Hendrick Research

GENCHASE / PUBLIC CATALOG

A workspace for
scientific curiosity.

One collection, many ways to explore. Each technique is a studio tab, with its implementation family shown alongside it. Browse by topic, find a method, or scan the studio index.

This is a public descriptive guide.
The implementation and source code are private.

How the workspace fits together

Art and print studio

Select a technique, adjust its controls and create a plate from a seeded simulation.

Check simulations

Run the workspace’s recorded checks locally.

Run experiments

Run bounded research experiments locally.

Browse all modules

Search registered techniques by name, equation, reference, topic and recorded evidence.

Type a formula

Choose a supported technique and edit a formula.

Seeds and recipes

Preserve the seed and selected parameters; exact results depend on version, precision, platform and resolution.

Gallery

Save selected recipes in local browser storage.

Timeline

Review session history and undo prior changes.

Print and export

Choose print dimensions, pixel density and optional caption parts; additional export formats depend on the technique.

Record

Capture clips of supported living plates.

Science report

Read the technique’s registered evidence and its limitations.

Ambient

Walk through techniques on a 30 second timer with fresh seeds.

Focus

Hide workspace controls to view the plate.

Techniques

135 entries

Catalog entries

Sample render of Artificial Life, preset Gliders

Sample render

Selected preset: Gliders

TechniqueExploratory

Artificial Life

Neuroscience and collective systems

Lenia, Flow Lenia and cellular automata

Family
life
Presets
9
Living simulation
Sample render of Physarum 3D, preset Cosmic web

Sample render

Selected preset: Cosmic web

TechniqueExploratory

Physarum 3D

Growth and patterns

slime mold agents building a filament network in a volume

Family
physarum3d
Presets
6
Sample render of Cortical Planforms, preset Spiral

Sample render

Selected preset: Spiral

TechniqueExploratory

Cortical Planforms

Neuroscience and collective systems

a neural field patterning, seen through the retinocortical map

Family
cortex
Studio tab
Cortex
Presets
7
Living simulation
Sample render of Nonlinear Active Mixture, preset Constant coupling

Sample render

Selected preset: Constant coupling

TechniqueChecks within stated limits

Nonlinear Active Mixture

Waves and fields

nonlinear nonreciprocal fields

Family
nonreciprocal
Studio tab
Active mixture
Presets
6
Living simulation
Sample render of Vortex Lattice, preset Abrikosov lattice

Sample render

Selected preset: Abrikosov lattice

TechniquePartial checks

Vortex Lattice

Neuroscience and collective systems

Gross-Pitaevskii, rotating

Family
bec
Studio tab
Condensate
Presets
7
Living simulationVector export
Sample render of Physarum, preset Veins

Sample render

Selected preset: Veins

TechniqueExploratory

Physarum

Growth and patterns

slime mold agents building a transport network

Family
physarum
Presets
8
Sample render of Phyllotaxis, preset Golden

Sample render

Selected preset: Golden

TechniqueChecks within stated limits

Phyllotaxis

Growth and patterns

discrete inhibitory growth inspired by Douady-Couder

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Presets
4
Living simulationVector export
Sample render of Hastings-Levitov, preset Lightning α=2

Sample render

Selected preset: Lightning α=2

TechniqueExploratory

Hastings-Levitov

Growth and patterns

conformal Laplacian growth

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
HL growth
Presets
4
Vector export
Sample render of Lichtenberg, preset Lightning η=4

Sample render

Selected preset: Lightning η=4

TechniqueExploratory

Lichtenberg

Growth and patterns

dielectric breakdown

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Presets
4
Vector export
Sample render of Gravner-Griffeath, preset Stellar dendrite

Sample render

Selected preset: Stellar dendrite

TechniqueExploratory

Gravner-Griffeath

Growth and patterns

mesoscopic snow crystal

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Snowflake
Presets
5
Living simulationVector export
Sample render of Differential Growth, preset Coral

Sample render

Selected preset: Coral

TechniqueExploratory

Differential Growth

Growth and patterns

buckling curves, coral and cortex folding

Family
growth
Presets
8
Vector export
Sample render of Cyclic Competition, preset Pinwheels

Sample render

Selected preset: Pinwheels

TechniqueChecks within stated limits

Cyclic Competition

Waves and fields

rock, paper, scissors in space

Family
rdx
Presets
6
Living simulation
Sample render of Drainage Networks, preset An island

Sample render

Selected preset: An island

TechniqueExploratory

Drainage Networks

Neuroscience and collective systems

stream-power incision against uplift

Family
landscape
Studio tab
Drainage
Presets
7
Vector export
Sample render of Rough Growth, preset Ballistic, KPZ

