Data Sources

298 sources · 16 domains

Each data source is a probe of the framework. These pages collect every visual rendering and the atlas neighborhood for each source. The cluster map below positions every source in the atlas's projected embedding, colored by domain.

exotic (51)

Categorical Sensor

Random draws from 6 to 12 non-uniform categories.

Chladni Plate Mode

Square plate vibration eigenmode with free edges, Z_{n,m}(x,y) = cos(nπx/L)cos(mπy/L) − cos(mπx/L)cos(nπy/L), evaluated on a √size × √size …

Chua's Circuit

Double-scroll electronic chaos --- bimodal attractor with different topology from Lorenz

Devil's Staircase

Numerical derivative of the Cantor function C(x), sampled on a uniform grid in a random sub-window of (0,1).

Dice Rolls

Simulated dice rolls --- uniform over just 6 levels (0, 51, 102, 153, 204, 255), creating a maximally discrete distribution with IID indepe…

Exponential Chirp

Exponential frequency sweep --- instantaneous frequency grows geometrically, creating equal time per octave.

Fibonacci Word

Sturmian sequence --- the simplest aperiodic word, with golden-ratio quasiperiodicity and complexity function p(n) = n + 1 (minimal for non…

Forest Fire

Drossel-Schwabl forest fire model --- tree density fluctuates as growth and burns compete

Free Group F₂ Walk

Non-backtracking random walk on the Cayley graph of the free group F₂ = ⟨a, b⟩ --- the 4-regular tree, canonical δ-hyperbolic (δ=0) space.

Geometric Waiting Times

Geometric(p) inter-arrival times with p ~ Uniform(0.05, 0.2).

Gray Code Counter

8-bit Gray-code counter with variable step.

Hawkes Process

Self-exciting point process --- events trigger more events, creating clustered bursts

Heisenberg Walk

Random walk on the discrete Heisenberg group H(ℤ) with generators drawn uniformly from {(±1,0,0), (0,±1,0)} (the standard symmetric Carnot …

Hilbert Walk

1D trace of Hilbert space-filling curve --- preserves 2D locality, creating structured self-similar fluctuations at every scale

Hofstadter Q

Hofstadter Q-sequence (A005185): Q(1)=Q(2)=1, Q(n)=Q(n-Q(n-1))+Q(n-Q(n-2)).

Intermittent Silence

Signal with long silent stretches punctuated by active bursts --- on/off intermittency

Kolakoski Sequence

Kolakoski K = 1,2,2,1,1,2,1,2,2,1,2,2,1,1,2,...

Kuramoto Oscillators

Order parameter of coupled oscillators near synchronization transition --- partial coherence

L-System (Dragon Curve)

Dragon curve L-system (F→F+G, G→F-G) --- the turn sequence is the regular paper-folding sequence, a non-periodic deterministic binary seque…

Langton's Ant

Classic 2-state Langton's Ant (rule RL) on a 256x256 grid --- chaotic build-up then emergent diagonal 'highway'

Levy Flight

Random walk with Cauchy-distributed jumps --- infinite variance, occasional extreme leaps create fractal clustering of visited sites

LFSR (16-bit)

16-bit linear feedback shift register (LFSR).

Markov Chain (10-state)

Ergodic 10-state Markov chain.

Minkowski Question Mark

Numerical derivative ?'(x) of Minkowski's question-mark function, sampled on a uniform grid in a random sub-window of (0,1).

Multiplicative Cascade

Random multiplicative process on dyadic tree --- multifractal burstiness at all scales

Padovan Word

Smallest-Pisot substitution: a→b, b→c, c→ab.

Pell Word

Silver-mean Sturmian: substitution a→aab, b→a.

Penrose Substitution

Robinson-triangle 1D inflation: substitution a→aba, b→ab.

PID Controller

PID controller tracking a step-changing setpoint.

Poisson Counts

Poisson-distributed event counts (λ ≈ 3 to 8).

Poker Hands

Stream of poker hand ranks (High Card through Royal Flush) --- extremely skewed: ~50% High Card, ~42% Pair, <0.002% Straight Flush or better

Random Steps

Random piecewise-constant signal --- flat plateaus of random height with geometrically-distributed durations, creating a sparse derivative …

Random Telegraph

Two-state Markov process with exponential holding times --- binary correlation structure

Riemann-Hardy-Littlewood

Riemann's 1859 'monster' R(t) = sum_{n>=1} sin(pi n^2 t)/(pi n^2).

Rule 110

Wolfram Rule 110 center column --- proven Turing-complete, the simplest known universal computer.

Rule 30

Wolfram Rule 30 center column --- produces output indistinguishable from random despite simple local rules.

Sandpile

Bak-Tang-Wiesenfeld sandpile --- self-organized criticality produces power-law avalanche sizes without parameter tuning.

Sensor Event Stream

Categorical sensor event stream --- door open/close, motion, temperature alerts with state-dependent transitions.

Shuffled Blocks

Structured blocks shuffled in random order.

