Riemann Sphere.