PHENOMENA STUDIES WEAVER AXIOM
Studies Archive About

Weaving physical phenomena into visual form.

Model-driven simulation, curated parameter exploration. Personal project.

EIGHT FAMILIES

A Reaction-diffusion & phase-field 07 STUDIES B Eigenmodes & standing waves 03 STUDIES C Chaos & attractors 04 STUDIES D Waves & optics 04 STUDIES E Growth & aggregation 04 STUDIES F Spins & phase transitions 04 STUDIES G Collective & discrete rules 05 STUDIES H Fluid dynamics 03 STUDIES
OBSERVATORY MAP EIGHT FAMILIES · EIGHTEEN PHENOMENA
A

Reaction-diffusion & phase-field

反応拡散・相場 07 STUDIES

fields that react and spread — one ping-pong engine, many chemistries

Belousov–Zhabotinsky Reaction 01  ·  OBSERVED Belousov–Zhabotinsky Reaction Oregonator (2-var, Tyson-Fife) Gray-Scott Reaction-Diffusion 02  ·  IN OBSERVATION Gray-Scott Reaction-Diffusion Gray-Scott BZ II — Thermal Fields 04  ·  IN OBSERVATION BZ II — Thermal Fields Oregonator x Arrhenius thermal field Phase Separation 08  ·  IN OBSERVATION Phase Separation Cahn-Hilliard BZ III — Scroll Waves 11  ·  IN OBSERVATION BZ III — Scroll Waves Oregonator 3D (scroll waves) Meinhardt Seashells 19  ·  IN OBSERVATION Meinhardt Seashells Gierer-Meinhardt activator-inhibitor (3-var, slow refractory hormone) Chemotaxis — The 8π Gate 31  ·  IN OBSERVATION Chemotaxis — The 8π Gate Patlak-Keller-Segel chemotaxis (parabolic-parabolic, volume filling + growth)
B

Eigenmodes & standing waves

定在波・固有モード 03 STUDIES

resonance — geometry written by vibration

Chladni Figures 03  ·  IN OBSERVATION Chladni Figures Chladni plate modes Quantum Billiards 23  ·  IN OBSERVATION Quantum Billiards Stadium billiard (Bunimovich) — Helmholtz eigenproblem Faraday Waves 29  ·  IN OBSERVATION Faraday Waves Damped Mathieu surface modes (Benjamin-Ursell 1954)
C

Chaos & attractors

カオス・アトラクタ 04 STUDIES

deterministic equations, unpredictable fates

Lorenz Attractor 05  ·  IN OBSERVATION Lorenz Attractor Lorenz system (1963) Magnetic Pendulum Basins 15  ·  IN OBSERVATION Magnetic Pendulum Basins planar magnetic pendulum de Jong / Clifford Maps 21  ·  IN OBSERVATION de Jong / Clifford Maps de Jong / Clifford iterated maps (2D, dissipative) Standard Map 32  ·  IN OBSERVATION Standard Map Chirikov standard map (kicked rotor, area-preserving)
D

Waves & optics

波動・光学 04 STUDIES

superposition and refraction — water and light as media

Wave Interference 06  ·  IN OBSERVATION Wave Interference point-source wave superposition Caustics 14  ·  IN OBSERVATION Caustics geometric-optics ray map Talbot Carpet 28  ·  IN OBSERVATION Talbot Carpet Paraxial Talbot mode sum (fractional revivals / Gauss sums) Kelvin Wake — Ship Waves 34  ·  IN OBSERVATION Kelvin Wake — Ship Waves Linear dispersive water waves, moving-pressure forcing (Kelvin 1887)
E

Growth & aggregation

成長・凝集 04 STUDIES

forms that build themselves, particle by particle

Diffusion-Limited Aggregation 09  ·  IN OBSERVATION Diffusion-Limited Aggregation DLA / dielectric breakdown (eta) Snowflake 16  ·  IN OBSERVATION Snowflake Gravner-Griffeath snowfake (2008) Viscous Fingering 22  ·  IN OBSERVATION Viscous Fingering One-sided radial Hele-Shaw (Saffman-Taylor) Cellular Froth — Grain Growth 27  ·  IN OBSERVATION Cellular Froth — Grain Growth Q-state Potts grain growth (Anderson–Srolovitz–Grest–Sahni 1984)
F

