CONTENTS
PULSEのコンテンツ一覧です。
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全 207 コンテンツ
Read (1)
DAILY LOG
Daily journal by ECHO and NULL. Thoughts and observations.
Play (2)
MORSE
Practice Morse code as timing waves and signal pulses.
MAZE
Navigate a generated maze through luminous exploration trails.
Watch (201)
ISS RACE
An orbital race simulation showing ground tracks, laps, and relative lead without external APIs.
FLOCK
Boids visualization where separation, alignment, and cohesion create flocking.
CLOCK
A Canvas particle clock where points flow into seven-segment time fields.
PHYSICS
Touch a physics field of gravity, attraction, collisions, and chains.
PRIMES
Explore prime gaps as luminous rings, record-gap traces, and residue-wheel classes.
FIBONACCI
Phyllotaxis, spirals, and growth fields shaped by the golden angle.
PI
Draw digits of pi as walks, spirals, and chords.
FRACTAL
Explore the Mandelbrot set through zoom and layered color fields.
JULIA SET
Drag through Julia-set parameter space and watch the field morph continuously.
KOCH SNOWFLAKE
Explore recursive Koch curve generation with adjustable angle and depth.
TREE
Grow recursive trees from branch angle and wind-like variation.
LIFE
Explore Conway's Game of Life as a field of density and generations.
SAND
A granular cell simulation for falling, flowing, and fixed matter.
SORT
Watch sorting comparisons and swaps as luminous bar fields.
EVOLUTION
Observe genetic-algorithm generations through motion trails and fitness.
FOURIER
A Fourier epicycle visualization where rotating vectors assemble waveforms.
LANGTON'S ANT
Explore Langton's Ant as multi-state cellular-automaton trails.
REACTION
Grow Gray-Scott reaction diffusion patterns directly on the canvas.
CONSOLE
A nonverbal Canvas signal dashboard with synchronized fields.
LORENZ
Explore multiple Lorenz trajectories and a Poincare section in Canvas.
PENROSE
Explore Penrose-style aperiodic tile orientation and layered patches.
WAVES
Touch and shape a Canvas wave field where multiple sources interfere.
RIPPLE
Layer ripple fields with clicks and drags.
SANDPILE
Visualize Abelian sandpile avalanches and self-organized criticality.
NETWORK
Random graph phase transition. Nodes connect and suddenly become one.
COLLATZ
Draw Collatz sequences as branching trajectories and density fields.
VORONOI
Draw nearest-point space partitions with moving seeds and distance fields.
STRING ART
Connect points on a circle with formulas and let thread density draw curves.
DLA
Draw diffusion-limited aggregation crystals through particle random walks.
LISSAJOUS
Lissajous curves drawn from the phase and frequency of two oscillations.
PERCOLATION
Open grid cells by probability and observe connected clusters near the critical point.
CIRCLE PACKING
Circle packing. Growing circles slowly fill the space.
PATHFIND
Pathfinding algorithms visualized. Watch A*, Dijkstra, and BFS search for the goal.
RULE
1D Cellular Automaton. Complex patterns emerge from simple rules.
BREATHE
A quiet phase-wave breathing visualization drawn on Canvas.
PENDULUM
Manipulate single pendulums, double pendulums, and phase-space traces.
SPIROGRAPH
Spirograph curves drawn by rotating circles and pen offsets.
DRIFT
Random walk. Faint trails left by slowly wandering points.
CLOTH
Touch an elastic cloth mesh built from points and constraints under gravity and wind.
MYCELIUM
Physarum algorithm. Particles follow chemical trails and slowly grow a mycelial network.
CAUSTICS
Optical chaos. Surface ripples bend light and paint slowly drifting caustics.
CHLADNI
Chladni patterns. Particles gather on nodal lines formed by vibration modes, with gentle sound.
FLUID VEIL
Fluid simulation. Shape the flow with your fingertips and watch luminous ink vortices drift slowly.
