Abstract
Fractals are self-similar patterns across scales. In Pattern Field Theory, this is enabled by Field-Level Inversion Patterning (FLIP) and wavelength anchoring, which replicate patterns within the meta-continuum. This article updates the classical fractal concept with modern field-based constructs and neuroscientific evidence.
1. Fractals and FLIP
Fractals in nature show nested self-similarity 29. FLIP is the field’s inversion mechanism enabling scale-aware replication:
P(n+1) = Invert_Flip(P(n)) * Scale
2. Wavelength Anchoring & Stability
Fractal anchoring occurs at discrete wavelengths λₖ = 2π/k. Stability when pattern frequency resonates:
R = 2π / λₖ
3. Fractal Brain Patterns
Brain structures and activity show scale-invariance—suggesting FLIP embedded neural fractality 30.
4. FLIP Mechanism Across Domains
| Domain | FLIP Trigger | Scale Mechanism | Example |
|---|---|---|---|
| Biological | Development cues | Branching morphogenesis | Lungs, vasculature |
| Neural | Synaptic loops | Dendritic hierarchy | Cortical architecture |
| Physical | Turbulence | Energy cascade | Clouds, rivers |
| Digital | Iterative code | IFS loops | Mandelbrot set |
5. Dimension & FLIP Iteration
Fractal dimension D calculated by:
D = ln(N)/ln(R)
6. Meta-Continuum & Fractal Emergence
The meta-continuum holds latent FLIP potential. Each inversion step resonates at an anchored wavelength, projecting coherent fractal structure across scales.
Conclusion
Fractals are visible expressions of nested field inversions and anchoring logic. FLIP and wavelength anchoring frame patterned reality from neurobiology to geology.