Hi scientists！I created some procedural seashells, with the goal of being as mathematically accurate as possible and striving to purely use VEX, as well as try my best to summarize the comprehensive types of shells in a concise algorithm.

In terms of polygon generation, it mainly provides the shape of equiangular spirals and cross-sectional ellipses that represent different types of seashells.

The schemes involved in pattern formation are several extensions of the reaction-diffusion system of the activator-inhibitor type. These equation sets essentially describe how the concentrations of the activator and its antagonist, the inhibitor, diffuse, react, catalyze, and decay over time along the growing edge. Additionally, this interaction is globally regulated by a hormone C, which also simultaneously engages in the interactions mentioned above. Based on their different coefficients, patterns such as stripes, traveling waves, oblique lines, tendril and drop-like patterns have been achieved.

I hope those who are also interested in math and wish to apply Houdini in interdisciplinary contexts will enjoy it. When working on this project, due to the involvement of many mathematical formulas, such as the diffusion equation and the discrete Laplacian operator, I had to review calculus from scratch. Although this took a lot of time, I was amazed that through Houdini, I could connect mathematics, chemistry, biology, and aesthetics together.

All my references come from Dr H Meinhardt, The Algorithmic Beauty of Sea Shells, Springer, 1998.