Analysis examples

These examples use deterministic inputs and state what the transformation changes. All figures are generated by scripts/docs_gallery.py. The Fourier and granularity datasets come directly from examples/readme_figures.py.

Thue–Morse: spatial spectral structure

Input: 1,048,576 binary terms, arranged on a 1024-square Hilbert grid. Operation: mean subtraction, separable Hann window, centred 2-D FFT magnitude, then log1p display scaling.

One million Thue-Morse terms on the Hilbert grid
Centred 2-D Fourier magnitude with Hann window

The spectral map displays repeated structure across scales. The input is aperiodic; its structure should not be described as a single hidden period. Changing the curve changes this spatial spectrum. Reproduction and interpretation.

Equal-density runs: separating periodic regions

Input: seeded interleaving of period-4 and period-6 binary runs with equal density. Operation: repeat the mean of each consecutive four-sample block.

Interleaved periodic runs without averaging
The same runs with granularity four

Period-4 runs become uniform while period-6 runs retain block variation. The regions are distinguished by response to averaging, not by different input means. Dataset construction and block-length dependence.

Curve locality: comparing geometric fields

Input: four curve constructions at the same resolution. Operation: average visit-index distance to up-to-eight spatial neighbours.

Visit-index distance field for curve 0 on the shared log scale
Visit-index distance field for curve 1 on the shared log scale
Visit-index distance field for curve 12 on the shared log scale
Visit-index distance field for curve 24 on the shared log scale

These plots do not use measurement values. The shared logarithmic scale makes both small and large distances visible. Field definition and numeric output.

RGB arrays: exact reconstruction and permutation

Input: a uint8 RGB test image containing a blue square, orange disk and green stripe. Operation: read its pixels along curve 0, then write the sequence using curve 0 or 12.

Original RGB test pattern
Identical pattern reconstructed with the same curve
Pixels rearranged by writing with curve twelve

The same curve recovers every channel value exactly. A different curve changes spatial placement while retaining the pixels. Conversion guarantees.

Color normalization: positive values across several scales

Input: exp(3*sin(i/37)), ranging from approximately 0.05 to 20.09. Operation: linear or logarithmic color normalization of the same mapped values.

Positive values with linear color normalization
The same values with logarithmic color normalization

Logarithmic color normalization changes visibility across value ranges; it does not transform the stored array or calculate a Fourier spectrum. Plotting options.