Middle-Square (von Neumann)
algorithmic-bytes · 37 views
algorithmic-byteshigh-entropy
What It Is
Von Neumann's 1949 middle-square PRNG --- famously degenerates to short cycles. Square the state, extract middle digits. Exhibits visible lattice structure.
Interpretation
Standard analysis sees: anti-persistent; homoskedastic; high-dimensional / space-filling; stationary. The atlas finds no named structure, but the source is distinctively extreme on Zipf–Mandelbrot (8-bit):entropy_nonstationarity (+4.5z) — beyond what the standard bank predicts for it. It sits beside Windows PE x86-64 in the atlas (standard-bank rank 131) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.23
asymmetry0.49
occupancy0.60
short-range corr0.19
long-range memory0.11
spectral colour0.77
periodicity0.53
complexity0.78
time-irreversibility0.74
volatility clustering0.15
multifractality0.45
dimensionality0.86
nonstationarity0.13
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Zipf–Mandelbrot (8-bit):entropy_nonstationarity | +4.5z | bank-miss 2.6σ |
Zipf–Mandelbrot (16-bit):zipf_r_squared | -2.5z | bank-miss 1.6σ |
Composition
dtypefloat64
range[0.0001539, 0.9999]
unique values12204 / 16384
mean ± std0.5 ± 0.289
Render Gallery
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Native > phase_plotraw
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Native > timeseriesraw
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Native > triple_latticeraw
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Boltzmann > lag_map
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Boltzmann > spin_grid
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Cayley > default
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Chladni > free_plate_nodal
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Chladni > plate_bottom
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Chladni > plate_top
_(centered)/signed_log_z/Middle-Square_(von_Neumann).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Middle-Square_(von_Neumann).png)
Heisenberg (Nil) (centered) > xy_path
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Hodge–Laplacian > default
/barcode/Middle-Square_(von_Neumann).png)
Inflation (Substitution) > barcode
/d_curve/Middle-Square_(von_Neumann).png)
Inflation (Substitution) > d_curve
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Information Theory > default
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Julia Set > escape_histogram
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Klein Bottle > default
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Laplacian > default
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Logarithmic Spiral > default
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Möbius-S³ > mobius_cylinder
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Möbius-S³ > s2_base_map
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Ordinal Partition > default
/phi_spectrum/Middle-Square_(von_Neumann).png)
Penrose (Quasicrystal) > phi_spectrum
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Persistent Homology > barcode
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Persistent Homology > h1_diagram
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Predictability > default
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Recurrence Quantification > default
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Spectral Analysis > default
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Spectral Graph > default
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Spirograph > mode_spectrum
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Spirograph > phasor_trajectory
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Symplectic > flux_grid
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Symplectic > phase_space
/default/Middle-Square_(von_Neumann).png)
Ulam Spiral (Sacks) > default
/default/Middle-Square_(von_Neumann).png)
Ulam Spiral (Square) > default
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Visibility Graph > default
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Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Windows PE x86-64 | 4.40 | |
| Linux ELF x86-64 | 4.42 | |
| macOS Mach-O (dyld) | 4.46 |
Which Geometries Light Up
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):hapax_ratio | rank 4/307 | 0.9020 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):entropy_nonstationarity | rank 3/307 | 0.5607 |
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