msketches | funnyscar

mmachine generated

yeah there are some days i just don't feel like waking up. def fatigued by the noise, so i decided to take a bit of a career break and do a little kaparthy/shannon-style exploration. I just let claude take a wack at a problem...to get a feel of its capabilities. on the other hand, it pushes you to try terrain no one tried before, like a stream of "what if this happened..." for all things software, it's decent and fast (just absolute no sense of aesthetics though). Anyways, here they are...

Three Möbius maps played as a chaos game, their fractal limit set wrapped over the Riemann sphere.

Complex Function Portraits

Domain-colouring phase portraits of any f(z) you type, with an adaptive contour mesh in the style of Ricky Reusser's complex function plotter.

Xmorphia — the Gray-Scott Parameter Map

One reaction-diffusion system whose feed and kill rates alone decide between spots, stripes, mazes and cells that split like bacteria.

Atomic Collapse in Graphene

Overload a charge on graphene and its electrons spiral inward instead of orbiting, a resonance diving below the Dirac point — the collapse predicted for superheavy nuclei.

Multi-Scale Turing Patterns

Turing's spot-making rule run at many sizes at once, each pixel following whichever scale makes its neighbourhood look calmest.

Fermi–Pasta–Ulam–Tsingou Recurrence

A weakly nonlinear string that refuses to thermalise, sloshing energy between low modes and back to the pluck.

Foucault Pendulum

A pendulum's swing plane precesses at exactly Ω sin(latitude), tracing a slow rosette that proves the Earth turns.

Bunimovich Stadium Billiard

A bundle of bouncing paths stays together in a circle forever but is flung apart by every curved-cap bounce in a stretched stadium.

Wilberforce Pendulum

A spring-borne mass trades bouncing for twisting and back again forever, two coupled normal modes beating like out-of-tune piano strings.

Aharonov–Bohm Effect

Double-slit fringes slide sideways when a hidden coil's flux changes, even though no electron ever touches its magnetic field.

Relativistic Starbow

Flying near light speed sweeps every star toward a blazing blue patch ahead while the sky behind fades to ember red.

Anderson Localization

A quantum wave spreads forever on a clean chain of sites but freezes in place the instant the site energies are scattered at random.

Weierstrass Function

A continuous curve with no slope anywhere — zoom in as far as you like and it keeps throwing out fresh wiggles instead of flattening.

Peregrine Rogue Wave

An exact nonlinear-Schrödinger solution: a calm wave train grows one crest to 3x height from nowhere, then sinks back without a trace.

Dirac Belt Trick

A belt twisted by one full turn stays stuck, but a second full turn the same way lets it be worked completely flat again.

A free electron's exact Dirac trajectory corkscrews in tiny loops around its average drift, the loop itself always moving at exactly c.

Peregrine Soliton

The exact closed-form shape of a rogue wave, rising to three times the surrounding height and vanishing without a trace.

A vibrated fluid surface shattering into standing stripes, squares, or hexagons that repeat at half the shaking rate.

XY Model & the Kosterlitz–Thouless Transition

A lattice of free-spinning compass needles whose bound vortex pairs tear apart into a scrambled gas above a critical temperature.

The Weierstrass Function

A continuous curve built from cosine ripples that has no slope anywhere, however far you zoom in.

Foucault's Pendulum

A pendulum that swings in a straight line while its floor trail slowly reveals the Earth turning underneath it.

Random Matrix Universality

Eigenvalues of random symmetric matrices piling into a semicircle and actively repelling their neighbours.

Feynman's Flashing Ratchet

Thermal noise on a lopsided potential turning into steady directed drift once the potential is flashed on and off.

A bundle of near-identical trajectories bouncing off one curved obstacle and fanning out into full chaos.

Arnold Tongues & the Devil's Staircase

A driven oscillator locking its beat to clean rational fractions of the drive, mapped out as widening tongues.

The Swinging Spring

A mass on a spring trading energy forever between bouncing and swinging once its two frequencies hit a 2:1 ratio.

Quantum Wavefunctions

Showing Quantum Wavefunctions in 3D space

Adventures of Stickman

A stickman running through a procedurally generated world, with physics, collisions, and a camera that follows the action.

Using quaternion Julia sets to create a 3D fractal, with orbit traps and distance estimation for ray marching.

Snell's Law to the Brachistochrone

A light beam refracting through a stack of ever-faster layers, its zig-zag path converging on the cycloid of fastest descent as the layers multiply.

The simplest chaotic electronic circuit, its three voltages tracing a double-scroll attractor you could build on a breadboard.

XY Model & Vortices

A field of compass needles whose disorder lives in vortex-antivortex pairs, the Kosterlitz-Thouless topological transition.

