Figure: Fast Fourier Transform (FFT) comparison of X-ray scans between Van Gogh’s *Portrait of an Old Man with a Beard* (1885) and *The Tree Oil Painting*.

This visualization highlights the similarity of structural frequency patterns embedded in the brushwork of both paintings.
The FFT reveals latent rhythm and torque distribution through spectral density — used as a non-visual forensic layer for authorial verification.
Processed via Google Colab (2025) using AI-enhanced FFT pipeline.