This parametric model turns mathematics, engineering, and art into a physical object.

The design follows the idea of a vector field, which can be understood as a mathematical structure that assigns a vector to every point in a space. In this model, each hexagonal tile represents one point of that field. The direction and length of the vector is translated into the sideways movement of the top tip, while the height settings can turn the field into a sculptural surface.

The result is a customizable 3D-printable sculpture that makes mathematical flow visible and turns it into a decorative object.

You can create your own version by choosing the field type, shape, and height behavior. Calm radial source fields, inward or outward spirals, sink fields, and Van der Pol oscillator patterns all create their own flow and visual character.

I got the idea from Herschel Shapiro on Youtube.

Want to build your own Field Wall Art?

Open the Parametric Model Maker and build your own design. The settings are grouped into sections.

1. Basic Shape:

   This section defines the overall size and outline of your design.

    

   - Outline Form

   1. Oval

      

   2. Rectangle

      

       

   - Outline Width/ Outline Height

        change how you like

    

   - Hex Base Width

         

    

   - Tip Width

         

2. Flow Design

   This Section controls the mathematical flow

    

   - Field Type

   1. Spiral Inward

      

       

   2. Spiral Outward

      

       

   3. Van der Pol Oscillator

      

       

   4. Source

      

       

   5. Sink

      

       

   6. Saddle

      

       

   7. Rotated Saddle

      

       

   8. Swirl

      

       

   9. Attractor Ring

      

   10. Shear Field

       

        

   - Field Origin

         Change coordinates of the field origin to make things interesting

          

    

   - Coordinate Scale

          Controls how quickly the field changes across the model

    

   - Flow Strength

          Controls the intensity of the field behaviour

    

   - Deflection Multiplier

          Controls how far the top tips move sideways

          

    

3. Height

   This section controls the vertical sculpture effect

    

   - Hex Height

          Defines the constant height of the Hex tiles

    

   - Dynamic Hex Height

          Defines how the height varies across the model

            

   1. None
   2. To Deflection
   3. To Field Strength
   4. Inverse Deflection
   5. Center High
   6. Edge High
   7. Wave
   8. Quantized

   9. Random

       

   - Dynamic Hex Height Amount

          Amount of max Height added on top 

    

4. Color

   This section defines the color gradiant taken on your model.

    

   -  Use Color Gradiant

         Enable/disable color gradiant.

    

   - Color Mode

          Algorithm how your color is put onto the hex tiles.

    

   - Color Steps

         Amount of gradients made between Color Start and Color End.

    

   - Swap Colors

         Swaps Color Start and Color End.

    

   - Color Start/ Color End

         Use RGB-Values to create your colors (0…255).

    

   - Default Hex Color

          If color gradiant is disabled.

    

5. Assembly

   This section defines how the sculpture is assembled

    

   - Assembly Mode

   1. Connected Plate

      

       

   2. Separate Tiles With Bowties

      

       

   3. Separate Tiles Without Bowties

      

       

   - Connection Thickness

           

    

   - Tile Gap Overlap

            

    

   - Bowtie Scale

       Scale of the bowtie connection 

    

   - Bowtie Height

       Height of the bowtie

    

6. Labels

   Labels help with assembly, especially for large designs.

    

   - Label Mode

   1. Fast

      Best for large models and MakerWorld generation

       

   2. Smart

      More accurate label placement

       

   3. Exact

      Most precise, but slower

       

   - Hex Text Size/ Hex Text Depth

         Controls the size and engraving depth of the bottom labels

    

7. Pattern Settings

   This section controls how the hex grid is aligned relative to the origin or field center.

    

8. Hanger Hole

   This section controls where and if a hanger hole should be placed.

    

   - Hanger Hole Labels

        Put in the Labels of the Hex pieces you want a hole to hang the piece on a nail.

    

   - Hanger Hole Diameter/ Hanger Hole Depth

         Dimension the hanger holes.