grad-noise-175k

This collection is complete and closed. Every expression in the space below was rendered and measured once, in a single batch run. Each row is one expression, and its coordinate links to it running live on uto.run.

The purpose is exploratory. There is no target texture and no attempt to resemble Perlin noise. A constant field, a strongly directional pattern or an odd value distribution is an observation, not a failure. The measurements describe textures so they can be sorted, filtered and compared. They are a lossy fingerprint, not a judgement of quality and not a substitute for looking.

The space

An ither formula with two layers:

• topo: expression trees of up to 64 nodes, built from unary (o1), binary (o2) and leaf (x) slots
• expr: fills those slots
  • leaves: P, D, R
  • unary: sqt log frc flr cil sgn nrm
  • binary: add sub mlt div pow mod lrg eql min dot dst

A coordinate t·x·u·b follows the formula's projection: t the topology, x the leaf choices, u the unary choices, b the binary choices. Points outside the space were omitted from the run. Two orderings ride along: ordinal is the point's position in ither's whole enumeration (gaps where points were omitted), and batch index is its place in the batch run's sequence, 0 to 175,796 (the run's inputs.expr, and the number in its frame's file name).

The apparatus

Each expression is evaluated at the corners of a rectangular lattice with quintic blending (LATT.RECT.QUINTIC), over coordinates mlt(C, 8), in a 256 × 256 field #A. One configuration per expression: the dimension and coordinate scale were fixed for the whole run.

Measurements are taken from #A's x channel, its stored values (not a screenshot), at step 7, after which the run moves to the next expression. The frame in each row is that field, remapped for display.

The measurements

Notation: f is the field value, E averages the whole field, and E_I averages the interior (C-space [-0.98, 0.98]², which keeps wrapped edges out of the spatial measures).

Value distribution

key	meaning
value_mean, value_abs_mean	E[f] and E[|f|]: signed offset, typical distance from zero
value_positive_fraction	share of values above 0 (field tolerance 0.0001)
value_variance, value_stddev	population variance and SD: contrast
value_min, value_max, value_range	sampled extrema and their difference
histogram_entropy_bits	entropy of a 32-bin histogram over [−1, 1], 0 (one bin) to 5 (uniform) bits
histogram_probability_sum	consistency check, ≈ 1

Local roughness (one-pixel differences dx, dy, and g = √(dx² + dy²))

key	meaning
gradient_energy_x, gradient_energy_y	E_I[dx²], E_I[dy²]
gradient_magnitude_mean	E_I[g]: roughness
gradient_magnitude_variance, _stddev, _max	how unevenly that roughness is spread, and its peak
gradient_magnitude_cv	SD / mean of g: uneven activity (quiet areas interrupted by edges), independent of amplitude
gradient_axis_bias	(Ex − Ey) / (Ex + Ey), −1 to 1: horizontal vs vertical preference. Zero does not mean isotropic (diagonals balance too)
gradient_nonzero_flag	1 if there is any gradient energy at all

Change of slope (four-neighbour Laplacian L)

key	meaning
laplacian_mean, laplacian_energy, laplacian_abs_mean	E_I[L], E_I[L²], E_I[|L|]. Sharp or high-frequency structure responds; a linear ramp does not

Normalised by contrast (comparable across amplitudes)

key	meaning
gradient_energy_over_variance	(Ex + Ey) / variance
laplacian_energy_over_variance	E_I[L²] / variance
variance_normalization_valid_flag, gradient_cv_valid_flag	whether the denominators above are meaningful (> 10⁻¹²). Filter on these before trusting a ratio

Three spatial scales (mean squared difference at a distance, over the central [-0.74, 0.74]²: 2, 8 and 32 pixels at this resolution)

key	meaning
scale_diff2_near, _mid, _far	raw difference energy at each distance
scale_diff2_near_over_variance, _mid_…, _far_…	the same, normalised. Low near and rising far suggests smooth structure; a dip at a longer distance can hint at repetition

Each record's json also holds value_histogram (the 32 bin probabilities) and scale_curve (the three scales with their distances).

Reading them, and their limits

• Clipping. #A kept its default signed domain, so values outside [−1, 1] were clipped before measuring. The diagnostics describe the clipped texture.
• Combinations say more than any one key. A large range with modest SD and a high gradient peak suggests a few strong excursions. A broad histogram with low normalised detail suggests smooth variation. Similar roughness with a different CV means the activity is concentrated differently.
• Entropy is about values, not space. A smooth ramp can have high entropy, and shuffling the pixels would not change it.
• Raw spatial measures depend on resolution and amplitude. Prefer the normalised keys for detail independent of contrast, after checking the validity flags.
• Not measured: full orientation, spectra or periodicity, lacunarity, tileability, colour, novelty, aesthetic merit.
• Validation. The suite compiled and ran on every expression. Systematic numerical controls (constants, ramps, stripes, checkerboards, random pixels) and a comparison against longer settling times were not done before this run. Treat the values as exploratory.

Provenance

• Apparatus: noiseBatch/one.uto, project SHA-256 b6fc8f27…be04d0
• Expression corpus: SHA-256 7d3ec029…d72266
• Run files (canonical), in ~/lab/data/grad-noise-175k/: the enumeration (grad-noise-175k.jsonl), the measurements (grad-noise-175k-output.jsonl, joined on inputs.expr), the formula (grad-noise-175k.manifest.json) and the frames (png/)