Sample render

Selected preset: Ballistic, KPZ

TechniquePartial checks

Rough Growth

Neuroscience and collective systems

ballistic deposition and the KPZ exponent

Family
kpz
Studio tab
Roughness
Presets
7
Vector export
Sample render of Foam & Grains, preset Coarsened grains

Sample render

Selected preset: Coarsened grains

TechniqueExploratory

Foam & Grains

Neuroscience and collective systems

the cellular Potts model, coarsening

Family
potts
Studio tab
Froth
Presets
7
Sample render of Liesegang Rings, preset Concentric rings

Sample render

Selected preset: Concentric rings

TechniqueExploratory

Liesegang Rings

Growth and patterns

periodic precipitation in a gel

Family
liesegang
Studio tab
Liesegang
Presets
7
Living simulation
Sample render of Force Chains, preset Poured under gravity

Sample render

Selected preset: Poured under gravity

TechniquePartial checks

Force Chains

Growth and patterns

a granular packing and the network that carries it

Family
grains
Studio tab
Chains
Presets
7
Vector export
Sample render of Magnetic Skyrmions, preset Neel skyrmion

Sample render

Selected preset: Neel skyrmion

TechniqueExploratory

Magnetic Skyrmions

Neuroscience and collective systems

chiral magnets

Family
skyrmion
Studio tab
Skyrmions
Presets
6
Living simulation
Sample render of Neural Populations, preset Driven population

Sample render

Selected preset: Driven population

TechniqueChecks within stated limits

Neural Populations

Neuroscience and collective systems

exact QIF mean-field model

Family
neural-mass
Presets
6
Vector export
Sample render of Flocking, preset Dense clusters

Sample render

Selected preset: Dense clusters

TechniqueExploratory

Flocking

Neuroscience and collective systems

Toner-Tu, a polar active fluid

Family
tonertu
Studio tab
Flock
Presets
7
Living simulation
Sample render of Hyperbolic Turing, preset Spots on {7,3}

Sample render

Selected preset: Spots on {7,3}

TechniqueExploratory

Hyperbolic Turing

Geometry and tilings

reaction-diffusion on a {p,q} tiling

Family
hyperbolic
Studio tab
Curved
Presets
7
Living simulationVector export
Sample render of Schramm-Loewner Evolution, preset Percolation, κ = 6

Sample render

Selected preset: Percolation, κ = 6

TechniquePartial checks

Schramm-Loewner Evolution

Geometry and tilings

the random curve of critical two-dimensional systems

Family
sle
Studio tab
SLE
Presets
7
Vector export
Sample render of Fractal Geometry, preset Mandelbulb

Sample render

Selected preset: Mandelbulb

TechniqueExploratory

Fractal Geometry

Quantum and optical structures

signed-distance raymarching of 3D fractals

Family
fractal
Presets
8
Sample render of Phase portraits, preset Rational function

Sample render

Selected preset: Rational function

TechniqueExploratory

Phase portraits

Other

domain coloring and enhanced phase portraits of complex functions

Family
dynamics
Studio tab
Phase
Presets
6
Sample render of Gravitational Lens, preset Einstein ring

Sample render

Selected preset: Einstein ring

TechniqueExploratory

Gravitational Lens

Waves and fields

thin-lens mapping

Family
lens
Studio tab
Lens
Presets
7
Sample render of Rotor Routers, preset The rotor quilt

Sample render

Selected preset: The rotor quilt

TechniqueExploratory

Rotor Routers

Geometry and tilings

rotor-router aggregation and internal DLA

Family
sandpile
Studio tab
Rotor
Presets
7
Sample render of Cosmic Web, preset Local universe

Sample render

Selected preset: Local universe

TechniqueExploratory

Cosmic Web

Growth and patterns

Zel'dovich adhesion

Family
web
Studio tab
Web
Presets
7
Sample render of Faraday Waves, preset Oscillon

Sample render

Selected preset: Oscillon

TechniqueExploratory

Faraday Waves

Waves and fields

parametrically driven layer

Family
faraday
Studio tab
Faraday
Presets
7
Living simulation
Sample render of Thin Film, preset Draining pane

Sample render

Selected preset: Draining pane

TechniqueExploratory

Thin Film

Growth and patterns

draining soap and oil

Family
film
Studio tab
Film
Presets
7
Living simulation
Sample render of Time Crystal, preset Rigid DTC

Sample render

Selected preset: Rigid DTC

TechniqueExploratory

Time Crystal

Waves and fields

Floquet Ising chain, period doubled

Family
timecrystal
Studio tab
Time crystal
Presets
7
Sample render of Growing Domain, preset Doubling cascade

