I’ve added a new experimental branch to Equation-Driven Pots: Field Modifier Pot Designer.

The project has already grown from stable equation-driven pot generation into texture workflows, quad-color pattern logic, and nonlinear field exploration. The new step is a little different. Instead of only changing the field itself, this tool changes how the field is sampled.

In the earlier tools, the main idea is simple: define a radius field and turn it into printable geometry.

For a cylindrical workflow that looks like:

 r = f(theta, z, v, R)

With the field modifier workflow, there is now an intermediate mathematical step:

theta' = theta + strength * M(theta, z, v)

and then the chosen field is evaluated using the modified coordinate:

r = f(theta', z, v, R)

So the modifier does not just make the equation “stronger.” It changes where the equation is sampled. That is an important difference.

In 3D design terms, this means I can now create forms where features move through the object rather than just growing or shrinking in place. Ribs can drift. Petals can migrate. Crowns can rotate. Rim details can fold or shear while the lower body stays calm. The current version intentionally modifies angular sampling only, which keeps the workflow much closer to printable pot geometry than a fully freeform deformation system.

That makes this tool a natural continuation of the nonlinear math work.

The nonlinear field tool explored operations like inverse trig, stepped phase behavior, wrapped domains, and quasi-periodic interference. Field modifiers take the next step: they let the project explore coordinate remapping as a design method. In other words, nonlinear math changes the field itself, while field modifiers change how the field is sampled.

The current Field Modifier Pot Designer supports:

• a modifier field M(...)
• a modifier strength
• a modifier target
• application to base shape, texture, patterns, or all supported fields

That last part is especially useful. It means I can keep the silhouette stable while only shifting the texture logic, or move the entire form through the modifier field when I want something more dramatic.

This is still an experimental branch of the project, but it is a very promising one. It stays true to the math-first modeling approach while opening up a more expressive and more dynamic design space for printable objects.

Right now I see this as the beginning of a larger “experimental math for 3D design” direction, likely leading toward:

• regional field activity
• modifier stacks
• field-specific targeting
• richer but still printable math-based forms

So this update is not just another preset library. It is a new modeling idea inside the project.

Tool file:

JavaScript/FieldModifierPotDesigner.html

Project direction:
experimental math for 3D design, built on top of the equation-driven pot workflow.