😃 Gemini sees things slightly different but, yes something like that. Gemini was spot on with palette suggestions for the art ‘studio’ update.

Title: Fourier Art Wave 2: A Morning of Math, AI, and Infinite Color

Sometimes you sit down to tweak a single algorithm, and before you know it, half the day has vanished into “Art Mode.” That’s exactly what happened to me this morning.

I was revisiting some older code for procedural image generation within my custom framework and ended up in a deep, brainstorming dialogue with an AI (Gemini). We were geeking out over the underlying mathematics of 2D inverse Fourier transforms, and that conversation sparked a massive upgrade to the code.

By the end of the morning, I had completely rewritten the color-mapping engine, pushing the project into what I am officially calling Fourier Art Wave 2.

Here is a peek under the hood at how these organic, flowing textures are actually generated, and how a morning chat with an AI helped take them to the next level.

1. The Blank Canvas (The Frequency Domain) When you paint normally, you pick a pixel and give it a color. For these images, I don’t start in the spatial realm of pixels at all. I start in the “frequency domain.” Imagine a completely zeroed-out, empty grid. Instead of adding paint, I am adding the instructions for waves.

2. Sculpting with Splines Rather than just dropping random wave frequencies across the grid, the code plots a set of random coordinates and connects them using smooth, mathematical curves (splines). As the algorithm “walks” along these invisible curves, it drops calculated sine and cosine amplitudes onto the grid. It’s essentially mapping out a deliberate, winding path of wave emitters.

3. The Magic Trick (The Inverse Transform) Once the frequency grid is populated with these paths for the red, green, and blue channels, I run an Inverse Fast Fourier Transform (FFT). This takes those abstract frequency instructions and converts them into the spatial domain. The result? Pure, intersecting waves that compound and collide, creating those incredibly complex, organic Moiré interference patterns you see in the final images.

4. Taming the Chaos (Range Normalization) Raw mathematical wave interference can be harsh. To fix this, the code dynamically scans the output to find the absolute minimum, maximum, and statistical mean values. It then smoothly scales the entire image down to a normalized range. This keeps the contrast rich but buttery smooth, ensuring no raw data is clipped.

5. “Wave 2”: The Color Dyad Upgrade This is where the morning’s AI dialogue really influenced the art. Originally, the math just outputted pure RGB interference. But during our chat, we discussed applying channel-based color dyads and multi-stop palettes to the normalized waves.

I updated the C# code on the fly to route the smooth wave data through custom color palettes. By defining multi-stop color paths—like mapping the red channel through a 16-step randomized neon gradient, or mapping all channels to warm browns and creams for a cohesive theme we called “Extra Sweet Macchiato”—the intersecting waves suddenly became deeply rich, topographical color maps.

Because these are generated with high-precision floating-point math rather than compressed noise, the gradients are pristine. They make fantastic, non-distracting backgrounds for phones, and mobile OS themes (like Android’s Material You) can easily extract perfect UI accent colors from them.

I’ve generated a whole batch of these new, palette-mapped images and uploaded them in high resolution.

Check out the full gallery, leave a comment, and grab a new wallpaper here: Fourier Art Wave 2 on Facebook