Brachistochrone

Beads racing down rival ramps under gravity, with the cycloid always beating the straight line to the bottom.

Hofstadter's Butterfly

The fractal energy spectrum of an electron in a crystal and a magnetic field, drawn from Harper's equation flux by flux.

Recamán's Sequence

A jump-back-or-forward number rule drawn as alternating semicircles, hiding an unsolved question about which integers it visits.

The vibration shapes of a circular membrane, with pitches fixed by the zeros of Bessel functions.

Lagrange Points

The five equilibrium points of a two-body rotating frame and the zero-velocity curves that trap Trojan asteroids.

Perihelion Precession

A tiny relativistic correction to gravity turns a closed Kepler ellipse into a slowly rotating rosette, as Mercury does.

Foucault Pendulum

A swinging pendulum whose plane precesses at Omega sin(latitude) because the Earth turns beneath it.

Buffon's Needle

Matchsticks tossed on a lined floor estimate pi from the fraction that cross a line, a circle constant with no circle.

Elementary Cellular Automata

A row of cells each following one three-neighbour lookup rule, growing fractals and, for rule 110, full computation.

Cyclic Cellular Automaton

Cells that can only tick forward on the colour wheel spontaneously wind random noise into endless spiral waves.

Mach Cone & Doppler

A moving sound source, its wavefronts bunching ahead as pitch rises and folding into a trailing shock cone past Mach 1.

Hénon Attractor

Two lines of arithmetic iterated on a point, collapsing onto a boomerang-shaped fractal of dimension ~1.26.

Chirikov Standard Map

Kicked rotors whose smooth ribbons dissolve into a chaotic sea dotted with surviving island chains as the kick grows.

Rössler Attractor

A spiralling sheet whose edge folds over each lap, the minimal stretch-and-fold recipe for chaos, in 3D.

Arnold's Cat Map

Repeated shearing dissolves an image into static, then Poincaré recurrence snaps it exactly back to the original.

Four random affine maps played as a chaos game trace a fern whose every frond is a copy of the whole.

An ant with a two-line rule scribbles chaos, then abruptly builds a periodic highway and drives off forever.

Ballistic Deposition (KPZ)

Flakes falling and sticking to their neighbours build a porous deposit with a self-affine rough surface.

Burning Ship Fractal

The Mandelbrot recipe with an absolute-value kink, burning the smooth bulbs into a jagged blazing skyline.

Double Pendulum Chaos

A thousand near-identical double pendulums diverging within seconds, deterministic yet unpredictable.

Ulam Prime Spiral

The whole numbers on a square spiral with every prime dotted, lining up along unmistakable diagonal streaks.

Forest-Fire Model

Trees grow, lightning strikes, fire spreads to neighbours; burn scars self-organise to every size at once.

Wave-Packet Dispersion

A bundle of water waves whose crests race forward through the envelope while the group crawls at half the speed.

Heighway Dragon Curve

A paper strip folded a dozen times and unfolded to right angles, tiling the plane and never crossing itself.

Beads bouncing left or right through a peg triangle, always stacking into the same bell curve.

Charged particles looping in a magnetic field and sliding sideways under an electric one, at right angles to both.

Lotka–Volterra Predator & Prey

Predator-vs-prey populations riding closed orbits forever, oscillating a quarter-cycle out of step.

Fermi–Pasta–Ulam–Tsingou Recurrence

A weakly nonlinear string that refuses to thermalise, sloshing energy between low modes and back to the pluck.

Elementary Cellular Automata

The 256 one-dimensional neighbour rules, scrolling as a GPU ping-pong, with Rule 30's chaos as the default.

Lyapunov Fractal

A stability map of the alternating-rate logistic map, coloured gold where the population locks to a cycle and blue where it stays chaotic.

Conway's Game of Life on a continuous domain, self-organising from noise into gliders and living membranes.

Physarum Networks

Tens of thousands of sniff-and-follow agents growing the branching transport network of a slime mould.

Iterated Function Systems

The chaos game painting Barnsley's fern and other affine-map attractors one random point at a time.

Fourier Epicycles

A chain of rotating circles from a discrete Fourier transform retracing a target drawing, one arm per frequency.

Sine-Gordon Ribbon

Topological kink solitons twisting along a chain of coupled pendulums, drawn as a 3D ribbon.

The linked great-circle fibres of the 3-sphere, stereographically projected into orbitable 3D and coloured by base point.

Random lattice clusters labelled on the GPU, with a giant spanning cluster appearing sharply at p ≈ 0.5927.

The hailstone sequence of every number up to a few thousand, drawn back from 1 as a branching turtle path.

The bifurcation diagram of x → r x(1−x), from a period-doubling cascade into chaos and the Feigenbaum constant.