Sample render

Selected preset: Doubling cascade

TechniqueExploratory

Growing Domain

Growth and patterns

Turing patterns on a domain that grows

Family
growdomain
Presets
7
Sample render of Neural-Field Pulse, preset The proved pulse

Sample render

Selected preset: The proved pulse

TechniquePartial checks

Neural-Field Pulse

Other

a traveling pulse of cortical activity

Family
neural-field
Studio tab
Neural Field
Presets
7
Sample render of Spin Ice, preset Almost ice

Sample render

Selected preset: Almost ice

TechniquePartial checks

Spin Ice

Neuroscience and collective systems

square ice, emergent monopoles

Family
spinice
Studio tab
Spin ice
Presets
7
Living simulation
Sample render of Vegetation Bands, preset Tiger bush

Sample render

Selected preset: Tiger bush

TechniqueChecks within stated limits

Vegetation Bands

Waves and fields

tiger bush on a dry hillside

Family
rdx
Presets
7
Living simulation
Sample render of Arctic Circle, preset Four frozen corners

Sample render

Selected preset: Four frozen corners

TechniqueChecks within stated limits

Arctic Circle

Geometry and tilings

random domino tilings of the Aztec diamond

Family
aztec
Presets
6
Vector export
Sample render of Skin Effect, preset Skinned

Sample render

Selected preset: Skinned

TechniqueChecks within stated limits

Skin Effect

Neuroscience and collective systems

non-Hermitian skin, Hatano-Nelson

Family
skin
Studio tab
Skin
Presets
7
Sample render of Random Matrices, preset Independence to rigidity

Sample render

Selected preset: Independence to rigidity

TechniqueChecks within stated limits

Random Matrices

Neuroscience and collective systems

beta-ensemble spectra and Dyson Brownian motion

Family
rmt
Studio tab
Matrices
Presets
7
Vector export
Sample render of Stealthy Points, preset Stealthy

Sample render

Selected preset: Stealthy

TechniqueExploratory

Stealthy Points

Growth and patterns

hyperuniform collective coordinates

Family
stealth
Studio tab
Stealth
Presets
7
Sample render of Lozenge Tilings, preset Arctic circle, a = b = c = 40

Sample render

Selected preset: Arctic circle, a = b = c = 40

TechniqueChecks within stated limits

Lozenge Tilings

Geometry and tilings

random lozenge tilings of a hexagon, exact by coupling from the past

Family
lozenge
Studio tab
Lozenge
Presets
7
Vector export
Sample render of Arago Spot, preset Arago spot

Sample render

Selected preset: Arago spot

TechniquePartial checks

Arago Spot

Waves and fields

Poisson bright spot behind a disk

Family
arago
Studio tab
Arago
Presets
6
Sample render of Spanning Trees, preset One uniform spanning tree

Sample render

Selected preset: One uniform spanning tree

TechniqueChecks within stated limits

Spanning Trees

Geometry and tilings

uniform spanning trees by loop-erased random walk

Family
ust
Studio tab
Trees
Presets
7
Vector export
Sample render of Neural Patterns, preset Silk

Sample render

Selected preset: Silk

TechniqueExploratory

Neural Patterns

Neuroscience and collective systems

compositional pattern-producing networks evaluated per pixel

Family
cppn
Presets
8
Sample render of Rogue Wave, preset Peregrine

Sample render

Selected preset: Peregrine

TechniqueChecks within stated limits

Rogue Wave

Waves and fields

Peregrine soliton, waves from nowhere

Family
rogue
Studio tab
Rogue
Presets
6
Sample render of Hodgkin-Huxley Membranes, preset Repeated responses

Sample render

Selected preset: Repeated responses

TechniqueChecks within stated limits

Hodgkin-Huxley Membranes

Neuroscience and collective systems

sodium and potassium gates

Family
hodgkin-huxley
Studio tab
Membranes
Presets
6
Sample render of Aharonov-Bohm, preset Shifted

Sample render

Selected preset: Shifted

TechniqueExploratory

Aharonov-Bohm

Waves and fields

phase from a field the particle never enters

Family
aharonov
Studio tab
Aharonov
Presets
6
Sample render of Double pendulum flip time, preset Full square

Sample render

Selected preset: Full square

TechniqueExploratory

Double pendulum flip time

Particles and dynamics

first flip of a chaotic double pendulum

Family
dynamics
Studio tab
Pendulum
Presets
6
Sample render of Double pendulum tangle, preset E = 0, in the proof

Sample render

Selected preset: E = 0, in the proof

TechniqueExploratory

Double pendulum tangle

Other

homoclinic tangle on the energy section

Family
dptangle
Studio tab
Tangle
Presets
6
Vector export
Sample render of Anderson, preset Localised

