Nobody draws the roads

Nothing in the cage is hand-placed. The map derives from the furniture, the roads from prices. The first pricing failed identically for opposite birds, because a toll on climbing telescopes to the same net rise; character came from taxing the journey, not the destination.

The cage is a dome over a box, which makes it convex: a straight line between any two points inside it stays inside. Every bird can see everywhere, so no bird needs a map. One gets built anyway, because it costs almost nothing to own. The authored surface is countable: where the furniture sits, three tags that name the furniture, and seven rows of four prices. Everything else derives. Sites, regions, cells, edges, roads, all of it falls out of those inputs, and reshaping the cage re-derives the lot. And since no flight needs the roads, the roads are free to be more than a way across. They can be character.

The map grows from eleven landmarks. Each one claims the ground nearer to it than to any other, and that patch becomes a region. The furniture's regions carry the furniture's own name for itself: the perch is the roost, the swing is the swing berth, because the tag says so. The empty cage names the rest by what it touches, floor to hearth, a low wall to a rail, the high dome to the spire, the curve between to the right rim. The three floor landmarks show the rule at work: the two whose patches reach a wall come back as corners, and only the middle one is the hearth. Each region splits into numbered cells, so a place has an address, the hearth·2. Adjacency is not stored anywhere. Walk the straight line between two cells and ask whose ground it crosses; if it crosses only theirs, they adjoin. Membership draws the graph, so the graph cannot disagree with the ground a bird stands on. Add a perch and it is one line: region, name, cells, edges, and roads all follow. A landmark with no tag gets named by wherever it lands.

One planner walks the graph, plain Dijkstra over thirty-odd cells; a heap would cost more than it saves. Each bird carries one row of prices. Climb, charged per pixel risen against the current down. Heat, a toll that rises where the flock has lately crowded. Rim, a discount for holding the boundary. Reluctance to climb looks like the knob that would make a floor-hugger. It makes nothing.

Send Ash and Pearl from the same low corner to the same high rim, in a quiet cage so no crowd tips the scales. Opposite birds: one dreads the climb, one ignores it. They come back with the same route, address for address. The reason is a piece of algebra hiding in the cost. Priced per pixel risen, the climb toll sums along any sensible route to the same number, the net height gained, which the destination already fixed. Every bird pays it in full whichever way it goes, so it cannot choose between roads. What chooses is where the traveling happens. Tax distance instead, weighted by how high it runs, and the two birds fall apart: the floor-hugger is not the one who hates climbing, she is the one who does her traveling low and leaves the climbing for last. Character is where you spend the trip, not what you pay at the end.

Read three roads, all between the same corner and the same rim. Ash holds the floor, the hearth·1 and then the hearth·2, before she climbs at all: up through the crossing·3 and the swing berth to the rim. Pearl pays no altitude tax, so she climbs from the first step, through the roost and the crossing·1 to the same rim. Flicker shuns the crowd and loves an edge: the left corner, three cells of the left rail, then across to the rim, the discount drawn on the wall. Three rows of prices, three roads.

A route is spent one cell at a time, and the first version handed every cell to the landing code as if it were the destination. So a bird crossing a waypoint it was meant to pass straight through braked politely a wingspan short and hovered at the edge of a cell it never entered. The rule that fixed it: a waypoint is flown through, and only the destination gets a landing. (The seat's own page learned where a landing belongs the hard way; this is that rule read from the route's end instead of the seat's.)

The one price that reads which way you have tilted the phone is the climb toll, and the climb toll is the one that changes no road. Everything that shapes a route was measured against the screen and stays there. Tilt all you like: the bodies fall the new way, and the map never turns. It was drawn once, and it holds.