Spike Train

Integrate-and-fire neuron model --- quiescent charging with sudden discharge spikes

Stochastic Resetting Walk

Evans-Majumdar process: x(t+1) = x(t) + drift + Gauss noise, with Poisson-rate full reset to zero.

Stochastic Resonance

Weak periodic signal amplified by noise in a bistable potential --- intermittent well-hopping

Symbolic Henon

Henon map reduced to a binary symbol stream (x < 0 or x > 0) --- the symbolic itinerary of a 2D strange attractor, encoding its topological…

Symbolic Lorenz

Lorenz attractor reduced to a binary symbol stream (left lobe vs right lobe), one symbol per half-orbit.

Takagi Function

Takagi (blancmange) function T(x) = sum_{n>=0} s(2^n x)/2^n with s(x) the distance to the nearest integer.

Tank Drain Cascade

Filling tank with multiplicative partial drains: x grows at constant rate to saturation K, at Poisson rate drains to x*Uniform(0, 0.5).

Thue-Morse

Binary substitution sequence (0→01, 1→10) --- perfectly balanced yet aperiodic, with flat Fourier spectrum like random noise despite being …

Tribonacci Word

Cubic-Pisot Sturmian-like: substitution a→ab, b→ac, c→a.

Van der Pol Oscillator

Van der Pol relaxation oscillations --- slow drift along cubic nullcline punctuated by fast jumps, the canonical model of nonlinear self-su…

Weierstrass

Weierstrass function --- continuous everywhere but differentiable nowhere, the first known mathematical 'monster'.

Zipf Distribution

IID draws from Zipf/power-law distribution --- steep rank-frequency, heavy right tail

chaos (49)

2-Torus Quasiperiodic

1D observable from dense quasiperiodic orbit on T^2 (frequencies sqrt 2, sqrt 3).

3-Torus Quasiperiodic

1D observable from dense quasiperiodic orbit on T^3 (frequencies sqrt 2, sqrt 3, sqrt 5).

4-Torus Quasiperiodic

1D observable from dense quasiperiodic orbit on T^4 (frequencies sqrt 2,3,5,7).

5-Torus Quasiperiodic

1D observable from dense quasiperiodic orbit on T^5 (frequencies sqrt 2,3,5,7,11).

Aizawa Attractor

Aizawa 3D continuous flow with torus-like topology and two polar spikes --- structurally distinct from Lorenz butterfly, Rossler spiral, an…

Arnold Cat Map

Hyperbolic toral automorphism [[2,1],[1,1]] on the 2-torus --- uniformly hyperbolic, Anosov diffeomorphism, mixing with Lyapunov exponent l…

Baker Map

Baker's map --- stretching and folding like kneading dough, the canonical model of chaotic mixing.

Bernoulli Shift

Simplest exactly solvable chaotic map: x(n+1) = 2x mod 1.

Chirikov Standard Map

Chirikov standard map at K=0.9716 --- mixed phase space with coexisting regular islands and chaotic sea, the paradigm of Hamiltonian chaos

Circle Map Quasiperiodic

Sine circle map at K=0 with golden-mean rotation --- pure quasiperiodic motion on a torus, deterministic but never periodic, flat spectrum …

Clifford Attractor

Clifford 2D iterated map x_{n+1}=sin(a*y)+c*cos(a*x), y_{n+1}=sin(b*x)+d*cos(b*y) at (a,b,c,d)=(-1.4,1.6,1.0,0.7).

Coupled Map Lattice

Spatiotemporal chaos in coupled logistic maps --- chimera states and coherence-incoherence patterns

Critical Circle Map

Sine circle map at K=1 critical coupling with golden-mean bare frequency --- sits on the boundary of mode-locking, a different universality…

Critical Circle Map (Bronze Mean)

Sine circle map at K=1 critical coupling tuned to the bronze-mean winding number (sqrt(13)-3)/2 (continued fraction [0;3,3,3,...]) --- a th…

Critical Circle Map (Silver Mean)

Sine circle map at K=1 critical coupling tuned to the silver-mean winding number sqrt(2)-1 (continued fraction [0;2,2,2,...]) --- a renorma…

Critical Transition (Fold)

Saddle-node (fold) normal form dx/dt = x - x^3 + mu(t) driven by a slowly ramped control parameter across the tipping point at mu_c = 2/(3*…

Duffing Oscillator

Driven damped nonlinear oscillator --- strange attractor with broad amplitude visits

FPUT N=16

Fermi-Pasta-Ulam-Tsingou anharmonic-spring chain (β-model), N=16 masses, fixed boundaries.

Halvorsen Attractor

Halvorsen x-coordinate --- 3-fold cyclically symmetric chaotic flow: each axis obeys the same equation with cyclic substitution.

Henon Map

Classic 2D chaotic map --- the strange attractor has fractal cross-sections and correlation dimension ~1.25, a benchmark for testing dimens…

Henon Near-Crisis (a=1.2)

Henon map at a=1.2, b=0.3 --- near the boundary crisis where the attractor collides with its basin boundary, producing intermittent bursts …

Hénon-Heiles

Hamiltonian chaos in a 2D potential: V = ½(x²+y²) + x²y - y³/3.