Sample render

Selected preset: Localised

TechniqueExploratory

Anderson

Waves and fields

waves that refuse to diffuse

Family
anderson
Presets
6
Sample render of FPUT Chain, preset Nonlinear chain

Sample render

Selected preset: Nonlinear chain

TechniqueChecks within stated limits

FPUT Chain

Particles and dynamics

nonlinear chain and mode energy

Family
fput
Studio tab
FPUT
Presets
6
Sample render of Schrödinger, preset Double slit

Sample render

Selected preset: Double slit

TechniqueChecks within stated limits

Schrödinger

Waves and fields

wave packet on a detector

Family
wavesflow
Presets
9
Living simulation
Sample render of Maxwell FDTD, preset Dielectric disk

Sample render

Selected preset: Dielectric disk

TechniqueChecks within stated limits

Maxwell FDTD

Waves and fields

electric and magnetic waves

Family
maxwell
Studio tab
Maxwell
Presets
6
Living simulation
Sample render of Kinetic Plasma, preset Two moving populations

Sample render

Selected preset: Two moving populations

TechniqueChecks within stated limits

Kinetic Plasma

Waves and fields

electrons in phase space

Family
plasma
Studio tab
Plasma
Presets
6
Living simulation
Sample render of Excitable Media, preset Spiral pair

Sample render

Selected preset: Spiral pair

TechniqueChecks within stated limits

Excitable Media

Waves and fields

spirals, targets and wave turbulence

Family
rdx
Presets
7
Living simulation
Sample render of KdV Soliton, preset Collision

Sample render

Selected preset: Collision

TechniqueChecks within stated limits

KdV Soliton

Waves and fields

a wave that will not disperse

Family
soliton
Studio tab
Soliton
Presets
6
Sample render of Cyclic Automaton, preset Griffeath 14

Sample render

Selected preset: Griffeath 14

TechniqueExploratory

Cyclic Automaton

Neuroscience and collective systems

cyclic and Greenberg-Hastings excitable automata

Family
lattice
Studio tab
Cyclic CA
Presets
7
Living simulation
Sample render of Chimera States, preset Classic chimera

Sample render

Selected preset: Classic chimera

TechniqueExploratory

Chimera States

Neuroscience and collective systems

identical oscillators that split into synchrony and chaos

Family
chimera
Presets
8
Sample render of SSH Edges, preset Topological

Sample render

Selected preset: Topological

TechniqueChecks within stated limits

SSH Edges

Waves and fields

states in a gap that the bulk forbade

Family
ssh
Studio tab
SSH
Presets
6
Sample render of Swarmalators, preset Rainbow ring

Sample render

Selected preset: Rainbow ring

TechniqueExploratory

Swarmalators

Particles and dynamics

oscillators that sync and swarm

Family
swarm
Presets
5
Living simulation
Sample render of Active Model B+, preset Bubbly phase separation

Sample render

Selected preset: Bubbly phase separation

TechniqueChecks within stated limits

Active Model B+

Waves and fields

active conserved phase field

Family
pde
Studio tab
Active B+
Presets
6
Living simulation
Sample render of Aubry-André, preset Localized

Sample render

Selected preset: Localized

TechniqueExploratory

Aubry-André

Quantum and optical structures

localization without disorder

Family
aubry
Studio tab
Aubry
Presets
6
Sample render of Cahn-Hilliard, preset Labyrinth

Sample render

Selected preset: Labyrinth

TechniqueChecks within stated limits

Cahn-Hilliard

Waves and fields

spinodal decomposition

Family
pde
Presets
5
Living simulation
Sample render of Ohta-Kawasaki, preset Lamellae

Sample render

Selected preset: Lamellae

TechniqueChecks within stated limits

Ohta-Kawasaki

Waves and fields

diblock copolymer

Family
pde
Presets
5
Living simulation
Sample render of Hopf Fibration, preset Linked circles

Sample render

Selected preset: Linked circles

TechniqueChecks within stated limits

Hopf Fibration

Quantum and optical structures

every circle linked with every other

Family
hopf
Studio tab
Hopf
Presets
6
Sample render of Swift-Hohenberg, preset Rolls

Sample render

Selected preset: Rolls

TechniqueChecks within stated limits

Swift-Hohenberg

Waves and fields

rolls, hexagons, localized states

Family
pde
Presets
5
Living simulation
Sample render of Phase-field crystal, preset Nucleus

Sample render

Selected preset: Nucleus

TechniqueChecks within stated limits

Phase-field crystal

Waves and fields

Elder density-wave crystal

Family
pde
Studio tab
PFC
Presets
6
Living simulation
Sample render of Lifshitz-Petrich, preset Dodecagonal

