Triple Pendulum vs Heaton Life

The motion of a triple pendulum is governed by a set of coupled ordinary differential equations. For certain energies its motion is chaotic. This application solves these differential equations using the Runge-Kutta method for the time stepping. You can influence the movement of the pendulum by holding your device in different positions.

Heaton Life is an app for exploring emergence: simple rules that grow complex, organic, surprisingly lifelike behavior. It brings the classic systems of artificial life together in one place, lets you paint and edit them, breeds brand-new rules, and keeps everything you make in a library of worlds. TEN KINDS OF LIFE • MergeLife — colorful cellular automata where every rule is a hex code. Start from the gallery of featured rules, then breed your own. • Life-like — Conway's Game of Life and its relatives: HighLife, Seeds, Day & Night, or any B/S rulestring you type. • Elementary — Wolfram's one-dimensional rules 0–255, drawn one row per generation. • Cyclic — states that consume one another into spirals and demons. • Wireworld — electrons on wires. Build circuits from the included clock and diode. • Lenia — three flavors (Classic, Asymptotic, Flow) of continuous Life, where smooth, gliding creatures emerge. • Gray-Scott — reaction-diffusion chemistry: spots, stripes, and dividing blobs. • Reynolds boids — flocking with no grid at all. Tap to scatter the flock. FOUR FRACTALS Mandelbrot, Julia, Burning Ship, and Newton. Tap to recenter, pinch or scroll to zoom — up to a trillion times (10¹²), with the center tracked precisely enough that the image never smears at depth. Or tap Auto and let the app dive toward the boundary by itself. PAINT, SELECT, PASTE Every world is editable without resetting it. Paint with each family's own ink — states, colors, intensities, chemistry — select and copy regions, paste with rotate and flip, and undo up to 24 steps. Paste accepts standard RLE text straight from LifeWiki, and the pattern zoo ships with gliders, spaceships, oscillators, methuselahs, the Gosper glider gun, HighLife's replicator, and Wireworld's clock and diode, alongside anything you capture yourself. BREED NEW RULES The built-in evolver is a genetic algorithm that breeds MergeLife rules and scores each one by how interesting its world stays over time, the way the original research trainer did. Watch the current best run live, keep the champions in a Finds catalog, open any find as a world, and decode any rule in the Rule Lab. A LIBRARY OF WORLDS Worlds are born saved: every world and fractal expedition lands in your library with a live thumbnail, saves itself when you leave, and reopens exactly where it was: same state, same generation. Name them, favorite them, snapshot any view to PNG, and import RLE patterns or MergeLife PNG exports.