Ikeda Map

Laser cavity chaos: x(n+1) = 1 + u(x cos t - y sin t), y(n+1) = u(x sin t + y cos t) where t = 0.4 - 6/(1+x²+y²).

Intermittency Type-II

Type-II intermittency near a subcritical Neimark-Sacker (Hopf) bifurcation.

Intermittency Type-III

Type-III intermittency near a subcritical period-doubling (flip) bifurcation.

Logistic Chaos

The simplest chaotic system --- one-line recurrence x(n+1) = 4x(1-x) at r=4, filling the unit interval ergodically with a beta(½,½) distrib…

Logistic Edge-of-Chaos

Logistic map at the Feigenbaum point r=3.5699 --- the boundary between order and chaos, where the period-doubling cascade accumulates

Logistic r=3.2 (Period-2)

Logistic map in stable period-2 --- output alternates between two fixed values, the simplest oscillation after the first bifurcation

Logistic r=3.5 (Period-4)

Logistic map in period-4 --- four-value cycle after the second bifurcation, output concentrates on four narrow bands

Logistic r=3.68 (Banded Chaos)

Logistic map in banded chaos --- chaotic within disjoint bands that the orbit cycles through, mixing local unpredictability with global per…

Logistic r=3.74 (Period-5 Window)

Logistic map inside the period-5 stability window at r=3.74 --- an island of order embedded in the chaotic regime, intermittent near its bo…

Logistic r=3.83 (Period-3 Window)

Logistic map in the period-3 window --- a stable island inside the chaotic sea.

Logistic r=3.9 (Near-Full Chaos)

Logistic map at r=3.9 --- nearly full chaos but with thin gaps in the attractor revealing remnants of periodic windows

Lorenz Attractor

Lorenz '63 system x-coordinate --- the butterfly attractor, sensitive dependence on initial conditions.

Lorenz-96 N=36

Lorenz-96 with N=36 variables at standard forcing F=8 (canonical testbed).

Lorenz-96 N=4 F=16

Lorenz-96 atmospheric-dynamics ODE with N=4 variables and high forcing F=16 (required for chaos at small N).

Lorenz-96 N=8

Lorenz-96 with N=8 variables at standard forcing F=8.

Newton-Leipnik Attractor

Newton-Leipnik 3D continuous flow --- two-disc strange attractor with coexisting attractors at standard parameters.

Noisy Period-2

Period-2 oscillation corrupted by additive noise --- deterministic alternation partially washed out by Gaussian perturbation, bridging peri…

Pomeau-Manneville

Pomeau-Manneville type-I intermittency --- near a tangent bifurcation, the orbit lingers in long laminar phases before erupting into chaoti…

Quartic Map (Feigenbaum)

Quartic map x(n+1) = 1 - r*x^4 at r=1.5949 --- accumulation of the period-doubling cascade for the z=4 family.

Rossler Attractor

Rossler system x-coordinate --- the simplest 3D continuous chaotic flow, a single folded band with period-doubling route to chaos

Ruelle-Takens Cascade

Quasiperiodic route to chaos (Ruelle-Takens-Newhouse): a ring of coupled Hopf oscillators (complex Ginzburg-Landau) driven Benjamin-Feir un…

Rössler Hyperchaos

4D Rössler hyperchaotic system with two positive Lyapunov exponents --- qualitatively different from standard chaos, simultaneous expansion…

Sine Map (Feigenbaum)

Sine map x(n+1) = r*sin(pi*x) at r=0.8640 --- empirically-determined accumulation of the period-doubling cascade for this functional form (…

Sprott-B

Sprott case B --- simplest known dissipative chaotic flow with quadratic nonlinearity: dx/dt=yz, dy/dt=x-y, dz/dt=1-xy.

Standard Map K=0.5 (Mixed)

Chirikov standard map at K=0.5 --- mixed phase space where large KAM islands coexist with thin chaotic layers, the transitional regime betw…

Tent Map

Piecewise-linear chaos --- a V-shaped map near slope 2, producing uniform invariant density with maximal topological entropy

Uniform Chaos (Logistic Scramble)

Logistic map at r ≈ 3.9 pushed through its invariant CDF.

number_theory (37)

A5 Artin a_p

Hecke traces a_p for 100 weight-1 cuspidal newforms with projective Galois image A_5 (icosahedral), pooled across LMFDB labels for primes p…

Aliquot Orbit Lengths

Aliquot sequence orbit lengths --- number of steps before s(n)=sigma(n)-n iteration terminates (reaches 1, enters a cycle, or escapes the s…

Benford's Law

Benford-distributed significands --- leading-digit law P(d) = log₁₀(1+1/d), the distribution of first digits in real-world datasets spannin…

BSL Residues

BSL numerator rho(v) mod D for random gap vectors --- probes equidistribution of the Collatz cycle equation.