Sample render

Selected preset: Dodecagonal

TechniqueExploratory

Lifshitz-Petrich

Quantum and optical structures

two-scale quasicrystal

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
12-fold
Presets
5
Living simulation
Sample render of Pendry Cloak, preset Cloaked

Sample render

Selected preset: Cloaked

TechniqueExploratory

Pendry Cloak

Waves and fields

a disk that light goes around

Family
cloak
Studio tab
Cloak
Presets
6
Sample render of XY / Kosterlitz-Thouless, preset Bound pairs

Sample render

Selected preset: Bound pairs

TechniqueExploratory

XY / Kosterlitz-Thouless

Neuroscience and collective systems

planar spins, bound vortices and the 1973 unbinding transition

Family
xy
Studio tab
XY / KT
Presets
8
Living simulationVector export
Sample render of Complex Ginzburg-Landau, preset Spiral chaos

Sample render

Selected preset: Spiral chaos

TechniqueChecks within stated limits

Complex Ginzburg-Landau

Waves and fields

spirals, defect chaos, frozen vortex glass

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
CGL
Presets
5
Living simulation
Sample render of Abrikosov, preset Relaxed field

Sample render

Selected preset: Relaxed field

TechniqueChecks within stated limits

Abrikosov

Particles and dynamics

fixed-field order-parameter relaxation

Family
vortex
Studio tab
Vortex
Presets
6
Sample render of Active Nematics, preset Extensile turbulence

Sample render

Selected preset: Extensile turbulence

TechniqueExploratory

Active Nematics

Waves and fields

self-driven rods, ±½ defects and active turbulence

Family
nematic
Studio tab
Nematics
Presets
8
Living simulation
Sample render of Dark Room, preset Dark vertex

Sample render

Selected preset: Dark vertex

TechniqueExploratory

Dark Room

Quantum and optical structures

a polygonal room that a candle cannot fill

Family
darkroom
Studio tab
Dark room
Presets
6
Sample render of Fluid, preset Ink drop

Sample render

Selected preset: Ink drop

TechniqueExploratory

Fluid

Waves and fields

Navier-Stokes dye advected by a stable-fluids solver

Family
fluid
Presets
8
Living simulation
Sample render of Abelian Sandpile, preset Medallion 2¹⁶

Sample render

Selected preset: Medallion 2¹⁶

TechniqueChecks within stated limits

Abelian Sandpile

Neuroscience and collective systems

self-organized criticality

Family
lattice
Studio tab
Sandpile
Presets
7
Sample render of Kakeya, preset Perron tree

Sample render

Selected preset: Perron tree

TechniqueExploratory

Kakeya

Geometry and tilings

a needle rotated in arbitrarily small area

Family
kakeya
Presets
6
Sample render of Kuramoto-Sivashinsky, preset Flame cells

Sample render

Selected preset: Flame cells

TechniqueChecks within stated limits

Kuramoto-Sivashinsky

Waves and fields

cellular flame chaos

Family
pde
Studio tab
KS chaos
Presets
5
Living simulation
Sample render of SG Breather, preset Breather

Sample render

Selected preset: Breather

TechniqueChecks within stated limits

SG Breather

Waves and fields

a lump that oscillates and never radiates

Family
breather
Studio tab
Breather
Presets
6
Sample render of Turing Patterns, preset Spots

Sample render

Selected preset: Spots

TechniqueChecks within stated limits

Turing Patterns

Waves and fields

spots, stripes and hexagons from two chemicals

Family
rdx
Presets
7
Living simulation
Sample render of Holomorphic dynamics, preset Seahorse valley

Sample render

Selected preset: Seahorse valley

TechniqueExploratory

Holomorphic dynamics

Geometry and tilings

escape-time and Newton basins in the complex plane

Family
dynamics
Studio tab
Holomorphic
Presets
9
Sample render of Klein Tunnel, preset Normal incidence

Sample render

Selected preset: Normal incidence

TechniqueExploratory

Klein Tunnel

Geometry and tilings

a barrier a Dirac electron does not notice

Family
klein
Studio tab
Klein
Presets
6
Sample render of Gyroid, preset Slice

Sample render

Selected preset: Slice

TechniqueChecks within stated limits

Gyroid

Geometry and tilings

a periodic nodal approximation

Family
gyroid
Presets
6
Sample render of Dendritic Growth, preset Snowflake

Sample render

Selected preset: Snowflake

TechniqueExploratory

Dendritic Growth

Growth and patterns

phase-field solidification: snowflakes and metal dendrites

Family
dendrite
Presets
8
Living simulation
Sample render of Purcell Swimmer, preset Purcell gait