Hyperbolic Tiling

The regular {7,3} heptagonal tiling of the hyperbolic plane, folded per-pixel in the Poincaré disk and streamed by a Möbius flow.

Airy Diffraction

The far-field diffraction pattern of a circular aperture, fifteen wavelengths summed so the Rayleigh-limited rings fringe into colour.

A density portrait of the Mandelbrot set traced from four million escaping orbits across three iteration-depth colour channels.

Lattice Boltzmann Flow

A D2Q9 lattice-Boltzmann fluid shedding a von Kármán vortex street behind a cylinder, coloured by vorticity.

Spinodal Decomposition

The Cahn–Hilliard equation unmixing a quenched blend into a slowly coarsening labyrinth of two phases.

The 8th-power Mandelbulb, the best-known 3D analogue of the Mandelbrot set, distance-estimated and sphere-traced with mouse orbit.

The gyroid triply-periodic minimal surface, sin x cos y + sin y cos z + sin z cos x = 0, ray-marched in 3D.

The recursively hollowed cube of Hausdorff dimension 2.727, distance-estimated by folding space, orbitable in 3D.

A hanging banner as a GPU mass-spring lattice with Verlet integration and per-frame constraint relaxation, in 3D.

Abelian Sandpile

Grains dropped on one site topple at height four, relaxing into a scale-invariant fractal of nested fans.

Jos Stam's unconditionally stable Navier-Stokes solver driving a turbulent rising thermal plume.

Vogel's sunflower model, with spiral-arm counts jumping between Fibonacci numbers as the divergence angle crosses the golden angle.

Finite-difference time-domain electromagnetics: a plane wave refracting through a glass lens to a bright focus.

A Metropolis spin lattice drifting across the Onsager critical point, showing scale-free critical opalescence.

2,304 point masses under brute-force Newtonian attraction undergoing gravitational collapse and violent relaxation.

Apollonian Gasket

The conformal fractal packing of mutually tangent circles, rendered as the limit set of nine circle inversions.

Seven plane waves interfering into a quasiperiodic sevenfold pattern that glides without ever repeating.

The exact nonlinear deep-water wave solution, ray-marched with sky reflection, sun glitter and crest foam.

Belousov-Zhabotinsky Reaction

An excitable-medium model of the oscillating chemical reaction, curling broken wavefronts into rotating spirals and target rings.

Thin-Film Interference

Soap-bubble iridescence from a two-beam interference model over a draining, rippling film.

Basins of attraction for Newton's method on z^5 - 1, with the self-similar fractal boundary between roots.

Curl-Noise Flow

Dye advected by a divergence-free curl-noise velocity field for incompressible, never-pooling motion.

Double-Slit Wave

A finite-difference solution of the 2D wave equation building the classic two-slit interference fan.

Kuramoto Lattice

A grid of coupled phase oscillators seeded with vortices that organise into rotating spiral waves.

Chladni Figures

Sand collecting along the nodal lines of a resonating square plate as it sweeps through vibration modes.

Magnetic Pendulum Fractal

Per-pixel integration of a damped pendulum over three magnets, coloured by which magnet captures it.

Lorenz Attractor

200,000 RK4 tracer particles winding onto the two-winged Lorenz strange attractor.

Dipole Field Lines

Exact flux iso-contours of several precessing in-plane magnetic dipoles reconnecting through null points.

The precessing curve traced by a Victorian pendulum drawing machine from sums of damped sinusoids.

Diffusion-Limited Aggregation

A tree-like dendritic patterns formed by a specific random walk

Lighting strike pattern formation

Young's Double Slit Experiment

Thomas Young's Double Split + Einstein's Photoelectric Effect

Extension of Ricky Reusser's GPU Boids

Statue of David

Roman statues rendering

Reaction-Diffusion

Gray-Scott equations in action (and in nature)

Cells Cells Cells

Mimicking living cells under a microscope

Clifford de Jong Attractor

The famous attractor clifford de jong

Wormhole rendering following DNEG/Kip Thorne's work in Interstellar

Rendering a blackhole in realtime

Complex Functions

Various famous complex functions visualized in the complex plane

Diffusion Base Cases

Watch the heat equation in action

A variation of ricky reusser's water caustics via shader glsl

Graphical explanation of z-pinches as found at Sandia National Laboratory

Cluster to Mosfets

Scaling compute from top to bottom

Spherical Orbitals shown in its probability density function.

Three-body problem and other chaotic systems with periods of stability

Instability Problems

Instability problems in fluid dynamics

Loss Landscapes

Visualization of loss landscapes in neural network optimization

convolutional neural networks

Double Pendulum

Remapping every pixel (theta1, theta2) moved by the double pendulum

Spherical Orbitals

Spherical orbitals derived in any quantum mechanics class