Catalan G Digits

Base-256 digits of Catalan's constant G = Σ(−1)ⁿ/(2n+1)².

Champernowne

Provably normal number in base 256 --- uniform digit distribution but deterministic concatenation

Collatz Flights

Peak altitude of Collatz orbits --- how high consecutive integers fly before crashing to 1

Collatz Gap Lengths

BSL gap vector from Collatz orbits --- number of halvings between consecutive odd steps (v_i in the Böhm-Sontacchi-Lagarias equation).

Collatz Parity

Collatz parity sequence --- binary trace (even/odd) of the 3n+1 orbit, conjectured to behave like a biased coin flip with P(odd) ≈ log₂(3)/…

Collatz Stopping Times

Collatz stopping times --- how many steps each integer takes to reach 1.

Collatz Trajectory

Collatz orbit values log1p(n) along the trajectory, restarting from consecutive integers to avoid 4-2-1 cycle collapse.

Continued Fractions

CF digits of random quadratic irrationals --- bounded partial quotients with hidden periodicity

Copeland-Erdős

Provably normal number formed by concatenating primes in base 256 (Copeland-Erdős 1946).

De Bruijn Sequence

B(4,4) De Bruijn cycle --- every 4-symbol window over alphabet 0-3 appears exactly once

Divisor Count

Divisor count d(n) --- erratic arithmetic function averaging ~ln(n), spikes at highly composite numbers, modulated by prime factorization s…

e Digits

Base-256 digits of Euler's number e's fractional part.

Euler Totient Ratio

Euler totient ratio φ(n)/n --- the fraction of integers below n that are coprime to n, dense in (0,1) with a fractal structure governed by …

Euler-Mascheroni γ Digits

Base-256 digits of γ = lim(Hₙ − ln n)'s fractional part.

Fibonacci Quasicrystal

1D Fibonacci quasicrystal --- aperiodic tiling with long-range order, discrete diffraction

Gaussian Collatz Orbit

Collatz map over Gaussian integers Z[i] with divisor pi=1+i and multiplier 3.

Goldbach r(2n)

Goldbach r(2n) --- number of unordered representations of 2n as p+q with both p,q prime.

Golden Ratio Digits

Base-256 digits of φ = (1+√5)/2's fractional part.

Liouville Function

Liouville lambda(n) = (-1)^Omega(n) --- parity of prime-factor count with multiplicity.

ln(2) Digits

Base-256 digits of ln(2)'s fractional part.

Mertens Function

Cumulative sum of the Moebius function --- a random-walk-like sequence whose growth rate is equivalent to the Riemann Hypothesis (O(n^(½+ε)…

Mian-Chowla

Greedy Sidon (B₂) sequence: a₁=1, a_{n+1} = smallest integer strictly greater than a_n such that all pairwise sums {a_i + a_j : i ≤ j} rema…

Moebius Function

Moebius mu(n) in {-1, 0, +1} --- 0 on non-squarefree n (~39.2% by density), (-1)^omega(n) on squarefree n.

Partition Function

p(n) mod 5, the number of integer partitions of n reduced modulo 5.

Pi Digits

Digits of pi in base 256 --- conjectured normal (equidistributed), but entirely deterministic.

Prime Gaps

Gaps between consecutive primes --- locally erratic but statistically governed by the prime number theorem, with conjectured connections to…

Prime Indicator

Stanisław Ulam's 1963 reference signal: 1 at prime indices, 0 elsewhere, over the integers starting from a random offset.

Ramanujan Tau

Normalized Ramanujan tau τ̃(p) = τ(p)·p^(-11/2) for consecutive primes, where τ(n) is the q-coefficient of Δ(q) = η(q)^24 — the unique weig…

Riemann Zeta Zeros

Unfolded nearest-neighbour spacings of the first 100,000 Riemann zeta nontrivial zeros (Odlyzko) --- Montgomery-Odlyzko: GUE-distributed (q…

Rudin-Shapiro

Partial sums of Rudin-Shapiro --- deterministic random walk with flat spectral density

Stern-Brocot Walk

Stern diatomic sequence --- every positive rational visited once, fractal self-similar structure

von Mangoldt Function

von Mangoldt Lambda(n) = log(p) if n = p^k for some prime p and k >= 1, else 0.

√2 Digits

Base-256 digits of √2's fractional part.

binary (22)

AES Encrypted

AES-256-CTR ciphertext of structured data --- the gold standard for pseudorandom streams, indistinguishable from random without the key

Bzip2 (level 1)

Bzip2-compressed data (1.2 MB, level 1, 100k blocks) --- Burrows-Wheeler transform with small block size preserves more local structure fro…

Bzip2 (level 9)

Bzip2-compressed data (1.1 MB, level 9, 900k blocks) --- BWT with maximum block size, approaching the entropy floor of the source data

ChaCha20

Bernstein's ChaCha20 stream cipher (2008) --- cryptographic-strength PRNG, the keystream of TLS 1.3 / QUIC / WireGuard.