Sample render

Selected preset: Purcell gait

TechniqueExploratory

Purcell Swimmer

Particles and dynamics

a scallop cannot swim in molasses

Family
purcell
Studio tab
Purcell
Presets
6
Sample render of Exceptional Point, preset Exceptional point

Sample render

Selected preset: Exceptional point

TechniqueChecks within stated limits

Exceptional Point

Quantum and optical structures

two eigenvectors become one

Family
exceptional
Studio tab
Exceptional
Presets
6
Sample render of Direct Gravity, preset Rotating disk

Sample render

Selected preset: Rotating disk

TechniqueChecks within stated limits

Direct Gravity

Particles and dynamics

every pair attracts

Family
direct-gravity
Presets
6
Living simulationVector export
Sample render of Meissner, preset Expelled

Sample render

Selected preset: Expelled

TechniqueChecks within stated limits

Meissner

Geometry and tilings

a field a perfect conductor would have frozen, expelled

Family
meissner
Presets
6
Sample render of Tennis Racket, preset Flip

Sample render

Selected preset: Flip

TechniqueChecks within stated limits

Tennis Racket

Particles and dynamics

the intermediate axis that will not spin

Family
tennis
Studio tab
Tennis
Presets
6
Sample render of Flow Field, preset Studio default

Sample render

Selected preset: Studio default

TechniqueExploratory

Flow Field

Growth and patterns

collision-avoiding strokes in a noise field

Family
flow
Presets
9
Vector export
Sample render of Chemotaxis, preset Spots

Sample render

Selected preset: Spots

TechniqueChecks within stated limits

Chemotaxis

Waves and fields

Keller-Segel aggregation

Family
rdx
Presets
6
Living simulation
Sample render of Smectic focal conics, preset TFCD foam

Sample render

Selected preset: TFCD foam

TechniqueExploratory

Smectic focal conics

Growth and patterns

Dupin cyclides

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Focal conics
Presets
4
Vector export
Sample render of Reaction-Diffusion, preset Coral

Sample render

Selected preset: Coral

TechniqueExploratory

Reaction-Diffusion

Waves and fields

Gray-Scott activator/inhibitor chemistry

Family
reaction
Presets
9
Living simulation
Sample render of Molecular Dynamics, preset Warm material

Sample render

Selected preset: Warm material

TechniqueChecks within stated limits

Molecular Dynamics

Particles and dynamics

Lennard-Jones particles

Family
molecular
Presets
6
Living simulationVector export
Sample render of Aperiodic Tilings, preset Penrose rhombs

Sample render

Selected preset: Penrose rhombs

TechniquePartial checks

Aperiodic Tilings

Geometry and tilings

tiles that cover the plane but never repeat

Family
tilings
Presets
11
Vector export
Sample render of Percolation, preset Site at p_c

Sample render

Selected preset: Site at p_c

TechniqueChecks within stated limits

Percolation

Neuroscience and collective systems

site and bond percolation on the square lattice

Family
lattice
Presets
7
Sample render of Maxwell-Cattaneo heat, preset Sparks

Sample render

Selected preset: Sparks

TechniqueExploratory

Maxwell-Cattaneo heat

Other

heat that travels as a damped wave

Family
cattaneo
Studio tab
Heat waves
Presets
7
Sample render of Shallow Water, preset Colliding drops

Sample render

Selected preset: Colliding drops

TechniqueChecks within stated limits

Shallow Water

Waves and fields

depth, flow and shock waves

Family
shallow
Presets
6
Living simulation
Sample render of Attractors, preset Clifford classic

Sample render

Selected preset: Clifford classic

TechniqueExploratory

Attractors

Particles and dynamics

strange attractors and harmonographs as density maps

Family
attractors
Presets
10
Sample render of Airy Beam, preset Accelerating

Sample render

Selected preset: Accelerating

TechniquePartial checks

Airy Beam

Waves and fields

a wave packet that accelerates with no force

Family
airy
Studio tab
Airy
Presets
6
Sample render of Chirikov map, preset KAM islands

Sample render

Selected preset: KAM islands

TechniqueExploratory

Chirikov map

Particles and dynamics

standard map

Family
swarm
Presets
5
Living simulation
Sample render of Hofstadter butterfly, preset Classic

Sample render

Selected preset: Classic

TechniqueChecks within stated limits

Hofstadter butterfly

Quantum and optical structures

almost-Mathieu spectrum

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Hofstadter
Presets
4
Sample render of Weierstrass, preset Weierstrass

Sample render

Selected preset: Weierstrass

TechniqueChecks within stated limits

Weierstrass

Geometry and tilings

finite lacunary Fourier sums

Family
weierstrass
Presets
6
Sample render of Helmholtz scars, preset Stadium n=520

