Dex & Loom
Dex Dex
Hey Loom, I've been playing with fractal generators—kind of like the repeating motifs you weave. Maybe we could compare the math behind our patterns and see what new ideas pop up.
Loom Loom
That sounds lovely, the way numbers repeat in a fractal is much like how I let a single thread echo across a tapestry, each loop feeding into the next, a quiet, patient symmetry that feels almost like a secret song. I'd love to see how the equations you’re using compare to the way I weave. Maybe we can sketch a pattern together, blend math and thread, and see what new motifs emerge.
Dex Dex
Sounds like a perfect blend of code and craft. Let me pull up the basic recursion formula, and you bring your thread patterns. We'll map the equations onto the weave and see what cool shapes show up. Ready?
Loom Loom
Sure, let’s do it. Bring the numbers, and I’ll bring the threads. We'll see what shapes unfold.
Dex Dex
Alright, I’ll start with a simple Mandelbrot recursion: z = z² + c. Let’s pick a small c range, maybe 0.0 to 0.5, step 0.01, and see how the magnitudes spiral out. Now, on your side, think of each iteration as a stitch—each loop in the thread is a step forward. If we map the number of iterations to stitch length, we might get a visible pattern in the tapestry. Let's sync up the loops and see what the final weave looks like.
Loom Loom
I’ll imagine the first loop of a thread as the very first z, a tiny, almost invisible filament. Each time the equation nudges it, the stitch length grows, like a thread reaching a new length. When the numbers spiral out, the stitches will elongate, forming a subtle gradient from tight to loose. As we line up the steps, the weave should reveal a gentle, almost imperceptible wave—like a fabric that gently rises where the math swells and settles where it calms. The result will be a quiet tapestry that mirrors the fractal’s rhythm, with each stitch a quiet echo of the equation.
Dex Dex
That’s a neat way to think about it. I’ll write a quick script that spits out iteration counts as a list, and then we can plot that against your thread lengths. Expect a subtle sine‑like curve once the numbers explode. Let's see how the fabric reacts.