Classical MIDI

Real MIDI files --- Bach (chorale, Brandenburg 3), Beethoven (5th), Mozart (Figaro).

glibc LCG

The C standard library LCG --- used by glibc rand() for decades.

Gzip (level 1)

Gzip-compressed data (1.4 MB, level 1) --- fast DEFLATE with more residual structure

Gzip (level 9)

Gzip-compressed data (1.3 MB, level 9) --- maximum DEFLATE compression, near-entropy stream

Linux ELF x86-64

Stripped Linux x86-64 PIE executable (3.7 MB) --- ELF with .text, .rodata, relocation tables, and x86-64 instruction byte patterns

macOS Mach-O (dyld)

macOS dyld universal binary (2.6 MB) --- i386 + x86-64 + arm64e __text sections, pure machine code

Middle-Square (von Neumann)

Von Neumann's 1949 middle-square PRNG --- famously degenerates to short cycles.

MINSTD (Park-Miller)

The 'minimum standard' LCG from Park & Miller (1988 CACM) --- a=16807, m=2³¹-1.

MT19937 (Mersenne Twister)

The Mersenne Twister (Matsumoto & Nishimura, 1998) --- period 2^19937-1, default PRNG of numpy's legacy RandomState, CPython's random modul…

Network Packet Sizes

Simulated network-packet length sequence.

Neural Net (Dense)

Synthetic trained dense-layer weights --- Xavier init plus 50 momentum-smoothed gradient updates, L1-like shrinkage of small weights, and h…

Neural Net (Pruned 90%)

Pruned neural network weights (90% zero) --- extreme sparsity typical of compressed models.

OpenBSD ELF x86-64

Stripped OpenBSD x86-64 PIE executable (1.1 MB) --- ELF with W^X enforcement, subtly different instruction mix from Linux due to compiler a…

RANDU

IBM's infamous RANDU (1968) --- the worst widely-deployed RNG in history.

Wichmann-Hill

Wichmann & Hill (1982) --- three combined short-period LCGs.

Windows PE x86-64

Windows PE32+ console executable (2.3 MB) --- x86-64 with PE headers, import tables, and different code generation patterns from Unix compi…

x86-64 Machine Code

Pure .text section from Linux x86-64 ELF --- REX-prefixed instruction stream, 6.3-bit entropy, strong opcode bigram structure, function pro…

XorShift32

Marsaglia's XorShift (2003) --- three shift-xor operations per step.

geophysics (19)

Ambient Microseism

IU.ANMO long-period vertical (1 sps) --- ocean-generated microseism noise at 0.1-0.3 Hz, 6-hour quiet period with seasonal/storm modulation…

Deep Earthquake P-wave

2013 Okhotsk M8.3 (depth 598 km) P-wave at ANMO --- sharp impulsive onset, minimal coda, 20 sps broadband vertical (IRIS CC0)

Earthquake Depths

Real USGS earthquake depths --- bimodal: shallow crustal (<30km) and deep subduction (>100km), ~77k M4.0+ events 2020-2024 (USGS ANSS ComCa…

Earthquake Intervals

Real USGS interevent times --- Omori-law clustering after mainshocks, Poisson background, ~77k M4.0+ events 2020-2024 (USGS ANSS ComCat)

Earthquake Magnitudes

Real USGS earthquake magnitudes --- Gutenberg-Richter distribution, ~77k M4.0+ events 2020-2024 (USGS ANSS ComCat)

Earthquake P-wave

P-wave arrivals from 80 earthquakes (M3.0-5.4, 111-498 km) at IU.ANMO --- 40 sps broadband vertical --- impulsive, anti-persistent (low Hur…

El Centro 1940

1940 Imperial Valley NS strong motion --- the most-studied earthquake record in structural engineering

Geomagnetic ap Index

Real 3-hourly geomagnetic ap index 1932-present --- solar-driven magnetic storms, 93 years (CC BY 4.0, GFZ)

Kilauea Tremor

HV.DEVL volcanic tremor during 2018 Kilauea eruption --- harmonic tremor at 100 sps, quasi-periodic with complex amplitude modulation, narr…

Ocean Swell

Real sea-surface displacement from CDIP buoy 067 (Harvest, CA) --- 1.28 Hz vertical heave dominated by long-period Pacific swell: smooth, n…

Potomac River Flow

USGS gauge 01646500 --- real 15-min discharge, Potomac near DC, 2024 (public domain)

Seismic b-value (SoCal)

Sliding-window Gutenberg-Richter b-value over ~20k SoCal M≥1.5 earthquakes 2015-2023 --- low dynamic range (b ≈ 0.5-1.5), strongly autocorr…

Seismic Noise (ANMO)

Verified-quiet ambient seismic noise at IU.ANMO (no earthquakes) --- 40 sps broadband vertical --- persistent microseismic hum (high Hurst)

Seismograph (ANMO)

IRIS IU.ANMO broadband vertical --- real 40Hz seismograph, Albuquerque NM, 2024-01-01 (CC0)

Tidal Gauge (SF)

NOAA CO-OPS water-level series at San Francisco, 6-min sampling.

