About the banner

Think of a fluffy snowfall, or sediment slowly settling onto an oozy lake bottom, or the soft matt of lint on the filter screen of the clothes dryer, or the gathering of dust bunnies under your bed. These are structures created by things that clump and cluster, by drifting particles that stick to each other when they touch, that form feathery or frondlike patterns when they collect on a solid substrate. The animated banner at the top of each bit-player page illustrates some of these processes of aggregation and agglomeration. The name I have given to these simulations began as a typographical error: aglorithms.

I wrote about computational models of aggregation in one of my early “Computing Science” columns: “Nature’s Algorithms,” American Scientist, May-June 1994 (PDF). The delicacy of the patterns appealed to me, and so I chose one example as the banner image for the first version of bit-player.org in 2006.

In a 2013 renovation of the website I realized I could do better than just a static image of the finished pattern. I could embed a program in the page that would show the aglorithm in action. For the latest version of the site (2025) I’ve added some more goofiness. Each time the program runs, it chooses at random among a dozen variations on the theme. The resulting patterns might resemble a pine forest, rockets launching, a grove of bamboo, corals or sponges or other reef ornaments, scraggly shrubs, a closeup view of astroturf.

Still another version of the program, below, invites you to set the parameters yourself and explore more variations on the aggregation process.

In all of these simulations, particles are released one at a time at the top of the panel and drift through the two-dimensional space until they hit something—either the substrate at the bottom of the panel or another particle that is already in contact—directly or indirectly—with the substrate. Once a particle has been deposited in this way, it stays put. The colors applied to deposited particles reflect the sequence in which they’re emitted, from deep purple (earliest) to bright yellow (latest).

The simulation has two main modes, controlled by the radio buttons labeled “Random” and “Ballistic.” In random-walk mode, each particle chooses a new direction after each step, wandering willy-nilly through the two-dimensional space until it eventually stumblees upon a fixed particle and becomes anchored there. In ballistic mode each particle is launched at a random angle to the horizontal but thereafter travels in a straight line until it collides with a fixed obstacle.

The array of eight check boxes labeled “Walk Directions” are active only in the random-walk mode. They determine the set of directions available to the meandering particle at each step. For example, activating only the up, down, left, and right boxes outlaws all diagonal moves and confines the particle to motions parallel to the x and y axes. These settings have no meaning in ballistic mode, and so the checkboxes are disabled when the ballistic algorithm is in use.

The other set of checkboxes, labeled “Sticky Directions,” pertains to the particles that have already been deposited. These checkboxes determine which sides of a settled particle are sticky and can therefore capture a new descending particle. For example, if only the top middle box is checked, then roving particles can adhere only if they happen directly on top of a settled particle.

The “Run” and “Erase” buttons require no explanation. “Defaults” restores the parameters to their initial state. “Capture” will open a new window or tab with a PNG image of the current pattern, which you can save to a file, in case you’d like a souvenir of your visit here.

Note: It‘s not hard to find settings that will cause the program to run for a very long time, use lots of cpu cycles, and do nothing, if you're into that sort of thing.

Here‘s a little gallery of specimen patterns, accompanied by the settings that produced them..

Sea fans. This foamy, frothy pattern was the emblem of bit-player.org for almost 20 years. It’s the product of one of the simplest deposition schemes: Particles rain down vertically, and stick to stationary particles along any exposed edge (but not a corner).

Emergence. Trees that poke above the forest canopy, towering over their neighbors, gather more light early and late in the day, when the sun’s rays are nearly horizontal. I don't know if that mechanism really explains the presence of emergent trees in forests, but it does work in this model of ballistic deposition. It’s a rich-grow-richer effect: The tallest tree intercepts particles that are sweeping by on nearly horizontal trajectories.

Bamboo. If deposited particles are sticky only on their upper surfaces, the aggregate can grow only by stacking particles one atop the other, creating vertical stems or stalks.

Hurricane. You might imagine that a strong wind is blowing from right to left, but in fact the bent-over fronds are accumulating particles on their left sides.

Pole beans. These sparse, scraggly plants grow when randomly wandering particles have the maximum freedom to

Christmas tree farm. A personal favorite, only recently discovered. With these settings the treelike forms are denser and more symmetrical.

By my count there are 65,536 combinations of settings for random-walk patterns, and an additional 256 for ballistic trajectories. Have fun exploring.

About the banner

Aglorithms