Prime Indicator

What It Is

Stanisław Ulam's 1963 reference signal: 1 at prime indices, 0 elsewhere, over the integers starting from a random offset. Density ≈ 1/ln(n) (PNT). Fed through the Ulam Spiral geometry this reproduces the classical prime-diagonal plot --- diagonal_alignment should approach 1.0.

Interpretation

Standard analysis sees: heavy-tailed; right-skewed; few distinct values; low-complexity (predictable, not noise-like); homoskedastic; multifractal. The atlas finds no named structure, but the source is distinctively extreme on Cantor Set:mean_gap (-5.0z) — beyond what the standard bank predicts for it.

Composition

Binary sequence — two distinct symbols.

Render Gallery

Native > phase_plotraw

Native > timeseriesraw

Native > triple_latticeraw

Boltzmann > lag_map

Boltzmann > spin_grid

Cayley > default

Chladni > free_plate_nodal

Chladni > plate_bottom

Chladni > plate_top

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

Inflation (Substitution) > d_curve

Information Theory > default

Julia Set > escape_histogram

Klein Bottle > default

Laplacian > default

Logarithmic Spiral > default

Möbius-S³ > mobius_cylinder

Möbius-S³ > s2_base_map

Ordinal Partition > default

Penrose (Quasicrystal) > phi_spectrum

Persistent Homology > barcode

Persistent Homology > h1_diagram

Predictability > default

Recurrence Quantification > default

Spectral Analysis > default

Spectral Graph > default

Spirograph > mode_spectrum

Spirograph > phasor_trajectory

Symplectic > flux_grid

Symplectic > phase_space

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Open in Atlas →

Which Geometries Light Up