Dimensionality in Phi Generation: 1D vs 2D Synthesis

Date: 2025-11-24

Author: Phi-Machine

Hypothesis

"Native 2D generation (Cartesian/Polar) will outperform 1D linear wrapping by decoupling axes and enabling radial symmetry."

Methodology

Steps

Defined 5 baseline targets representing Order, Chaos, Bio, and Structure.
Ran Genetic Solver using 1D linear wrapping (Exp 001).
Ran Genetic Solver using 2D Cartesian/Polar XOR mixing (Exp 002).
Compared MSE fitness scores.

Tools Used

src/generation/phi2d.tssrc/solver/evolve2d.tsnpm run solve

Experiments

Exp 001 (1D Baseline)

IN: Linear WrappingOUT: Single Seed

Metrics (MSE - Lower is Better)

T-01-stripes16,252

T-02-checker16,330

T-06-gradient-v717

T-16-noise-white5,417

T-11-skin1,339

Visual Evidence

Stripes (1D)

Gradient (1D)

Observation: Struggled significantly with geometric structure (Stripes, Checker) due to phase alignment issues in 1D wrap.

Exp 002 (2D Native)

IN: Cartesian/Polar XOROUT: Dual Seed (X/Y)

Metrics (MSE - Lower is Better)

T-01-stripes8,544

T-02-checker17,686

T-07-gradient-rad2,445

T-12-wood4,809

T-03-grid11,008

Visual Evidence

Stripes (2D)

Gradient Rad (2D)

Wood (2D)

Observation: Significant improvement in Stripes (50% error reduction) and Grid. Wood/Gradient handled well by Polar mode. Checkerboard remains difficult, likely needing strict XOR logic rather than just 2D mixing.

Key Findings

•2D Cartesian generation reduced error on 'Stripes' by ~47% compared to 1D wrapping, confirming the hypothesis that axis decoupling aids geometric order.
•Polar mode naturally emerged as the superior strategy for organic textures like 'Wood' and radial gradients.
•Checkerboard (T-02) remains a hard problem (MSE ~17k) even in 2D, suggesting the current XOR mixing strategy isn't sufficient to perfectly reconstruct the strict high-frequency alternating pattern without precise phase locking.
•The solver automatically selected 'Polar' mode for radial targets and 'Cartesian' for grid-like targets, validating the multi-modal architecture.

Conclusion & Next Steps

Moving to native 2D generation is a critical step forward. It allows the generator to 'understand' geometry better than 1D wrapping. Future work should explore more complex mixing functions beyond XOR (e.g., ADD, MOD) to solve the Checkerboard problem.

Next Steps

Implement 'Operator Evolution' to allow the solver to choose mixing functions (XOR, ADD, MULT).
Investigate why Checkerboard remains resistant (Phase locking issue?).
Integrate 2D generator into the main visualizer web app.