Limitations in ChatGPT’s Execution of Geometric Tessellation Requests

ChatGPT Feature requests
1

I’ve been working with ChatGPT (GPT-4 and GPT-4o) to explore geometric tessellations, specifically Escher-style transformations based on regular polygons (e.g., hexagons with subtracted and added edges forming interlocking motifs like cats). While the assistant demonstrates an excellent understanding of the mathematical and artistic theory behind tessellation — including symmetry groups, edge transformations, rotational symmetry, and historical examples — the execution through image generation (e.g., via DALL·E) fails to meet those theoretical standards.

Specifically, when asked to:

*Subtract from one side of a polygon and add to the opposite (edge-pair transformation),

  • Maintain perfect rotational symmetry (e.g., 120° around a center point),
  • Keep shape constraints (edge length, angle, vertex continuity),
  • Execute modular Escher-style tiling based on a base hexagon tile,

…the outputs tend to rely on visual repetition, stylistic motifs, or general interlocking shapes, rather than actual geometric constraint logic. There is no true implementation of:

  • Edge-matching constraints,
  • Preserved symmetry groups (beyond superficial alignment),
  • Precision tiling verification or error checking.

This results in patterns that appear tessellated but fall apart under scrutiny — they’re not mathematically or constructively valid. There is also no support for user-defined tile logic, vector overlays, or labeled modular components.

Suggestions for Improvement:

  1. Introduce a constraint-driven image generation mode, where edge and angle rules (e.g., 6 sides, 120° rotations) are enforced by the model.
  2. Provide tessellation-aware templates with editable geometry (e.g., SVG-based tiling systems).
  3. Integrate symbolic geometry engines (like GeoGebra or custom graph systems) with image output to allow logic-first pattern creation.
  4. Allow for user-defined edge transforms — even abstract ones — to be visualized across a tiling grid.
  5. Offer transparent vector export (e.g., SVG) from visual tiles for real use in design workflows.

GPT’s current capability in understanding is impressive, but the execution gap — especially for users with background in design, mathematics, or education — is limiting.

I believe this is a meaningful area of improvement that could unlock more powerful, usable applications of AI for design, geometry, and art.