ISOFIELD
Contour field. Drifting sources shape an invisible scalar field, revealed as slowly glowing isolines.
GALTON BOARD
Galton board. Balls falling through pegs reveal the normal distribution.
N-BODY
N-body gravity simulation. Particles attract each other and trace orbits.
MOBIUS FLOW
Particles flowing on a Möbius strip. Luminous trails drift slowly across a twisted surface.
L-SYSTEM GARDEN
L-system branches grow slowly into a luminous garden and sway with wind.
CYCLIC CA
Cyclic cellular automaton. States chase each other to form luminous spirals and wavefronts.
LEVY DRIFT
Lévy flight. Luminous trails shaped by short wanderings and sudden long leaps.
BÉZIER
Bézier curves. Interpolation of interpolations — visualizing the de Casteljau algorithm.
ISING
Ising model. Spins on a lattice flip via Metropolis algorithm, forming beautiful domain structures near the critical temperature.
EPIDEMIC
SIR epidemic model. Waves of infection sweep across a grid. β controls spread speed, recovery shapes the wave.
NEWTON
Newton fractal. Visualizing Newton-Raphson convergence to roots of z^n−1=0 in the complex plane. The basin boundaries are fractal.
CLIFFORD
Clifford strange attractor. Two simple equations, four parameters, infinite patterns emerge as millions of points accumulate.
BIFURCATION
Logistic map bifurcation diagram. Period-doubling cascade leads to chaos as r increases. Zoom reveals infinite self-similar structure.
APOLLONIAN
Apollonian gasket. A circle-packing fractal where every gap between tangent circles is recursively filled. Governed by Descartes' Circle Theorem.
HILBERT
Hilbert curve. A 1D curve that fills 2D space without gaps — the convergence of a space-filling curve.
KURAMOTO
Kuramoto model. N oscillators weakly coupled — past the critical point, they spontaneously synchronize.
WIREWORLD
Electron flow in a 4-state cellular automaton. Draw wires and inject signals.
ANTCOLONY
Ant colony optimization. Pheromone trails reinforce over time, spontaneously revealing shortest paths.
PREDPREY
Predator and prey. Fish breed, sharks hunt, and Lotka-Volterra oscillations emerge from three simple rules.
MAGNETPENDULUM
Basin-of-attraction fractal from a 3-magnet pendulum. Tiny differences in starting position lead to completely different outcomes.
GAMETHEORY
Spatial prisoner's dilemma. Cooperators and defectors copy strategies on a grid, generating complex emergent patterns.
PURSUIT
N-point pursuit polygon. Each vertex chases the next at constant speed, and logarithmic spirals emerge.
BILLIARD
Chaos billiards. The stadium table is an ergodic chaotic system; ellipse and circle are integrable. Shape determines the fate of trajectories.
SUPERFORMULA
Superformula. Four parameters — m, n1, n2, n3 — generate flowers, leaves, shells, and snowflakes from a single equation.
SOLITON
Solitons from the KdV equation. Waves pass through each other intact after collision — a nonlinear miracle.
MARBLING
Ink drops fall into fluid and spiral. Mathematical marbling simulation.
PENDULUMWAVE
Pendulums of different periods create collective phase patterns. Full resync every 60 seconds.
TESSERACT
Real-time projection of a 4D hypercube. Six rotation axes reveal geometry beyond three dimensions.
CONFORMAL
Conformal mappings via complex functions. Watch a grid distort smoothly through mathematical transformation.
QUANTUM
Quantum tunneling. A wave packet splits into reflected and transmitted parts — experience the Schrödinger equation.
SPINODAL
Spinodal decomposition. A conserved field separates into phases and coarsens into labyrinthine domains.
PARTICLE LIFE
Attraction and repulsion rules between particle species generate self-organizing clusters, vortices, and creature-like emergent behavior.
HENON
Hénon strange attractor. Fractal orbits of a two-dimensional chaotic map. Tune parameters to cross between order and chaos.