Sample render

Selected preset: Stadium n=520

TechniqueExploratory

Helmholtz scars

Quantum and optical structures

stadium and cardioid eigenmodes

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Scars
Presets
5
Living simulation
Sample render of Kitaev Chain, preset Majorana ends

Sample render

Selected preset: Majorana ends

TechniqueChecks within stated limits

Kitaev Chain

Quantum and optical structures

a fermion that is its own antiparticle, stuck to the ends

Family
kitaev
Studio tab
Kitaev
Presets
6
Sample render of Optical caustics, preset Pool floor

Sample render

Selected preset: Pool floor

TechniqueExploratory

Optical caustics

Quantum and optical structures

folds and cusps of a light field

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Caustics
Presets
4
Sample render of Veselago Lens, preset n = −1 focus

Sample render

Selected preset: n = −1 focus

TechniquePartial checks

Veselago Lens

Waves and fields

a slab that focuses because n is negative

Family
veselago
Studio tab
Veselago
Presets
6
Sample render of Devil's Staircase, preset Arnold tongues

Sample render

Selected preset: Arnold tongues

TechniqueChecks within stated limits

Devil's Staircase

Geometry and tilings

finite-time circle-map rotation estimates

Family
devil
Studio tab
Devil
Presets
6
Sample render of Talbot carpet, preset Classic carpet

Sample render

Selected preset: Classic carpet

TechniqueChecks within stated limits

Talbot carpet

Quantum and optical structures

near-field self-imaging

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Talbot
Presets
4
Sample render of Hydrogen orbitals, preset 3d z² torus

Sample render

Selected preset: 3d z² torus

TechniquePartial checks

Hydrogen orbitals

Particles and dynamics

hydrogen atom probability density |ψₙₗₘ|²

Family
dynamics
Studio tab
Orbitals
Presets
7
Sample render of Loschmidt Echo, preset Loschmidt echo

Sample render

Selected preset: Loschmidt echo

TechniqueExploratory

Loschmidt Echo

Particles and dynamics

a gas that unmixes when you flip every arrow

Family
loschmidt
Studio tab
Loschmidt
Presets
6
Sample render of Fisher-KPP, preset Growth rings

Sample render

Selected preset: Growth rings

TechniqueExploratory

Fisher-KPP

Other

invasion fronts and arrival times

Family
fisher-kpp
Presets
7
Sample render of Wave volume, preset Crossed waves

Sample render

Selected preset: Crossed waves

TechniqueChecks within stated limits

Wave volume

Waves and fields

three-dimensional wave equation

Family
volume-wave
Presets
5
Living simulation
Sample render of Boy's Surface, preset Boy

Sample render

Selected preset: Boy

TechniqueExploratory

Boy's Surface

Geometry and tilings

a projective plane sewn into R³

Family
boy
Studio tab
Boy
Presets
6
Sample render of Indra's Pearls, preset Necklace

Sample render

Selected preset: Necklace

TechniqueExploratory

Indra's Pearls

Growth and patterns

Schottky limit set

Family
cgl-hofstadter-scars-caustics-smectic-hl-phyllotaxis
Studio tab
Pearls
Presets
4
Vector export
Sample render of Ising Model, preset Critical point

Sample render

Selected preset: Critical point

TechniqueChecks within stated limits

Ising Model

Neuroscience and collective systems

Metropolis Monte Carlo on the square lattice

Family
lattice
Studio tab
Ising
Presets
7
Living simulation
Sample render of Thouless Pump, preset Chern 1

Sample render

Selected preset: Chern 1

TechniqueExploratory

Thouless Pump

Quantum and optical structures

a clock that pumps a whole electron per turn

Family
thouless
Studio tab
Thouless
Presets
6
Sample render of Rayleigh-Bénard, preset Plumes

Sample render

Selected preset: Plumes

TechniqueChecks within stated limits

Rayleigh-Bénard

Waves and fields

heated from below

Family
wavesflow
Studio tab
Convection
Presets
7
Living simulation
Sample render of Reuleaux, preset Rotated overlays

Sample render

Selected preset: Rotated overlays

TechniqueChecks within stated limits

Reuleaux

Geometry and tilings

a non-circle of constant width

Family
reuleaux
Presets
6
Sample render of Parametric Surfaces, preset Enneper saddle

Sample render

Selected preset: Enneper saddle

TechniqueChecks within stated limits

Parametric Surfaces

Geometry and tilings

Enneper, Dini and the catenoid-helicoid family

Family
surfaces
Studio tab
Surfaces
Presets
6
Vector export
Sample render of Apollonian, preset Gasket

Sample render

Selected preset: Gasket

TechniqueChecks within stated limits

Apollonian

Geometry and tilings

finite tangent-circle packing

Family
apollonian
Presets
6
Sample render of Chladni & Waves, preset Classic plate

