Lucas' spiral

Lucas' spiral, also known as the geometric spiral, is a type of curve that appears to grow outward in a smooth, often elegant pattern. It is created by repeatedly turning a line segment by a fixed angle and then scaling it by a constant factor, resulting in a spiral that maintains a consistent shape as it expands. This pattern can be seen in shells, galaxies, and other natural forms. Mathematically, it combines rotation and scaling, producing a continuous, self-similar curve that is both aesthetically pleasing and useful in understanding natural growth patterns and design.