reach(row, col, directions)

Returns the seed cell’s reach as a number-field quadrille — 0 at the seed, steps-to-reach elsewhere, and empty where out of reach — computed as a breadth-first wavefront over any quadrille: filled cells are obstacles, empty cells are passable. The field renders as gray levels for free, and one field serves any number of agents: compute it from the target and every agent descends it. Seeding on a filled or invalid cell yields a fully empty field — an agent cannot stand in a wall.

Example

(move the mouse to seed the field; click to regenerate the maze)

code

Quadrille.cellLength = 30;
let board;
let wall;
let dirs;

function setup() {
  createCanvas(15 * Quadrille.cellLength, 11 * Quadrille.cellLength);
  wall = color('#0b332b');
  board = createQuadrille(15, 11).maze(wall);
  dirs = createCheckbox('8 directions', false);
  dirs.position(10, height + 15);
  dirs.style('color', 'magenta');
}

function draw() {
  background('#138a72');
  const field = board.reach(board.mouseRow, board.mouseCol, dirs.checked() ? 8 : 4);
  drawQuadrille(field, {
    outlineWeight: 0,
    numberDisplay: ({ value, cellLength }) => {
      noStroke();
      fill(constrain(255 - 5 * value, 40, 255));
      rect(0, 0, cellLength, cellLength);
    }
  });
  drawQuadrille(board, { outlineWeight: 0.5 });
}

function mousePressed() {
  board.maze(wall);
}

The wavefront brightens toward the seed (0 renders lightest under this numberDisplay override) and vanishes where it cannot go: hover a wall — or leave the board — and the field goes fully empty. With 8 directions the wave cuts corners, mirroring flood fill semantics; any other directions value warns and falls back to 4.

reach is defined and meaningful on any quadrille, not only mazes: on a game board it is pathfinding distance around the pieces; on an empty quadrille it is plain grid distance. Its natural companion is path, which descends the field.

Emptiness is the field’s failure signal, and it composes with the read convention: field.isEmpty(row, col) reads as out of reach — including out-of-bounds cells, since an out-of-bounds read returns undefined, which counts as empty.

Syntax

reach(row, col, [directions = 4])

Parameters

Param	Description
`row`	Number: seed row index [0..height]
`col`	Number: seed column index [0..width]
`directions`	Number: neighborhood, `4` (default) or `8` (corner-cutting); other values warn and fall back to `4`

search(pattern, strict)path(row1, col1, row2, col2, directions)