sketches

tiny local rules, surprising global behaviour

• vicsek
  Each particle turns to the average heading of whoever is within one radius, then takes a fixed step, and a random angle of width η spoils the turn. Nothing in the rule prefers a direction — below a critical η four thousand of them pick one anyway. The corner panel is not an illustration: it plots the flock's own order parameter φ against η as the run measures it, one dot at a time, and the dots spray hardest exactly where the transition is. After Vicsek, Czirók, Ben-Jacob, Cohen & Shochet (1995).
• primordial-particles
  One line of motion law and dust condenses into cells that feed, grow and divide. Each cell carries a hue; daughters inherit it, so heredity appears in a world with no genes. After Schmickl, Stefanec & Crailsheim (2016).
• sandpile
  Grains fall one at a time; four grains topple. Nobody tunes anything, and the pile settles at the exact edge where an avalanche can be any size — then draws an apparent power law in the corner. Centre mode: the same rule without noise grows a crystal instead. Sibling reading of the BTW model to aftershock's causal memory. After Bak, Tang & Wiesenfeld (1987).
• aftershock
  A sandpile teaches itself to fail at every scale. The image is not the grains but the fading memory of their avalanches: quiet pressure, hairline slips, world-sized rupture.
• friend-enemy-dots
  Each dot picks one friend and one enemy: step toward the friend, away from the enemy, drift toward centre. Clusters chase clusters. After @IsaacKing314.
• firefly-sync
  Every firefly blinks on its own clock; a neighbour's flash nudges its phase forward. Random twinkling tips into unified pulsing (Kuramoto synchronisation).
• rps-ecology
  Three tribes in a cycle: each chases its prey and flees its predator, converting on contact. Spiral waves and population booms from three lines of logic.
• slime-mold
  Physarum agents build highways between the food you paint, around the walls you draw. Four palettes (incl. paper-ink), four regime presets, and an essay on stigmergy.
• tiny-worlds
  A raymarched fractal landscape unpacked from a formula about the length of a tweet. Five preset worlds, and a mutate button that goes looking for one nobody has seen. After @YoheiNishitsuji's #つぶやきGLSL.
• gossip-dynamics
  Wandering dots hold opinions as colours, drifting toward who they trust and away from who they distrust. Consensus, polarised camps, collapse.
• apparent-self
  Ball bearings roll in and out of their own straight grooves on a wobbling red platter. Nothing couples them, and yet one breathing creature appears. After @jechacas's kinetic sculpture.
• chimera
  Seven hundred identical oscillators on a ring, one identical rule — and the ring divides itself into a locked arc and a drifting one. Drawn as its own recent history, so the split reads as silk beside embers. After Kuramoto 2002 / Abrams & Strogatz 2004.
• desire-paths
  Nobody draws the roads: walkers prefer worn ground, ground heals when unused, and a road network precipitates out of the difference. Drag a town and watch its old roads fade to ghosts. After Helbing, Keltsch & Molnár (Nature 388, 1997).
• biome
  Two chemicals, two numbers, a gradient: spots, worms, mazes and a desert living next to each other on one plate. Textbook Gray–Scott shows one animal; this is a living slice of Pearson's map. The interesting object is the front between climates.
• chladni
  Dust settles where the plate is still. Two notes at once, not a textbook eigenmode: the figure is the silence they share. Pull one note and the diagonal the chord was ringing comes back as a specimen.
• otherwise
  A walk that takes every turn it didn’t. Every walk ends; the drawing is what it leaves. Desire Paths inverted: one walker, every road.