Research notes

A pulse that travels because recovery follows. Quiet tissue ignores weak taps, but a suprathreshold kick launches a front that leaves a refractory wake; broken fronts can curl into spirals. Global wave geometry grows from a short local cycle—rest, excitation, recovery, readiness—

Picture a grid in which each site belongs to a cell or to medium. The tissue evolves not by smooth PDE flow but by countless small proposals: copy one site’s identity onto a neighbour and ask whether the move lowers an energy. Contacts between cell types have costs; cells prefer

Law without long-range foresight. Traces follow the same deterministic equation, yet nearby starts can stretch apart while remaining confined to a strange attractor. The luminous butterfly or dust field is not a creature in ordinary space—it is a portrait of the states a system r

A food web written in space. Plants renew, herbivores and predators meet or miss one another, and each animal’s energy decides whether it reproduces or dies. Abundance is not commanded by a global population equation; booms, lags, crashes and recovery emerge from countless local

Coordinated motion without a conductor. When many agents only avoid crowding, match nearby headings and stay near their neighbours, streams, turns and recoveries can appear from above even though no agent carries a map of “the flock.” The sphere is an invitation to watch order as

A current assembled from local collisions. Lattice populations stream and relax until a fluid-like velocity field appears—bending around obstacles, shedding wakes and carrying dye. The sphere makes transport visible and also asks what a computational flow may honestly claim once

A picture discovered by iteration. Each point in the complex plane is asked the same question—escape, converge, or linger—and coasts, basins and ghostly densities appear where neighbouring answers diverge under magnification. Nothing is drawn stroke by stroke; the boundary is wha

One attractive rule, many histories. Sideways motion can bend into orbit; inward bias collapses toward a sink; several wells divide and twist streams. The sphere is a stylised gravitational laboratory—softened, finite-range and capturing—so visitors can feel how initial condition

A landscape is not a static sculpture. Rain falls, water is routed, and moving water removes material where drainage area and slope combine into erosive power. Soft rock yields; hard rock resists; uplift slowly raises the stage again. As channels deepen, they steal water from nei

Growth that rewards exposure. A harmonic field concentrates attachment chance at tips; each advance screens the recesses behind it. Dendrites and needles are not drawn—they are the irreversible record of boundary-by-boundary competition under Laplace’s equation.

Lenia replaces the harsh on/off cells of Conway’s Game of Life with a continuous field. Each point holds a value between 0 and 1. A radial kernel measures a soft neighbourhood mass; a bell-shaped growth map decides whether that neighbourhood should increase or decrease the local

A material world from categorical swaps. Sand falls, water spreads, oil floats, fire propagates and lava quenches—not because a continuum solver draws those shapes, but because each cell follows local rules for motion, heat and transformation. The sphere is a falling-sand laborat

Form from one learned local rule. Every living site applies the same tiny network to its neighbourhood, so a seed can grow a patterned body that persists—and sometimes regenerates—without a runtime blueprint. The spectacle is not a single drawing pass, but a rule that can carry i

Organisation before biology. Give particles almost nothing—a colour, a velocity and a directed table of attractions and repulsions—and asymmetric pair rules can still assemble clusters, rings and chase waves. The sphere asks how much morphology can appear when no particle carries

A mixture that sorts itself. Composition separates into two phases across soft interfaces, then coarsens as necks retract and larger domains consume smaller ones. The world organises by becoming geometrically simpler while roughly conserving how much of each phase exists.

Networks grown from traffic. Sensing agents deposit and follow a diffusing trail until motion and memory lock into branching corridors. In the two-colony world those preferences become territorial: each population follows its own trace and turns from the rival’s—an implementation

Ties that rewrite the nodes that rewrite the ties. Agreement can thicken a link; discord can strain and break it; exploration can open a new bridge. Consensus, echo chambers and fragmentation are not preset layouts—they are histories the network remembers in its changing topology

Coordination written into the environment. Agents leave traces or reshape material; later agents read those changes and alter their paths in turn. Routes and ridges can form without anyone holding a colony map, while decay and diffusion keep the past from freezing into permanence

Clocks that also move. Each agent carries a phase as well as a place; nearby phases can synchronise while phase similarity rewrites spatial attraction. Clusters, rings and travelling colour appear because organisation in one domain continually changes the conditions of organisati

Morphology without a template. Two reacting, unequally diffusing fields can turn a seeded disturbance into spots, bands or labyrinths—or erase it back to uniformity. Pattern here is a sustained organisation of concentrations, held open by replenishment, removal and transport rath