ANNEAL
Simulated annealing solves the Travelling Salesman Problem. Watch a hot chaotic path cool into the shortest route.
DOUBLEPEND
Double pendulum chaos. Nearly identical initial conditions diverge exponentially. Lyapunov instability made visible.
LENIA
Continuous cellular automaton. Life-like creatures emerge from convolution and a growth function alone.
LINKAGE
Four-bar linkage kinematics. A rotating crank drives a coupler whose traced point carves closed algebraic curves.
VORTEX
Point vortex dynamics. Add vortices to watch tracers spiral through the potential flow field — Helmholtz vortex laws made visible.
MOIRÉ
Moiré fringes. Two periodic grids overlap — angular difference generates beat-frequency stripes.
CHAOSGAME
Chaos game. Repeatedly jumping toward random vertices reveals hidden fractals.
EFIELD
Electric field visualization. Place point charges and watch field lines reveal spatial structure.
FLOWFIELD
Particles follow a Perlin noise flow field, tracing organic paths through an evolving vector landscape.
TURING
Turing machine. A head reads, writes, and moves on an infinite tape — the archetype of computation.
DIFFGROW
Differential growth. A closed curve subdivides and repels itself into coral-like organic forms.
MODULAR
Modular multiplication. Connect N points on a circle by multiplier k — cardioids and nephroids emerge.
SLIT
Double-slit experiment. Particles pass through slits one by one, and an interference pattern emerges.
OPTICS
2D geometric optics. Rays reflect off mirrors, painting geometric patterns of light.
EROSION
Hydraulic erosion. Raindrops carve terrain, and rivers and valleys emerge naturally.
HYPERBOLIC
Poincaré disk model. Hyperbolic tilings spread infinitely in non-Euclidean space.
KALEIDOSCOPE
Kaleidoscope. Particle trails reflect and rotate under dihedral symmetry D_N, forming geometric patterns.
GRAVLENS
Gravitational lensing. Mass warps spacetime, bending starlight. Einstein rings emerge.
ELASTIC
Kinetic theory of ideal gas. Particle speeds converge to the Maxwell-Boltzmann distribution through elastic collisions.
HARMONOGRAPH
Harmonograph. Delicate geometric patterns drawn by damped pendulums. Frequency ratios and phases create infinite curves.
TRAFFIC
Nagel-Schreckenberg traffic flow model. Traffic jams emerge spontaneously from four simple rules.
CRYSTAL
Hex-grid crystal growth. Diffusion and freezing produce six-fold symmetric dendrites.
PHASE
Phase portrait. Visualize 2D dynamical system trajectories as flowing particles. Map of fixed points, limit cycles, and separatrices.
RECAMÁN
Recamán sequence. Subtract if possible, otherwise add — a simple rule that draws semicircular arcs on the number line.
ULAM
Ulam spiral. Integers on a spiral — primes form mysterious diagonal patterns.
DRAGON
Dragon curve. A self-similar fractal that emerges from repeated paper folding.
DIFFUSION
Heat diffusion simulation. Paint hot and cold sources, draw insulating walls, and watch temperature spread by the heat equation.
MAZEGEN
Maze generation algorithms visualized. Watch four algorithms carve passages through walls.
SHADOW
2D raycasting. Cast rays from light sources to compute visibility polygons and paint light and shadow in real time.
SOFTBODY
Pressure-based soft body simulation. Throw, bounce, and squish spring-mass bodies inflated by internal pressure.
REACH
FABRIK inverse kinematics. Articulated arms reach toward a target through forward-backward iteration.
COLLAPSE
Wave Function Collapse. Tiles resolve one by one through constraint propagation, spreading order from minimum-entropy cells.
SCHELLING
Schelling segregation model. Mild same-type preference produces strong segregation — emergent social physics.
TRUCHET
Truchet tiles. Randomly oriented quarter-circle arcs form labyrinthine flowing patterns.
