The butterfly curve is a stunning example of how mathematics can produce natural, almost lifelike beauty through simple equations. It’s defined by parametric functions involving exponential and trigonometric components that combine to create a shape resembling a butterfly with delicate wings and a slender body. As the parameter moves through its range, the curve traces elegant, symmetrical loops that expand and contract smoothly, giving it the visual impression of fluttering motion. Despite its

4.1K views · 233 reactions | Western monarch butterflies are making a comeback, but there’s still work to be done. The best way to start your very own butterfly garden is with native plants! | Garden for Wildlife | Facebook