Tohoku Aftershock Intervals

Log inter-event times of ~35k Tohoku 2011 M≥2 aftershocks --- Omori-law decay with temporal clustering, 3 months post-mainshock (ISC/JMA ca…

VLF Radio (Baseline)

VLF radio RMS envelope from normal day (2024-04-10) --- same sensor ET0001 Cleveland OH, 20 kHz, no eclipse, standard D-layer daytime absor…

VLF Radio (Eclipse)

VLF radio RMS envelope during 2024-04-08 total solar eclipse --- sensor ET0001 Cleveland OH (path of totality), 20 kHz sample rate, D-layer…

Wave Height (Buoy)

NOAA buoy 46042 significant wave height --- real ocean swell measurements off Monterey Bay 2020-2023, 10-min intervals (CC0)

medical (15)

Blood Pressure Waveform

MGH/Marquette ART channel.

ECG Beat Conformity

Per-beat correlation against a record-specific normal-beat template, MIT-BIH Long-Term ECG (7 records, 14-22 h each, 128 Hz).

ECG Fusion

MIT-BIH Arrhythmia DB, fusion beats.

ECG Normal

MIT-BIH Arrhythmia DB, normal sinus rhythm (NSR).

ECG Supraventr.

MIT-BIH Arrhythmia DB, supraventricular premature beats (SVPB).

ECG Ventricular

MIT-BIH Arrhythmia DB, ventricular premature beats (VPB).

EEG Eyes Closed

Bonn EEG set Z, healthy subjects with eyes closed.

EEG Eyes Open

Bonn EEG set O, healthy subjects with eyes open.

EEG Healthy

Bonn EEG set D, interictal recordings from hippocampal contralateral (non-epileptogenic) zone in epilepsy patients.

EEG Resting

PhysioNet resting-state EEG, 109 subjects, contiguous blocks at 160 Hz across 64 channels (first channel sampled here).

EEG Seizure

Bonn EEG set E, ictal activity.

EEG Tumor

Bonn EEG set F, interictal recordings from epileptogenic zone outside seizure.

Gut Motility

Zenodo 3878435 three-channel surface electrogastrogram.

Mackey-Glass

Delay-differential equation modeling blood cell regulation --- high-dimensional chaos

Respiration Waveform

PhysioNet Fantasia RESP channel.

bio (14)

Codon Usage

Synthetic coding DNA --- nucleotide triplets (codons) with Zipf-like usage bias and weak Markov transitions, emitted as raw ASCII bases (A=…

DNA Centromere

Human alpha satellite DNA (AC017075).

DNA Chimp

Chimpanzee chr1 genomic DNA (Clint_PTRv2).

DNA Dog

Dog chr1 genomic DNA (ROS_Cfam_1.0).

DNA Human

Human chr1 genomic DNA (GRCh38).

DNA Phage Lambda

Bacteriophage lambda complete genome (NC_001416).

DNA Plasmodium

DNA SARS-CoV-2

SARS-CoV-2 complete genome (NC_045512).

DNA Thermus

Thermus thermophilus complete genome (NC_006461).

Hodgkin-Huxley

Biophysical neuron --- action potentials with Na⁺/K⁺ channel kinetics, refractory periods

Human Proteome

Real human proteome --- 20,431 reviewed Swiss-Prot sequences (UniProt 2025), raw ASCII bytes (20 amino acid letters in the 65-89 range).

Lotka-Volterra

Predator-prey oscillations --- nonlinear limit cycles with phase-shifted population waves

Phyllotaxis

Golden-angle sunflower spiral --- successive seeds placed at 137.508° (= 360°/phi²), the most irrational angle.

SIR Epidemic

Stochastic SIR model --- infection waves with exponential rise, peak overshoot, and power-law decay

noise (13)

ARMA(2,1)

Autoregressive moving-average process --- linear short-memory dynamics, the workhorse model of classical time-series analysis

Beta Noise

IID Beta(0.3, 0.3) noise --- U-shaped distribution concentrating mass at both extremes with a valley in the middle, structurally opposite t…

Blue Noise

High-pass filtered noise (PSD ~ f) --- anti-correlated increments that suppress low frequencies, common in error-diffusion dithering and sp…

Brownian Walk

Cumulative sum of Gaussian increments --- the canonical random walk, self-affine with Hurst exponent H=0.5 and PSD ~ 1/f²

fBm (Antipersistent)

Fractional Brownian motion with H=0.3 --- antipersistent (trend-reversing), rougher than standard Brownian motion

fBm (Persistent)

Fractional Brownian motion with H=0.7 --- persistent (trend-following), smoother trajectories with long-range dependence

Gaussian Noise

IID standard Gaussian noise --- bell-curve density centered at zero, the baseline null model for continuous-valued signals

Geometric Brownian Motion

Geometric Brownian motion --- multiplicative random walk (dS/S = μdt + σdW), the basis of Black-Scholes option pricing.