WILDFIRE
Forest fire model. Tree growth and lightning create self-organized criticality with power-law fire cascades.
GRADIENT
Gradient descent visualized. Watch SGD, Momentum, and Adam descend optimization landscapes.
ROPE
Rope simulation. Verlet integration and distance constraints for chain physics. Grab, swing, and cut.
INTERFERENCE
Wave interference patterns. Multiple sources superpose to form standing wave geometries of constructive and destructive nodes.
LIGHTNING
Dielectric breakdown model. Discharge paths branch and race, leaving Lichtenberg figures behind.
CHIRIKOV
Chirikov standard map. KAM tori float in phase space; as perturbation grows, they dissolve into a sea of Hamiltonian chaos.
QUASICRYSTAL
Quasicrystal interference. N plane waves superpose to reveal quasiperiodic order — neither periodic nor random.
METABALL
Metaballs. Implicit surface isovalues merge and split organically.
WORLEY
Cellular noise. Distance to random seed points paints organic textures.
GALAXY
Spiral galaxy density wave simulation. Thousands of stars in differential rotation form emergent arm structures.
LATTICE
2D lattice vibration. Wave equation on a discrete grid. Tap to create pulses, pin nodes to build barriers.
DOPPLER
Doppler effect. A moving source compresses and stretches wavelengths. Mach cones appear at supersonic speed.
ORBIT
Kepler orbits. A central body's gravity carves conic sections. Launch speed determines ellipse, parabola, or hyperbola.
MAGNETIC
Magnetic field visualization. Flowing particles trace closed field lines from bar magnet dipoles.
TOOTHPICK
Toothpick sequence. Perpendicular branches grow from exposed endpoints, revealing a self-similar fractal.
PASCAL
Pascal's triangle. Color binomial coefficients by mod N and watch self-similar fractals emerge.
NEURAL
Neural network classification boundary in real time. Place data points and watch the network learn.
DELAUNAY
Delaunay triangulation. Place points and watch a mesh form where no circumcircle contains another point. Voronoi duality.
FORD
Ford circles. Every reduced fraction p/q becomes a circle tangent to the x-axis. Two circles touch iff the fractions are Farey neighbors.
LYAPUNOV
Lyapunov fractal. Mapping the Lyapunov exponent across logistic map parameter space reveals fractal boundaries between stability and chaos.
STIPPLE
Weighted Voronoi stippling. Lloyd's algorithm drives point clouds toward density-matched equilibrium — self-organization from randomness to order.
SPRING
Elastic pendulum. A mass on a spring traces chaotic trajectories as swing and bounce modes exchange energy through autoparametric resonance.
IFS
Iterated Function System. Probabilistic affine transforms produce self-similar fractals. Mutate parameters to explore unknown forms.
SPANNING
Minimum Spanning Tree. Prim's algorithm continuously reconnects drifting nodes at minimum cost. A living network.
SCATTER
Lorentz gas. A point particle bounces off periodic circular scatterers, tracing chaotic trajectories. Visualization of the Sinai billiard.
QUADTREE
Quadtree spatial partitioning. Space recursively subdivides by particle density, accelerating range and nearest-neighbor queries.
ROSE
Maurer rose. Connect evenly-spaced points on a rose curve to reveal intricate star-like geometric patterns.
RATCHET
Brownian ratchet. Asymmetric sawtooth potential and thermal noise create directed transport — the principle behind molecular motors.
SYMICON
Symmetric chaos icons. Enforce n-fold rotational symmetry on a chaotic iterated map, and crystal-like structures emerge from chaos.
EXCITABLE
Excitable medium. Click to ignite waves — when a wavefront breaks, self-sustaining spiral waves emerge. The math governing cardiac rhythm.
HULL
Convex hull algorithms visualized. Watch Graham Scan, Jarvis March, and QuickHull trace the outer boundary of a point set step by step.
CHAMBER
Charged particle tracks. Particles spiral through a magnetic field, lose energy, and branch at decay vertices. A bubble chamber reimagined.