Sample render

Selected preset: Classic plate

TechniqueChecks within stated limits

Chladni & Waves

Quantum and optical structures

standing waves, nodal lines and interference

Family
chladni
Presets
8
Vector export
Sample render of Track, preset Spiral

Sample render

Selected preset: Spiral

TechniqueExploratory

Track

Growth and patterns

a breather that paves the index it runs on, drawn as its worldline

Family
track
Presets
7
Sample render of Knotted Light, preset Weave

Sample render

Selected preset: Weave

TechniqueExploratory

Knotted Light

Geometry and tilings

a trefoil of darkness, an open book, a bark with no tangent

Family
knotlight
Studio tab
Knot
Presets
6
Sample render of Caustic Sea, preset Fold lock

Sample render

Selected preset: Fold lock

TechniqueExploratory

Caustic Sea

Waves and fields

a sea that focuses its own light, and the light that writes the sea

Family
causticsea
Studio tab
Sea
Presets
6
Living simulation
Sample render of Soliton Web, preset Y-junction

Sample render

Selected preset: Y-junction

TechniqueExploratory

Soliton Web

Waves and fields

resonant line-soliton webs of the Kadomtsev-Petviashvili equation

Family
kp
Studio tab
KP
Presets
7
Living simulation
Sample render of Gerstner, preset Gentle swell

Sample render

Selected preset: Gentle swell

TechniqueChecks within stated limits

Gerstner

Waves and fields

trochoidal waves, the exact Euler deep-water solution

Family
gerstner
Presets
7
Living simulationVector export
Sample render of Figure Eight, preset Figure eight

Sample render

Selected preset: Figure eight

TechniqueChecks within stated limits

Figure Eight

Particles and dynamics

three equal masses chasing on a planar figure-eight

Family
eight
Studio tab
Eight
Presets
7
Living simulationVector export
Sample render of Peakon, preset One peakon

Sample render

Selected preset: One peakon

TechniqueChecks within stated limits

Peakon

Waves and fields

Camassa-Holm peaked traveling waves

Family
peakon
Presets
7
Living simulation
Sample render of Photon Sphere, preset Photon ring

Sample render

Selected preset: Photon ring

TechniqueChecks within stated limits

Photon Sphere

Waves and fields

Schwarzschild photon sphere

Family
photon
Studio tab
Photon
Presets
7
Sample render of Crapper, preset Ripple

Sample render

Selected preset: Ripple

TechniqueExploratory

Crapper

Waves and fields

exact finite-amplitude pure-capillary waves

Family
crapper
Presets
7
Living simulationVector export
Sample render of Hasimoto, preset Loop

Sample render

Selected preset: Loop

TechniqueChecks within stated limits

Hasimoto

Waves and fields

a soliton on a vortex filament

Family
hasimoto
Presets
7
Living simulationVector export
Sample render of Lump, preset One lump

Sample render

Selected preset: One lump

TechniqueChecks within stated limits

Lump

Waves and fields

KP-I lumps

Family
lump
Presets
7
Living simulation
Sample render of Equal-pair three-vortex collapse, preset Octant lock

Sample render

Selected preset: Octant lock

TechniqueChecks within stated limits

Equal-pair three-vortex collapse

Particles and dynamics

ω₀ t_c ≥ √2 on Gröbli's collapsing triangle, circulations (1, 1, −1/2)

Family
three-vortex-bound
Studio tab
Equal-pair collapse
Presets
8
Living simulationVector export
Sample render of Parallelogram lock, preset Lock

Sample render

Selected preset: Lock

TechniqueChecks within stated limits

Parallelogram lock

Particles and dynamics

|ω₀| t_c ≥ 3√5/4 on Novikov-Sedov's parallelogram

Family
parallelogram-lock
Studio tab
Parallelogram
Presets
7
Living simulationVector export
Sample render of Quincunx lock, preset Lock

Sample render

Selected preset: Lock

TechniqueChecks within stated limits

Quincunx lock

Particles and dynamics

|ω₀| t_c ≥ 3√33/16 on Novikov-Sedov's five-vortex quincunx

Family
quincunx-lock
Studio tab
Quincunx
Presets
7
Living simulationVector export
Sample render of Polygon collapse bounds, preset Minimum

Sample render

Selected preset: Minimum

TechniqueChecks within stated limits

Polygon collapse bounds

Particles and dynamics

Two regular polygons

Family
double-triangle-bound
Studio tab
Polygon bounds
Presets
7
Living simulationVector export

Images are sample renders, not scientific validation. Evidence labels describe recorded internal checks and their stated limits. Techniques without recorded validation are marked exploratory.

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