Spins & phase transitions

磁性・相転移 04 STUDIES

order against heat — criticality and topology

Ising Model 10  ·  IN OBSERVATION Ising Model 2D Ising (Metropolis) XY Model — Vortex Unbinding 17  ·  IN OBSERVATION XY Model — Vortex Unbinding 2D XY (Berezinskii-Kosterlitz-Thouless) Percolation — The Threshold 26  ·  IN OBSERVATION Percolation — The Threshold 2D site percolation, square lattice Ferrofluid — Rosensweig Instability 33  ·  IN OBSERVATION Ferrofluid — Rosensweig Instability Rosensweig interface-energy gradient flow (Cowley–Rosensweig / Gailitis)
G

Collective & discrete rules

集団・同期・離散規則 05 STUDIES

many simple agents, one emergent order

Kuramoto Model 07  ·  IN OBSERVATION Kuramoto Model Kuramoto mean-field Vicsek Model 13  ·  IN OBSERVATION Vicsek Model Vicsek flocking (1995) Lenia — Emergent Individuality 20  ·  IN OBSERVATION Lenia — Emergent Individuality Lenia (Chan 2019, single-kernel) Physarum 24  ·  IN OBSERVATION Physarum Jones multi-agent Physarum approximation (2010) Abelian Sandpile — Self-Organized Criticality 30  ·  IN OBSERVATION Abelian Sandpile — Self-Organized Criticality Abelian sandpile (Bak-Tang-Wiesenfeld), threshold 4, open boundary
H

Fluid dynamics

流体 03 STUDIES

flow — vortices, wakes and convection

Kármán Vortex Street 12  ·  IN OBSERVATION Kármán Vortex Street von Karman point-vortex street Rayleigh–Bénard Convection 18  ·  IN OBSERVATION Rayleigh–Bénard Convection 2D Boussinesq, vorticity–streamfunction (Saltzman 1962, free-slip) Kelvin–Helmholtz Instability 25  ·  IN OBSERVATION Kelvin–Helmholtz Instability 2D Boussinesq, vorticity–streamfunction (tanh shear layer)
FEATURED CHAPTERS 8 FAMILIES · FULL-BLEED
obs 01 — spiral wavefront f 1.8 · q 0.001 ε 0.030 — collision band

STUDY #01  ·  2026-07  ·  FAMILY A

Belousov–Zhabotinsky Reaction

A visual study of an oscillating chemical reaction — one that refuses to settle, cycling instead through waves, spirals, and labyrinths.

REACTION-DIFFUSION · OREGONATOR-STYLE · SPIRAL WAVEFRONT

EXPLORE STUDY →
OBS — LIVE FIELD f 1.8 · q 0.001 · ε 0.030

STUDY #03  ·  2026  ·  FAMILY B

Chladni Figures

Sand fleeing the antinodes and gathering on the nodal lines — standing waves made visible, drawn by matter.

PLATE EIGENMODES · NODAL LINES · SELF-ORGANISATION

EXPLORE STUDY →
AMBIENT LOOP — DISC ECLIPSE Ω 2.5 · eccentric drive

STUDY #05  ·  2026  ·  FAMILY C

Lorenz Attractor

The first picture of chaos — three equations that never repeat, yet always fall onto the same two-winged shape. Drawn as a long exposure.

DETERMINISTIC CHAOS · ORBIT DENSITY · BUTTERFLY ⇄ TWIN GALAXIES

EXPLORE STUDY →
OBS — ORBIT DENSITY · LONG EXPOSURE σ 10 · ρ 28 · β 8/3 · view spin

STUDY #14  ·  2026  ·  FAMILY D

Caustics

The dancing web of light on a pool floor — every ripple a lens, the refracted rays folding into bright lines. Only two letters exist: smooth folds and pointed cusps.

CATASTROPHE OPTICS · REFRACTION · FOLD + CUSP

EXPLORE STUDY →
OBS — FOCUSING ARC · d̃ 0.45 ⇄ 2.6 4.2M photons · real dispersion · noon pool

STUDY #09  ·  2026  ·  FAMILY E

Diffusion-Limited Aggregation

Particles wander in one at a time and freeze on first touch. Tips screen the interior, so the cluster branches into a self-similar frost.