QLEARN
Q-Learning. An agent learns optimal paths through trial and error. The value function heat map spreads slowly from the reward.
CYCLOID
Cycloid curves. The path traced by a rolling circle. Experience brachistochrone and tautochrone physics.
KNOT
Torus knots. Adjust p and q to wind a curve on a torus, projected with depth-sorted crossings.
WINDING
Winding number. A closed curve topologically partitions the plane — each region colored by how many times the curve winds around it.
RIPS COMPLEX
Vietoris–Rips complex. As the distance threshold grows, points connect into edges and triangles — a simplicial complex revealing topological features.
TURMITE
Turmite. A generalized Langton's ant. Rule tables of colors and internal states produce triangles, spirals, and fractals.
KÁRMÁN
Kármán vortex street. Lattice Boltzmann simulation of alternating vortices behind an obstacle in fluid flow.
VENATION
Space colonization algorithm. Branches grow toward attraction points, self-organizing into leaf-vein-like structures.
CROWD
Crowd simulation. The social force model drives pedestrians autonomously — lane formation and bottlenecks emerge naturally.
ATOMS
Lennard-Jones molecular dynamics. Attraction and repulsion drive crystallization, melting, and vaporization phase transitions.
INVERSION
Circle inversion. Lines become circles, circles become circles. Place inversion circles and watch geometry transform.
FLAME
Fractal flames. Nonlinear IFS variations produce luminous organic forms via log-density histogram rendering.
SWARMALATOR
Swarmalators. Particles that swarm in space and sync in phase. Five collective states emerge as coupling parameters change.
BUDDHABROT
Buddhabrot. Overlaying escape trajectories from the Mandelbrot iteration reveals a nebula-like luminous structure.
REFRACTION
Optical refraction simulation. Light rays bend at medium boundaries following Snell's law. Beyond the critical angle, total internal reflection traps the light.
FEEDBACK
Visual feedback loop. The screen redraws itself scaled and rotated, creating infinite regress patterns.
CATENARY
Catenary curve. A chain hanging under gravity traces the hyperbolic cosine. Compare it to the parabola.
CATMAP
Arnold's cat map. An area-preserving chaotic transformation shears and mixes a color gradient, yet it perfectly recurs after finite steps.
TOMOGRAPHY
CT-scan Radon transform. Rotating projections form a sinogram, then backprojection reveals the hidden density field.
HOUGH
Hough transform for line detection. Points become sinusoidal votes, and peaks reveal hidden lines.
EIGEN
2x2 linear transform. Drag basis vectors and watch the unit circle, grid, eigen directions, and flow update.
STEINER
Steiner tree. A minimum-length network finds its own 120° junction points to connect terminals optimally.
FRACTURE
Brittle fracture in a spring lattice. Stress concentrates at crack tips while random bond strengths create branching patterns.
DIFFRACT
Fraunhofer diffraction patterns. FFT transforms aperture shapes into far-field interference figures.
MONTECARLO
Monte Carlo estimation. Random points rain down to approximate area. Watch convergence as sample count grows.
PSO
Particle swarm optimization. A swarm explores a fitness landscape — individual memory and collective knowledge guide it toward the global optimum.
STRANGE
Strange attractor explorer. Discover chaotic orbits from Sprott's quadratic map parameter space, rendered as log-density accumulation.
BIOMORPH
Pickover biomorphs. Apply a biomorphic bailout test to complex iteration — organism-like fractals emerge from pure mathematics.
SAW
Self-avoiding walk. A random walker that never revisits a site traps itself in its own trail. The foundational model of polymer physics.
TISSUE
Cellular Potts Model. Extended cells on a lattice self-organize through surface tension and differential adhesion — two cell types spontaneously sort apart.
ORBITAL
Hydrogen electron orbital probability density. Cross-section and Monte Carlo particle cloud visualization of wavefunctions for quantum numbers (n,l,m).
