I’ve always been fascinated by the shapes resulting from data expressed on Cartesian diagrams, so I thought about training a specific LoRA to see what the results could be. 😊

Cartesian Curves is a style LoRA that transforms any subject into an artistic representation based on mathematical principles. Using curves, grids, and Cartesian axes, this LoRA combines art and mathematics, creating unique images. It’s ideal for those who love geometric aesthetics, science, and abstract art. 📈

The LoRA works with both simple and complex prompts, offering different results, naturally influenced by the seed used. The trigger word to use in prompts is c4rt3si4n_curv3s (although from some tests, it doesn’t seem strictly necessary).

Here are some example prompts used to create the sample images:

• c4rt3si4n_curv3s, a beautiful flower represented in a Cartesian coordinate system, with petals defined by mathematical curves, vibrant colors, and a grid background showing x and y axes, intricate and elegant design, blending art and mathematics

• c4rt3si4n_curv3s, a butterfly with wings defined by sinusoidal curves, vibrant blue and orange colors, set in a Cartesian coordinate system with a grid background, x and y axes labeled, symmetrical and elegant design, blending art and mathematics

• c4rt3si4n_curv3s, a tree with branches defined by parabolic curves, lush green leaves and brown trunk, set in a Cartesian coordinate system with a grid background, x and y axes labeled, natural and mathematical harmony

• An ultra-realistic, high-resolution cinematic of a 3D nebula with gas clouds defined by fractal curves, ethereal shades of pink, purple, and blue, set in a Cartesian coordinate system with a grid background, x, y, and z axes labeled, cosmic and mathematical mystery.

• An ultra-realistic, high-resolution cinematic of a 3D supernova explosion with shockwaves defined by parabolic curves, vibrant bursts of red, blue, and yellow colors, set in a Cartesian coordinate system with a grid background, x, y, and z axes labeled, explosive and mathematical beauty.

• An ultra-realistic, high-resolution cinematic of a 3D black hole with gravitational distortion defined by hyperbolic curves, swirling gas and light bending around the singularity, set in a Cartesian coordinate system with a grid background, x, y, and z axes labeled, cosmic and mathematical intensity.

If you liked this LoRA, I’d love to see your creations posted here. If you feel like it, please give the LoRA a thumbs up 👍 and follow me if you haven’t already! 😊