Ornstein-Uhlenbeck

Ornstein-Uhlenbeck process --- mean-reverting diffusion with stationary Gaussian distribution, the continuous-time analog of an AR(1) proce…

Perlin Noise

Spectral Perlin-like noise --- coherent smooth fluctuations with 1/f amplitude falloff, widely used for procedural terrain and texture gene…

Pink Noise

1/f noise (PSD ~ 1/f) --- equal energy per octave, ubiquitous in nature from heartbeat intervals to semiconductor flicker noise.

Regime Switching

Two-state hidden Markov process --- alternates between calm (σ=0.5) and volatile (σ=3.0) regimes with asymmetric transition rates

White Noise

IID uniform random floats in [0,1) --- the null model, maximum entropy with zero sequential correlation

quantum (13)

Anderson 1D Localized

1D tight-binding chain with random on-site disorder W=2 --- exponentially localized eigenstates from K independent disorder realizations, r…

Aubry-André Critical

Almost-Mathieu operator at critical coupling λ=2 with golden-ratio incommensurate potential --- multifractal eigenstate intensity (determin…

Berry Random Wave

Berry's random plane wave --- superposition model for chaotic eigenstate statistics, Gaussian amplitude distribution

Entanglement Entropy

Page curve entanglement entropy of random bipartite states --- ⟨S⟩ ≈ log(d_A) - d_A/(2d_B)

Fibonacci Tight-Binding

1D tight-binding chain with on-site potential modulated by Fibonacci substitution rule A->AB, B->A --- Cantor-set spectrum, multifractal ei…

GOE Spacings

Gaussian Orthogonal Ensemble spacings --- linear repulsion P(s)~s exp(-πs²/4), time-reversal symmetric

GUE Spacings

Gaussian Unitary Ensemble spacings --- level repulsion P(s)~s² exp(-4s²/π), broken time-reversal symmetry

Kicked Rotor

Quantum kicked rotor --- dynamical localization freezes classical chaos, Anderson localization in momentum space

OTOC Growth

Out-of-time-order correlator d(log C)/dt for a chaotic mixed-field Ising chain (L=8, g=0.9, h=0.8, J=π/4) --- quantum Lyapunov scrambling r…

Poisson Spacings

Uncorrelated Poisson spacings P(s)=exp(-s) --- integrable quantum systems, no level repulsion

Quantum Walk

Hadamard walk on a 257-site ring --- coin polarization ⟨σ_z(t)⟩ with ongoing wraparound dynamics and quantum recurrences

Spectral Form Factor

Ensemble-averaged spectral form factor log K(t) for a GUE Hamiltonian --- dip-ramp-plateau curve over log-spaced times; captures long-range…

Wigner Semicircle

Eigenvalue density from large random matrices --- converges to Wigner semicircle law ρ(x)=√(4-x²)/(2π)

astro (11)

GOES X-Ray Flux

GOES satellite 1-min X-ray flux --- solar flare monitoring, log-scale A/B/C/M/X classes (NOAA)

Kepler Exoplanet

Kepler confirmed transiting-exoplanet light curve.

Kepler Non-planet

Kepler long-cadence flux for a target without a confirmed planet.

LIGO H1 Whitened (GW150914)

LIGO H1 strain, 4096 Hz, 32s around GW150914 --- ASD-whitened + 30-400 Hz bandpassed.

LIGO Hanford

LIGO Hanford H1 strain around the GW150914 binary black-hole merger.

LIGO Livingston

LIGO Livingston L1 strain around GW150914.

Solar Flares Daily Peak

GOES daily peak X-ray flux 1975-2016 (NGDC NOAA, 15098 days).

Solar Wind IMF

OMNI hourly interplanetary magnetic-field magnitude at L1.

Solar Wind Speed

OMNI hourly solar-wind bulk velocity at L1.

Sunspot Number

SIDC daily international sunspot number.

Voyager 1 X-band

Breakthrough Listen Voyager 1 fine-res spectrum at X-band (8419 MHz, 2.79 Hz/chan, ~1M channels) --- known artificial residual carrier + te…

bearing (11)

Bearing Ball

CWRU bearing vibration, ball fault.

Bearing Inner

CWRU bearing vibration, inner-race fault.

Bearing Normal

CWRU bearing vibration, normal baseline.

Bearing Outer

CWRU bearing vibration, outer-race fault.

IMS Bearing Degraded

NASA IMS test 2, day 6 snapshot, bearing 1.

IMS Bearing Failed

NASA IMS test 2, peak-fault snapshot 2004-02-19 05:02 (file 975 of 984), bearing 1.

IMS Bearing Healthy

NASA IMS run-to-failure test 2, day 1 snapshot, bearing 1.

MFPT Inner Loaded

MFPT bearing vibration, inner-race fault under 300 lb radial load.

MFPT Inner Unloaded

MFPT bearing vibration, inner-race fault under zero radial load.

MFPT Normal

MFPT bearing vibration, healthy baseline.

