One of the biggest updates to Equation-Driven Pots so far is the addition of a new browser tool: Nonlinear Field Pot Designer.

Until now, most of the project has focused on stable equation-driven workflows built around cylindrical and spherical radius fields, surface texture, and later multi-part color separation. Those tools are still the core of the project, but I wanted to push the design space further into more unusual mathematical behavior.

The new nonlinear tool does exactly that.

Instead of relying only on the smoother harmonic style of sin, cos, envelopes, and interference patterns, this version opens the door to more aggressive and more sculptural operations such as:

• inverse trig shaping like atan and asin
• stepped phase behavior using functions like floor
• wrapped angular domains with mod
• compressed ripple behavior with log 
• quasi-periodic interference using irrational frequency mixes

That changes the kind of forms the generator can produce.

The older tools are good at stable, elegant, printable variations: ribs, petals, twists, scales, lattices, color masks, and other structured surface logic. The nonlinear tool is more about folds, terraces, arc-shaped petals, phase jumps, compressed ridges, and stranger field interactions that do not repeat as obviously.

In practice, it feels less like adding a few new presets and more like opening a new branch of the design language.

A few examples of what this makes possible:

• ATan Fluting creates flutes with flatter faces and sharper transitions than ordinary cosine ribbing
• Arc-Petal Crown uses inverse trig behavior to generate cleaner arc-like petal forms
• Stepped Crown Phase introduces discrete rotational phase jumps along height
• Compressed Wave Stack turns layered wave fields into more terraced sculptural forms

The tradeoff is stability.

This tool is much more experimental than the earlier ones. Some parameter combinations produce invalid geometry or forms that are no longer printable, so I am treating it as an exploration tool rather than a replacement for the more stable designers. The more established tools are still better when I want predictable output. The nonlinear version is where I go when I want to discover shapes I would not have arrived at with ordinary harmonic equations alone.

That also makes it exciting.

The project is gradually turning into a family of related design environments:

• a stable textured pot workflow
• a quad-color pattern workflow
• a nonlinear experimental workflow
• a guided sweep workflow that connects back into Fusion 360 development

So this update is not just “more math.” It is really about expanding what kinds of form can be described, explored, and fabricated directly from equations.

I’ll keep refining the nonlinear presets and the guardrails around them, but even in its unstable state it is already producing some of the most interesting shapes in the project so far.

Tool file: 

JavaScript/NonlinearFieldPotDesigner.html