Avalanche sandpile. The Bak–Tang–Wiesenfeld model of self-organized criticality: a system that drives itself to the edge of instability, where one more grain can do nothing or set off an avalanche of any size.

• Each cell holds up to three grains, shaded light to dark.
• A cell that reaches four topples, passing one grain to each neighbor. Grains off the edge are lost.
• Neighbors that reach four topple in turn, flashing in color, until everything is stable again.

Try it: hover to pour grains, click to dump a handful. Avalanche sizes follow a power law, which is why one rule makes both ripples and banner-wide slides.

Bak, Tang & Wiesenfeld (1987). Self-organized criticality. Physical Review Letters.

Independent cascade. A standard model of how information and behavior spread through a social network.

• Each cell knows its four neighbors. A few also have a long-range tie to someone far away, drawn as a faint arc.
• When a person first hears something, they get one chance to pass it to each contact with probability p. Then they are done.
• People fade back to light after a few seconds and can hear it again. When nothing is spreading, a new seed drops.

Try it: click to seed a cascade and slide p under settings. The tipping point here is p = 0.5: below it cascades fizzle, above it they take over. The long-range ties let an outbreak leap across the banner.

Goldenberg, Libai & Muller (2001). Talk of the network. Marketing Letters. Kempe, Kleinberg & Tardos (2003). Maximizing the spread of influence through a social network. KDD.

Particle monogram. My initials as dots that scatter from the cursor and spring back. Click for a pulse, or explode (Shift+E) to blow them apart and watch them reassemble. Now and then a bomb drops in and goes off on its own. Not a model of anything, just a bit of fun.