That’s a fascinating thought—nature’s code is literally in the math of the patterns. The shapes on butterfly wings are usually described with fractal geometry, especially the self‑similar patterns you see in the veins and color bands. When you zoom in, you find the same basic motif repeating at smaller scales, which is a hallmark of a fractal. The underlying equations often involve iterative functions and differential equations that model how pigment cells move during development. On a slightly deeper level, you can think of the wing as a kind of biological Turing pattern, where chemical reactions and diffusion produce the repeating stripes and spots. So the “program” is really a set of nonlinear equations that encode symmetry, growth, and pigment distribution. If you’re curious, looking into the reaction‑diffusion model of morphogenesis and the Mandelbrot set might give you a good sense of how the math works.