DENDRITES · FRACTAL GROWTH · ARRIVAL TIME

EXPLORE STUDY →
OBS — GROWTH ARC · D ≈ 1.71 η 1 · point seed · frost

STUDY #17  ·  2026  ·  FAMILY F

XY Model — Vortex Unbinding

Topological defects that are born in pairs and can only die in pairs, imaged like a liquid-crystal film between crossed polarizers. A phase transition with no broken symmetry.

KOSTERLITZ–THOULESS · VORTEX PAIRS · SCHLIEREN

EXPLORE STUDY →
OBS — PAIR ANNIHILATION · Σq = 0 T_KT 0.893 · defects 21940 → 20

STUDY #13  ·  2026  ·  FAMILY G

Vicsek Model

Thousands of self-propelled particles, each turning toward its neighbours' average heading — lower the noise and a flock ignites out of a gas. The hue on screen is the order parameter.

FLOCKING · SELF-PROPELLED · HUE = HEADING

EXPLORE STUDY →
OBS — ORDER PARAMETER va · hue spread η 4.8 ⇄ 0.22 · starling

STUDY #12  ·  2026  ·  FAMILY H

Kármán Vortex Street

Vortices peel alternately off a wake — one spin warm, the other cool — and drift downstream in the staggered double row that hums in wires and trails downwind of islands.

VORTEX SHEDDING · STREAKLINES · h:l ≈ 0.28

EXPLORE STUDY →
OBS — STAGGERED ROWS · h/l ≈ 0.30 St 0.22 · a 0.70 · satellite
INDEX / ARCHIVE EIGHTEEN STUDIES · EIGHTEEN PHENOMENA
  1. 01 Belousov–Zhabotinsky Reaction OBSERVED
  2. 02 Gray-Scott Reaction-Diffusion IN OBSERVATION
  3. 03 Chladni Figures IN OBSERVATION
  4. 04 BZ II — Thermal Fields IN OBSERVATION
  5. 05 Lorenz Attractor IN OBSERVATION
  6. 06 Wave Interference IN OBSERVATION
  7. 07 Kuramoto Model IN OBSERVATION
  8. 08 Phase Separation IN OBSERVATION
  9. 09 Diffusion-Limited Aggregation IN OBSERVATION
  10. 10 Ising Model IN OBSERVATION
  11. 11 BZ III — Scroll Waves IN OBSERVATION
  12. 12 Kármán Vortex Street IN OBSERVATION
  13. 13 Vicsek Model IN OBSERVATION
  14. 14 Caustics IN OBSERVATION
  15. 15 Magnetic Pendulum Basins IN OBSERVATION
  16. 16 Snowflake IN OBSERVATION
  17. 17 XY Model — Vortex Unbinding IN OBSERVATION
  18. 18 Rayleigh–Bénard Convection IN OBSERVATION
  19. 19 Meinhardt Seashells IN OBSERVATION
  20. 20 Lenia — Emergent Individuality IN OBSERVATION
  21. 21 de Jong / Clifford Maps IN OBSERVATION
  22. 22 Viscous Fingering IN OBSERVATION
  23. 23 Quantum Billiards IN OBSERVATION
  24. 24 Physarum IN OBSERVATION
  25. 25 Kelvin–Helmholtz Instability IN OBSERVATION
  26. 26 Percolation — The Threshold IN OBSERVATION
  27. 27 Cellular Froth — Grain Growth IN OBSERVATION
  28. 28 Talbot Carpet IN OBSERVATION
  29. 29 Faraday Waves IN OBSERVATION
  30. 30 Abelian Sandpile — Self-Organized Criticality IN OBSERVATION
  31. 31 Chemotaxis — The 8π Gate IN OBSERVATION
  32. 32 Standard Map IN OBSERVATION
  33. 33 Ferrofluid — Rosensweig Instability IN OBSERVATION
  34. 34 Kelvin Wake — Ship Waves IN OBSERVATION
ABOUT / COLOPHON

Phenomena Studies is an online museum of physical phenomena — collected aesthetically and computationally. Each study pairs a model-driven simulation with curated parameter exploration: the model runs live, the parameters are swept, and every image is chosen by eye.

A personal visual research project by Satoshi N. One phenomenon at a time, observed until it holds a picture.

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