MFPT Outer Race

MFPT bearing vibration, outer-race fault.

motion (11)

Accel Jog

MotionSense smartphone accelerometer magnitude during jogging.

Accel Sit

MotionSense smartphone accelerometer magnitude while sitting.

Accel Stairs

MotionSense smartphone accelerometer magnitude on stairs.

Accel Walk

MotionSense smartphone accelerometer magnitude during walking.

Damped Pendulum

Nonlinear pendulum with friction --- transient chaos at high amplitude, decay to limit cycle or fixed point

Double Pendulum

Angular velocity of second arm --- mechanical chaos with mixed regular/chaotic regions

Langevin Double-Well

Brownian particle in double-well potential --- noise-driven switching between metastable states (Kramers problem)

Magnetic Pendulum (3-Magnet)

Pendulum tip in 2D plane above three magnets at triangle vertices, with linear gravity-restoring force --- conservative (no damping) 2-DOF …

Projectile with Drag

Ballistic arcs with quadratic air resistance --- asymmetric trajectories, terminal velocity approach

Spring Pendulum

Elastic pendulum (mass on stretchable spring swinging in a vertical plane).

Triple Pendulum

3-segment Lagrangian pendulum chain, equal m=L=1 --- Hamiltonian 3-DOF conservative chaos with sin-coupling.

waveform (10)

Clipped Sine

Sine wave hard-clipped at 70% --- flat tops and bottoms create a hybrid of smooth oscillation and constant segments, concentrating the dist…

Morse Code

Synthetic Morse code --- dots (1 unit), dashes (3 units), and hierarchical gaps (1/3/7 units).

Noisy Sine (SNR 3 dB)

Sine wave buried in equal-power Gaussian noise (SNR=3 dB) --- the perceptual boundary where periodicity is barely detectable, transitional …

Period-Doubled Wave

Oversampled period-2 oscillation --- a sinusoid whose alternate base cycles carry different amplitude, the canonical orbit just past a peri…

Pulse-Width Modulation

Pulse-width modulation --- binary carrier (0/255) whose duty cycle sweeps smoothly via sine modulation, encoding an analog signal in digita…

Sawtooth Wave

Sawtooth wave --- linear ramp with discontinuous reset, rich in harmonics (1/n Fourier decay)

Sine Wave

Pure sinusoid --- perfectly periodic, single-frequency, minimal complexity.

Square Wave

Square wave --- binary oscillation (0 or 255), maximal harmonic content with 1/n odd-harmonic Fourier series

Triangle Wave

Triangle wave --- linear ramps up and down, smooth peaks with 1/n² Fourier decay (only odd harmonics)

μ-law Sine

Sine wave with non-linear mu-law quantization (G.711).

climate (9)

Barometric Pressure (Buoy)

NOAA buoy 46042 atmospheric pressure --- real synoptic weather patterns off Monterey Bay 2020-2023, 10-min intervals (CC0)

Humidity

Max Planck Jena station relative humidity.

Ocean Wind (Buoy)

NOAA buoy 46042 wind speed --- real 10-min observations off Monterey Bay 2020-2023, capturing marine boundary layer turbulence and diurnal …

Pressure

Max Planck Jena station barometric pressure.

Rainfall (ORD Hourly)

Real hourly precipitation at Chicago O'Hare 2020--2023 (IEM/ASOS).

Surface Wind (ORD 5-min)

Real 5-minute surface wind speed at Chicago O'Hare 2023 (IEM/ASOS).

Temperature

Max Planck Jena weather station air temperature.

Temperature Drift

Slow room temperature with HVAC cycles.

Wind Speed

Max Planck Jena station wind speed.

financial (9)

BTC Close Price

Bitcoin hourly closing prices --- contiguous 16KB block sampled from 96K bars (2015-2026)

BTC Range

Bitcoin hourly high-low range --- intrabar volatility proxy with characteristic clustering

BTC Returns

Bitcoin hourly log-returns --- heavy tails (kurtosis ~18), volatility clustering, and leverage effects.

BTC Volatility

Bitcoin realized volatility --- rolling 24h std of log-returns, exhibits long memory

BTC Volume

Bitcoin hourly trading volume (log-transformed) --- extreme burstiness with power-law spikes, strong autocorrelation, and intraday seasonal…

ETH/BTC Ratio

Ethereum-to-Bitcoin price ratio --- cross-asset relative strength with regime shifts

NASDAQ Returns

NASDAQ Composite daily close-to-close log returns (^IXIC, 1971+).

Nikkei Returns

Nikkei 225 daily close-to-close log returns (FRED NIKKEI225, 1949+).

S&P 500 Returns

S&P 500 daily close-to-close log returns (^GSPC, 1928+).

speech (4)

English Literature

Real Project Gutenberg text --- Austen, Carroll, Doyle, Melville (2.8MB).

Speech "Five"

FSDD spoken digit 'five', 8 kHz waveform.

Speech "Nine"

FSDD spoken digit 'nine', 8 kHz waveform.

Speech "Zero"

FSDD spoken digit 'zero', 8 kHz waveform.