Lattice

Left click the grid to strike it with force, in whatever direction the compass shows, applied to every dot within a radius (both power and radius adjustable above, default 1 and 4). Click the dot in the center of the compass to select no direction: instead of one uniform push, each struck dot is shoved further away from the click, in whichever cardinal direction it lies relative to the click's center — dots north of the click get a northern push, east get eastern, south get southern, and west get western. Right click and drag instead to paint walls — the grid starts with walls all the way around its outer border. A wall accepts a force share from a non-wall neighbor the same way an ordinary dot would (see Wall Reflect below for what happens to it once it arrives), but never hands force to a neighboring wall cell; toggle Erase mode to make right click remove walls instead of drawing them.

Every tick, a dot's horizontal force and vertical force are each handed onward independently, and each spreads to all three neighbors lying in that direction rather than just the one straight ahead: a rightward force reaches the upper-right, right, and lower-right neighbors; a downward force reaches the lower-left, down, and lower-right neighbors; and so on for the other five directions. The straight-ahead neighbor is genuinely closer (1 cell away) than the two diagonal ones (√2 cells away), so it gets a bigger cut — about 41% to the straight neighbor and ~29% to each diagonal — rather than splitting evenly three ways. Because the two diagonal neighbors sit at a 45° angle rather than straight ahead, each also picks up a small perpendicular kick equal in magnitude to its share — e.g. an eastward transfer gives its upper-right neighbor a touch of north as well as east, and its lower-right neighbor a touch of south as well as east. Nothing is taken from the sender to pay for this: the two kicks are always equal and opposite, so they cancel to zero across the pair. Negative and positive force behave as exact mirror images of each other: a leftward or upward force spreads the same way, just toward the opposite trio of neighbors. The total handed off each tick is either a fixed rate (default 0.25, adjustable) or, in percentage mode, a share of what the dot currently holds (default 100%, meaning it empties out completely each tick), then divided among the three neighbors by that same weighting. If a neighbor is off the grid, its share simply stays behind in the sending dot instead of being lost; a wall neighbor, by contrast, actually receives the share (see Walls and Wall Reflect below for what happens there) — except when the sending dot is itself a wall, in which case a neighboring wall never receives anything and the share stays behind, same as off-grid. Either way, if the amount handed off exceeds what the dot holds, it still sends the full amount and goes negative — recoiling and pushing the opposite way next tick. Each dot's force is capped at ±10 magnitude. Color runs along whichever palette is selected above, always with black at exactly zero force, jumping onto the spectrum the instant a dot holds any force at all, up to full saturation at the cap. Rainbow (the default) runs red through orange, yellow, green and blue to violet; Thermal and Ocean mimic heat-camera and deep-water gradients; Viridis is a perceptually uniform purple-to-yellow scale built to stay distinguishable for all common forms of color blindness. A dot's position also drifts slightly in the direction of its force. Walls render as a flat steel tile regardless of force or palette.

Vertical wall, when toggled on, changes what a right click does: instead of placing (or, with Erase mode on, removing) just the clicked cell, it places or removes an entire vertical column of walls at that x position in one action — drag across several columns to wall off (or open up) multiple at once. Edge Decay, when toggled on, pulls the force magnitude of every dot along the outer border down by a fixed amount each tick (default 0.25, adjustable) — note that with the default border walls in place, this has nothing to act on unless you erase some of the border. Wall Reflect, on by default, controls what a wall does with a force share arriving from a non-wall neighbor: multiply it by -1 before storing it (on), or store it unchanged (off). Either way the wall hands whatever it's holding back into the lattice over later ticks exactly like any other dot, just never to a neighboring wall. Show right-edge force values lists the live x, y, and magnitude of every dot in the grid's right-most column in the sidebar below.

Sensors are placed and removed the same way as walls — right click and drag, with Sensor mode toggled on so the drag drops sensors instead of walls, and Erase mode removing whichever is present. Unlike a wall, a sensor doesn't block or zero out force; it behaves like an ordinary dot, and its position and current force magnitude are listed live in the sidebar. The one difference from an ordinary dot is that a sensor's force is never capped at ±10 — every other dot in the lattice is, so a sensor is the one place you can watch force build up past that ceiling.

Music pixels are placed and removed the same way as walls and sensors — right click and drag, with Music mode toggled on so the drag drops music pixels instead, and Erase mode removing whichever is present. Like a sensor, a music pixel never blocks or alters force propagation; it just listens. Each live music pixel plays a continuous tone in the waveform (sine, sawtooth, square, or triangle) selected at the moment it was placed, with its volume rising and falling with that atom's own force magnitude, and going silent while the atom is at rest. A pixel's pitch is fixed by its position in the grid rather than by force: the Low/High frequency settings are split equidistantly from left to right and logarithmically from bottom to top, and a pixel's tone is the sum of its left-right frequency and its bottom-top frequency.