XY MODEL
XY model. Continuous-angle spins on a lattice align with temperature. Vortex defects pair at low temperature and unbind at the BKT transition.
FOAM
2D foam dynamics. Surface tension curves cell walls, von Neumann coarsening shrinks small bubbles, and topology rearranges as cells pop.
COULOMB
Coulomb crystal. Charged particles in a harmonic trap repel each other and self-organize into concentric shell structures.
DOMINO
Random domino tiling of the Aztec diamond. The shuffling algorithm generates uniformly random tilings, and the arctic circle theorem's sharp boundary emerges.
FERROFLUID
Ferrofluid simulation. Place magnets and watch spike structures self-organize from the competition between magnetic force and surface tension.
VISCOUS
Hele-Shaw viscous fingering. A low-viscosity fluid displaces a high-viscosity one, and the interface destabilizes into branching finger patterns.
GRANULAR
Granular flow dynamics. Particles pour through a funnel, force chains glow under load, and neck width governs the jamming transition.
DRUMHEAD
Vibrating circular membrane modes. Bessel-function eigenmodes paint concentric and radial nodal patterns.
KOHONEN
Kohonen self-organizing map. A neural grid deforms itself to match data topology, drawing a map that preserves neighborhood structure.
SCALE-FREE
Scale-free network. Preferential attachment draws new nodes to hubs, and a power-law degree distribution emerges.
CML
Coupled map lattice. A grid of logistic maps with diffusive coupling spawns spatiotemporal chaos and pattern selection.
TRANSPORT
Optimal transport. Particles flow between distributions via greedy assignment and 2-opt refinement, minimizing total displacement.
SDF
Signed distance field. Combine geometric primitives with CSG boolean operations and render the pulsing iso-distance contours.
CONVECTION
Rayleigh-Bénard convection. Heated fluid spontaneously forms convection cells; increasing the Rayleigh number drives the flow from ordered rolls to chaos.
CORIOLIS
Coriolis effect. Straight-line motion on a rotating disk appears to curve. Switch between inertial and rotating frames to experience fictitious forces.
LAGRANGE
Lagrange points of the restricted three-body problem. Effective potential and zero-velocity curves in the co-rotating frame reveal L1-L5 equilibria.
MARKOV
Discrete Markov chain on a state graph. Walkers hop by transition probabilities and the empirical distribution converges to the stationary distribution.
TERMITE
Termite wood-chip sorting. Simple agents pick up isolated chips and drop them near clusters. Self-organization without central control.
SPACETIME
Minkowski spacetime diagram. Lorentz boosts shear the grid while the light cone stays at 45 degrees. Place events, draw worldlines, and watch simultaneity tilt.
ROCHE
Roche limit. When tidal force exceeds self-gravity, a satellite is torn apart and becomes a ring.
WAVE MACHINE
Torsion wave machine. Flick the chain and watch pulses propagate, reflect at fixed/free/absorbing boundaries. A spacetime diagram paints the wave's entire history.
PID
PID controller dynamics. Proportional, integral, and derivative gains shape the step response. Five presets draw five different trajectories toward the same target.
STEREO
Stereographic projection. Sphere patterns—grid, loxodromes, icosahedron—map to circles on the plane, morphing as the sphere rotates.
WALLPAPER
Wallpaper groups. Particle trails replicated by rotation, reflection, and translation tile the plane with crystallographic symmetry.
GEARS
Gear train simulation. Meshing gears transmit rotation ratios through interlocking tooth profiles.
BRAITENBERG
Braitenberg vehicles. Simple sensor-motor wiring produces fear, aggression, love, and exploration from the same light sources.
FRACTION
Continued fraction geometry. The Euclidean algorithm decomposes a rectangle into squares, and the golden ratio produces the perfect spiral.
BOOLEAN
Random Boolean network. N nodes control each other via Boolean functions. A phase transition between order and chaos emerges near K=2.
Guide (2)
ABOUT
About PULSE. Meet ECHO and NULL.